Recognition, decoding and tracking of vortex patterns is of increasing importance in many fields reaching from astronomical observation of distant galaxies to turbulence phenomena in liquids or gases. Currently, coherent light beams with orbital angular momentum (OAM) are of particular interest for optical communication, metrology, micro-machining or particle manipulation. One common task is to identify characteristic spiral patterns in pixelated intensity maps at real-world signal-to-noise ratios. Recently, Fast Fourier Transform (FFT) was applied to the quantitative analysis of spiral interference patterns of OAM beams. Our study considers this approach in more detail. It is demonstrated that specific information can be extracted by combining conformal mapping by polar transform with determining one- or two-dimensional angular frequency spectra either in spatially fixed or scanning mode. Results of proof-of-principle experiments are presented.

In this paper, a kind of single-walled carbon nanotube nonlinear model is developed, and the strongly nonlinear dynamic characteristics of such carbon nanotubes subjected to random magnetic field are studied. The nonlocal effect of microstructure is considered based on the theory of nonlocal elasticity. The natural frequency of the strongly nonlinear dynamic system is obtained by the energy function method, the drift coefficient and the diffusion coefficient are verified. The stationary probability density function of the system dynamic response is given and the fractal boundary of the safe basin is provided. Theoretical analysis and numerical simulation show that stochastic resonance occurs when varying the random magnetic field intensity. The boundary of safe basin has fractal characteristics and the area of safe basin decreases when the intensity of the magnetic field permeability increases.

In order to alleviate the problems regarding conventional damping modeling techniques in nonlinear structural simulations, using concentrated plasticity formulation including rotational end springs with no damping plus middle elastic parts with modified assigned damping has recently been proposed. However, a proper selection for springs’ stiffness is a source of contention. In this paper, the effect of choosing different ratios for springs’ rotational stiffness to the elastic part of the elements on the seismic performance of RC moment frames was investigated. Incremental Dynamic Analysis (IDA) was performed and the derived responses were used for seismic performance assessment methodology. The results demonstrate that using flexible springs may lead to a greatly conservative estimation of collapse capacity, annual losses, and repair costs compared to a rigid one. Due to lack of experimental data, it is not possible to certainly assert the most appropriate ratio. However, such variation in the seismic performance of a building model with different stiffness modification necessitates more investigation on this modeling strategy.

In order to improve the stiffness of the flexible robot,this paper proposes a variable-stiffness elastic actuator to improve the rigidity of flexible robots. The actuator integrates the working principles of a pneumatic drive, wedge structure, and particle blockage. the tensile stiffness of the actuator is nonlinearly negatively correlated with the air pressure because of the structural and material properties.The compressive stiffness and lateral stiffness increases nonlinearly as air pressure increases, being 3and 121 times greater at 0.17 MPa compared to 0 MPa, respectively. Beyond 0.17 MPa, the two stiffness of the actuator experiences incremental growth due to wedge impedance forces.

In wireless sensor networks (WSNs), each sensor node can estimate the global parameter from the local data in distributed manner. This paper proposed a robust diffusion estimation algorithm based on minimum error entropy criterion with self-adjusting step-size, which are referred to as diffusion MEE-SAS (DMEE-SAS) algorithm. The DMEE-SAS algorithm has fast speed of convergence and is robust against non-Gaussian noise in the measurements. The detailed performance analysis of the DMEE-SAS algorithm is performed. By combining the DMEE-SAS with diffusion minimum error entropy (DMEE) algorithms, an Improving DMEE-SAS algorithm is proposed, in non-stationary environment where tracking is very important. The Improving DMEE-SAS algorithm can avoid insensitivity of the DMEE-SAS algorithm due to the small effective step-size near the optimal estimator, and obtain a fast convergence speed. Numerical simulations are given to verify the effectiveness and advantages of these proposed algorithms.

The chiral optical Tamm state (COTS) is a special localized state at the interface of a handedness-preserving mirror and a structurally chiral medium such as a cholesteric liquid crystal or a chiral sculptured thin film. The spectral behavior of COTS, observed as reflection resonances, is described by the temporal coupled-mode theory. Mode coupling is different for two circular light polarizations because COTS has a helix structure replicating that of the cholesteric. The mode coupling for co-handed circularly polarized light exponentially attenuates with the cholesteric layer thickness since the COTS frequency falls into the stop band. Cross-handed circularly polarized light freely goes through the cholesteric layer and can excite COTS when reflected from the handedness-preserving mirror. The coupling in this case is proportional to anisotropy of the cholesteric and theoretically it is only anisotropy of magnetic permittivity that can ultimately cancel this coupling. These two couplings being equal results in a polarization crossover (the Kopp--Genack effect) for which a linear polarization is optimal to excite COTS. The corresponding cholesteric thickness and scattering matrix for COTS are generally described by simple expressions.

The numerical implementation of the controllers allows the use of very complex algorithms with ease. However, in practice, due to its proven advantages, the PID controller (and its variants) is widely used in industrial control systems as well as in many other applications that require continuous control. Most of the methods for tuning the parameters of PID controllers are based on time-invariant linear models of the processes, which in practice can lead to poor performance of the control system. The paper presents an application of reinforcement learning algorithms in tuning of PID controllers for the control of some classes of continuous nonlinear systems. Tuning the parameters of PID controllers is done with the help of Twin Delayed Deep Deterministic Policy Gradients (TD3) algorithm which presents a series of advantages compared to other similar methods from Machine Learning dedicated to continuous state and action spaces. TD3 algorithm is an off-policy Actor-Critic based method and was used as it does not require a system model. The presented technique is applied for control of a biotechnological system which has a strongly nonlinear dynamic. The proposed tuning method is compared to the classical tuning methods of PID controllers. The performance of the tuning method based on the TD3 algorithm is demonstrated through simulation illustrating the effectiveness of the proposed methodology.

This paper proposed an optimal tracking control scheme through adaptive dynamic programming(ADP) for a class of partially unknown discrete-time nonlinear systems based on radial basis function neural network(RBF-NN). In order to acquire the unknown system dynamics, we use two RBF-NNs, the one is used to construct the identifier, and the another is used to directly approximate the steady-state control input, where a novel adaptive law is proposed to update neural network weights. While the optimal feedback control and the cost function are derived via feedforward neural networks approximating, it is proposed to regulate the tracking error, the critic network and the actor network are then trained online to obtain the solution of the associated Hamilton–Jacobi–Bellman (HJB) equation being built under the ADP framework. Simulations verify the effectiveness of the optimal tracking control technique using the neural networks.

While numerous studies have explored the correlation between the built environment and ride-hailing demand, few have assessed their nonlinear interplay. Utilizing ride-hailing order data and multi-source built environment data from Nanjing, China, this paper uses the machine learning method, eXtreme Gradient Boosting (XGBoost), combined with SHapley Additive exPlanations (SHAP) and Partial Dependence Plots (PDP) to investigate the impact of built environment factors on ride-hailing travel demand, including their non-linear and threshold effects. The findings reveal that dining facilities have the most significant impact, with a contribution rate of 30.75%, on predicting ride-hailing travel demand. Additionally, financial, corporate, and medical facilities also exert considerable influence. The built environment factors need to reach a certain threshold or within a certain range to maximize the impact of ride-hailing travel demand. population density, land use mix and distance to the subway station collectively influence ride-hailing demand. The results are helpful for TNCs to allocate network ride-hailing resources reasonably and effectively.

The use of haptic devices in rehabilitation of impaired limbs has become rather popular, given the proven effectiveness in promoting recovery. In a standard framework, such devices are used in rehabilitation centers, where patients interact with virtual tasks, presented on a screen. To track their sessions, kinematic/dynamic parameters or performance scores are recorded. However, as Internet access is now available at almost every home, and in order to reduce the hospitalization time of the patient, the idea of doing rehabilitation at home is gaining wide consent. Medical care programs can be synchronized with the home rehabilitation device; patient data can be sent to the central server that could redirect to the therapist laptop (tele-healthcare). The controversial issue is that the recorded data do not actually represent the clinical conditions of the patients according to the medical assessment scales, forcing them to frequently undergo clinical tests at the hospital. To respond to this demand, we propose the use of a bilateral master/slave haptic system that could allow the clinician, who interacts with the master, to assess remotely and in real time the clinical conditions of the patient that uses the home rehabilitation device as the slave. In this paper, we describe a proof of concept to highlight the main issues of such an application, limited to one degree of freedom, and to the measure of the stiffness and range of motion of the hand.

In this paper, we consider a fourth-order suspension bridge equation with nonlinear damping term |u_t|^m-2u_t and source term |u|^p-2u. We give necessary and sufficient condition for global existence and energy decay results without considering the relation between m and p. Moreover, when p>m, we give sufficient condition for finite time blow-up of solutions. The lower bound of the blow-up time T_max is also established. It worth to mention that our obtained results extend the recent results of Wang (J. Math. Anal. Appl., 2014) to the nonlinear damping case.

An analysis of the stiffness theory reveals that coal mass compression bumps occur only when both the failure criterion and the stiffness criterion are simultaneously satisfied. Then a new structural factor called uneven stiffness coal seam structure (USCS) is proposed, which consists of an uneven stiffness coal seam along with continuous roof and floor. The USCS serves the dual functions of pressure concentration and stiffness reduction. The former facilitates stress concentration from the low stiffness zone (LSZ) to the high stiffness zone (HSZ), thus raising the risk (rF) of failure. The latter reduces the stiffness of the surrounding rock of the HSZ, allowing the system to meet the stiffness criterion even with a hard roof, thereby reconciling the contradiction between the stiffness theory and engineering experience and raising the risk (rI) of instability. The HSZ of the USCS, including thinning zones, bifurcating areas, magmatic intrusion areas, and remnant pillar affected areas, is more susceptible to coal bump incidents than a conventional coal seam. Mechanical analysis and simple numerical simulations validate the pressure concentration and stiffness reduction functions of the USCS. The results demonstrate the following: 1) The normal stress of the HSZ positively correlates with ER, HR, KH, and SL, but negatively correlates with KL and SH; The stiffness of surrounding rock of the HSZ negatively correlates with HR, KH, SL, and SH, but positively correlates with ER and KL. 2) Failures within the HSZ of the USCS enables the roof strata to release bending deformation energy without undergoing fracturing. 3) The alignment between the HSZ of an existing USCS and the HSZ of an artificial USCS advancing with the working face intensifies stress concentration and reduces stiffness, thereby significantly increases the risk (rCB) of coal bump. By applying the stiffness theory and relevant USCS findings, new explanations can be provided for engineering phenomena such as the time-delayed coal bumps, the inefficient pressure relief in ultra thick coal seams, and the “microseism deficiency” observed prior to certain coal bumps.

In current transportation hubs, it is a common phenomenon that passengers travel with necessary wheeled-luggage or suitcases. Due to the fact that most luggage occupies certain space within dense passenger crowds with giant mass inertia, its abnormal motions, such as drifting, frequently trig unavoidable local disturbances and turbulence in surrounding pedestrian flows, further increasing security risk. While, current researches primarily concentrate on examining the impact of luggage on crowd evacuation efficiency through scenario-based experiments and analyzing the spatial characteristics of crowd distribution in surveillance videos. There still lacks of the dynamic disturbance mechanisms and crowd stability associated with the combined motion of passengers and luggage. Therefore, this study considers the luggage-laden passenger as a deformable particle, the resulting disturbance on surrounding non-luggage passengers is analyzed and quantified into a nonlinear pressure term. Subsequently, the disturbance propagation model of passenger-luggage is developed by adapting the classical Aw-Rascle traffic flow model with incorporation of the pressure term. Simulation experiments of disturbances caused by luggage drifting and retrograding validate that the proposed propagation model aligns with real-world situations in transportation hubs. Quantitively, when luggage-laden passenger drifted left, the disturbing force of left side crowd can reach a peak of 238N in the passenger density of 3.0 p/m2, and the maximum difference between the left and right sides disturbing force can reach 153N. Furthermore, it is recommended that the proposed model can be applied to crowd flow analysis and risk assessment.

This paper aims to address the exponential stability and stabilization problems for a class of delayed nonlinear Markov jump systems under randomly occurring Denial-of-Service (DoS) attack and packet loss. Firstly, the stochastic characteristics of DoS attack and packet loss are depicted by the attack success rate and packet loss rate. Secondly, a Period Observation Window (POW) method and a hybrid-input strategy are proposed to compensate for the impact of DoS attack and packet loss on the system. Thirdly, A Dynamic Event-triggered Mechanism (DETM) is introduced to save more network resources and ensure the security and reliability of systems. Then, by constructing a general common Lyapunov functional and combining with the DETM and other inequality analysis techniques, the less conservative stability and stabilization criteria for the underlying systems are derived. In the end, the effectiveness of our result is verified through a numerical example.

The world’s population is growing at a rapid pace, thus increasing the need for shelter, which, because of increased carbon emissions, is making our planet less inhabitable. Thus, supplementary cementitious materials (SCMs) are used to reduce the embodied carbon emissions in the building sector. Wood ash, as a replacement for cement in soil treatment, seems to be a promising material. In this study, we considered the strength, stiffness, and microstructural behavior of marine clay treated with cement and wood ash as a cement replacement. Since clay is abundant in nature, it could help stabilize waste to improve the mechanical behavior of produced composites. Portland cement (7%, 10%, and 13%) was replaced with various amount of wood ash (5% and 10%) with two different dry densities (1400 and 1600 kg/m3) and three distinct curing periods (7, 28, and 60 days). Unconfined compressive strength, direct shear, porosity, pulse velocity, x-ray diffraction, and scanning electron microscopy tests were performed on selected specimens to evaluate the structural and microstructural effect of clay–wood ash–cement interaction. The results revealed that the replacement of cement with 5% of wood ash yielded superior performance. The microstructure investigation of wood ash–cement–clay blends further showed the formation of a densified matrix with stable bonds. Furthermore, the porosity and strength properties of blends developed unique relationships, which were further confirmed by other supplementary materials and soils.

This paper addresses the analysis for the nonlinear vibration response of a rectangular tube with a flexible end and non-rigid acoustic boundaries. This is a further work of the linear structural acoustic problem in a well-known acoustic book. In fact, the acoustic boundaries of an enclosed space sometimes are non-rigid and the structural vibration responses are nonlinear. These two points are the focuses of this paper. The multi-level residue harmonic balance method is applied to this nonlinear structural acoustic problem. The results obtained from the multi-level residue harmonic balance method and numerical method are generally in good agreement. The effects of excitation magnitude, tube length, and phase shift parameter etc. are examined.

In recent times, the soft robotics field is gaining numerous research focus owing to its high level of manipulation capabilities unlike traditional rigid robots, which gives room for an increasing use in other areas. However, compared to traditional rigid gripper robots, being capable of controlling/obtaining overall body stiffness when required is yet to be further explored since soft gripper robots have inherently less rigid properties. unlike previous designs with very complex variable stiffness systems, this paper demonstrates a soft gripper design with minimum system complexity while being capable of varying the stiffness of a continuum soft robotic actuator and proves to have potential applications in gripping objects of various shapes, weights & sizes. The soft gripper actuator comprises two separate mechanisms; the pneumatic mechanism for bending control and the mechanical structure for stiffness variation by pulling tendons using stepper motors which compresses the actuator, thereby changing the overall stiffness. The pneumatic mechanism was first fabricated and then embedded into another silicon layer during which it was as well merged with the mechanical structure for stiffness control. By first pneumatically actuating the actuator which causes bending and then pulling the tendons, we found out that the actuator stiffness value can be increased up to 145 % its initial value, and the gripper can grasp & lift a weight of up to 2.075 kg.

The paper examines the impact of inward remittances flows on per capita GDP growth in Bangladesh during 1976-2012. We find that the growth effect of remittances is negative at first but becomes positive at a later stage, an evidence of a non-linear. Unproductive use of remittances was rampant in the beginning when they were received by migrant families but better social and economic investments led to more productive utilisation of remittances receipts at later periods. This was the possible mechanism behind the U-shaped relationship. Unlike what is suggested in the literature that the effect of remittances is more pronounced in a less financially developed economy, our evidence do not show that the effect of remittances on per capita GDP growth in Bangladesh is conditional on the level of financial development.

AFM nanoindentation showed variation in stiffness (Elastic modulus) due to heterogenous nature of the collagen fibres. The S values varied from 5 N/m to 11.11 n/m corresponding to an E change of 2.25 to 1.38 GPa. The variation in effective modulus (Eff) with respect to displacement indicated crossing the parabolic limit. A softening index n was proposed due to the heterogenous behaviour of the biomaterials

In the framework of the self-consistent Maxwell-Pauli theory, the non-linear Pauli equation is obtained. Stationary and nonstationary solutions of the nonlinear Pauli equation for the hydrogen atom are studied. We show that spontaneous emission and the related rearrangement of the internal structure of an atom, which is traditionally called a spontaneous transition, have a simple and natural description in the framework of classical field theory without any quantization and additional hypotheses. The behavior of the intrinsic magnetic moment (spin) of an electron wave in an external magnetic field is considered. We show that, according to the self-consistent Maxwell-Pauli theory, in a weak magnetic field, the intrinsic magnetic moment of an electron wave is always oriented parallel to the magnetic field strength vector, while in a strong magnetic field, depending on the initial orientation of the intrinsic magnetic moment, two orientations are realized: either parallel or antiparallel to the magnetic field strength vector.

Imperfection sensitivity of large amplitude vibration of curved single-walled carbon nanotubes (SWCNTs) is considered in this study. The SWCNT is modeled as a Timoshenko nano-beam and its curved shape is included as an initial geometric imperfection term in the displacement field. Geometric nonlinearities of von Kármán type and nonlocal elasticity theory of Eringen are employed to derive governing equations of motion of nano-beam. Spatial discretization of governing equations and associated boundary conditions is performed using differential quadrature (DQ) method and the corresponding nonlinear eigenvalue problem is iteratively solved. Effects of value and location of the geometric imperfection, and the nonlocal small-scale parameter on the nonlinear frequency ratio and imperfection sensitivity of a curved SWCNT for various boundary conditions are investigated. The results show that the geometric imperfection plays a significant role in the nonlinear vibration characteristics of curved SWCNTs.

As a new type of gear, bevoloid gears have the advantages of compensating axial error, smooth transmission, and eliminating turning error, and they are widely used in applications requiring high transmission accuracy and stability. However, research on calculating the time-varying mesh stiffness of bevoloid gears is still limited, and there is an urgent need to propose a method that can calculate the stiffness of bevoloid gears quickly and accurately. This paper first establishes the bevoloid gear tooth profile expressions, then assumes a pair of bevoloid gears meshing with the same rack and derives the contact line equations of parallel axis bevoloid gear pairs, and analyze the contact process of bevoloid gears. We propose an analytical algorithm that uses the slicing method to calculate the stiffness of helical gears, straight bevoloid gears, and helical bevoloid gears, change the parameters of helical bevoloid gears respectively, and analyze the influence of different parameters on stiffness. Finally, the finite element method is used to verify the analytical method, and the correctness of the analytical calculation results is verified, and the errors are analyzed.

In the laboratory practice, several standards for testing the bending stiffness of corrugated board are used. There are often cases of tests where the results depend on the way the sample is placed on the supports. The problem arises when the board is five-ply (with two corrugated layers with different corrugation heights) or when the board has asymmetrically selected papers on the flat layers. In this article, we focus our attention on the problem related to boundary conditions, with particular attention to the local effects of the support of the sample. Since the cardboard layers, both flat and corrugated, have a small thickness, a slight deformation of the papers can always be observed at the point of contact between the sample and the support, which affects the readings of the measured stiffness. The paper presents theoretical and numerical analyzes showing how much the method of supporting the sample affects the measured bending stiffness of various samples. Numerical observations were also compared with the results of analyzes presented by other scientists as well as with experimental results.

In a bid to resolve lingering problems in cosmology, more focus is being tilted towards cosmological models in which physical constants of nature are not necessarily real constants, but varying with cosmic time. In this paper we have study cosmology in nonlinear electrodynamics with the Newton's gravitational constant $G$ not a constant but vary in form of power-law of the scale factor of the universe. The evolution of the scale factor $a (t)$ is studied in this model which depends on nonlinear electrodynamics fine tuning term of $\alpha$. Then we check the stability of the model using the speed of sound.

We discuss methods for calculation of critical indices and amplitudes from the perturbative expansions. Several important examples of the Stokes flow through 2D and 3D channels are brought up. Power series for the permeability derived for small values of amplitude are employed to calculation of various critical exponents in the regime of large amplitudes. Special nonlinear approximations valid for arbitrary values of the wave amplitude are derived from the expansions. The technique developed for critical phenomena is applied then for relaxation phenomena. The concept of time-translation invariance is discussed, its spontaneous violation and restoration considered. Emerging probabilistic patterns correspond to a local breakdown of time-translation invariance. Their evolution leads to the timetranslation symmetry complete (or partial) restoration. We estimate typical time extent, amplitude and direction for such restorative process. The new technique is based on explicit introduction of origin in time. After some transformations we come to the exponential and generalized, exponential-type solution with explicit finite time scale, which was only implicit in initial parametrization with polynomial approximation. The concept of crash as a relaxation phenomenon, consisting of time-translation invariance breaking and restoration, is put forward. COVID-19 related mini-crash in the time series for Shanghai Composite is discussed as an illustration.

Time evolution of the quantum correlation of the hybrid qubit-qutrit system in multilocal and global dephasing under the effect of a classical noises environment is presented. We considered the qutrit in z direction and the qubit x direction. In addition, our system presents two configurations: the different and the common environment and our discussion involves three types of noises: A Static Noise (SN), Random Telegraph Noise (RTN) and Ornstein- Uhlenbeck noise (OU). By using the density matrix approach to determine the evolution of the state of the system, the found that the static noise is fatal for the quantum entanglement, the quantum correlation and for RTN and OU noises the quantum entanglement, the quantum correlation decreases monotonically with a sufficiently long time. Therefore, we can say that, entanglement and the quantum correlation are more robust to the noise precisely those Random telegraph noise and Ornstein-Uhlenbeck noise.

This paper considers a nonlinear model for population dynamics with age structure. The fertility rate with respect to age is non constant and has the form proposed by . Moreover, its multiplicative structure and the multiplicative structure of mortality makes the model separable. In this setting it is shown that the number of births in unit time is given by a system of nonlinear ordinary differential equations. The steady state solution together with the equilibrium solution is found explicitly.

Introduction: Systemic lupus erythematosus (SLE) is an autoimmune disease associated with an increased risk of cardiovascular diseases (CVD), leading to elevated mortality rates among patients. We aimed to evaluate the levels of cardio-ankle vascular index (CAVI), global longitudinal strain (GLS), ventricular-arterial coupling (VAC) and high-sensitivity cardiac troponin (hsTn), in SLE patients and to explore their relationship with clinical parameters. Methods: This cross-sectional study enrolled 82 SLE patients without evident cardiac or kidney impairment and 41 age- and sex matched healthy controls. We comparatively evaluated CAVI, GLS, VAC, and hsTn between SLE patients and controls, and we assessed their association among SLE patients with disease activity based on the SELENA-SLEDAI Activity Index. Multivariate regression analysis was performed to identify independent predictors of CAVI and hsTn within the SLE cohort. Results: In comparison to healthy controls, SLE patients presented with significantly higher CAVI, GLS and hsTn levels, while VAC was significantly reduced (p<0.001). Further, SLE patients with active disease (SELENA-SLEDAI≥4) exhibited higher levels of CAVI and troponin than those with inactive disease (p<0.001). SLEDAI was an independent predictor of CAVI, while VAC and SLEDAI were independent determinants of hsTn in SLE cohort. Conclusion: SLE patients displayed abnormal levels of CAVI, VAC, GLS, and troponin compared to healthy individuals. Our findings implicate the potential of those CV novel CVD risk factors to refine screening and therapeutic strategies for this specific population.

It is necessary to address the scarcity of crushed stones for pavement structural layers. So fly ash can be proved to be promising solution as more than 270 tonnes of fly ash is generated in India. Though, numerous research has been conducted for the use of fly ash intreated and untreated form, high volume of fine particles and brittleness of the stabilized fly ash pose a great problem for its use in subbase and base. Moreover, stiffness or modulus of stabilized fly ash is vital elastic parameter which is used for mechanistic pavement design. Hence, in this study an extensive experimental investigation is carried out to study its strength and stiffness properties such as compressive strength, indirect tensile strength and flexural strength, cyclic indirect tensile modulus and flexural modulus of fiber reinforced cement stabilized fly ash, stone dust, aggregate mixtures. The stone dust and aggregates have been added to enhance the gradation of the composite’s mixture. The study presents the effect of fiber on strength and stiffness properties. The experimental result reveals that addition of polypropylene (PP) fibers up to 0.25 wt.% enhances the compressive strength and any further addition of fiber results in decrease of the strength. However, indirect tensile strength and flexural strength increases with increase in fiber percentage up to 0.5 wt.%. Cement content is observed to be the dominant parameter for stabilized materials. Suitable relationships have been developed between strength and modulus parameters for stabilized mixtures. Based on the strength and stiffness study, 70% fly ash and 30% stone dust-aggregate and 60% fly ash and 40% stone dust-aggregate with 6% cement can be considered for the base layer. Based on the indirect tensile strength and flexural strength behavior, 0.35% is considered as the optimum fiber percentage.

Antioxidants reduce arterial stiffness but the effects previously reported are weak. The present study evaluated the effects of 2 weeks of therapy with a combination of antioxidants (l-cysteine, thiamine, pyridoxine and ascorbic acid) compared to placebo on stiffness index (SI) a measure of arterial stiffness that is strongly correlated with central pulse wave velocity (PWV), using a Pulse Trace recorder in a diverse group of 78 volunteers. SI fell by 1.7 m/sec relative to placebo (95% confidence intervals 0.6 to 2.7 m/sec), a reduction of 19% (95% confidence intervals 9% to 31%). The Glass effect size was 1.4, indicating a very strong treatment effect which was substantially greater than found in previous studies of the effects of antioxidant therapy on arterial stiffness. The magnitude of reduction in SI was positively correlated with increasing age (r = 0.362 P = 0.02). The change in RI, a measure of compliance of small to medium size arteries, did not differ between the antioxidant and placebo groups The combination of antioxidants studied reduced PWV to a much greater extent than reported for other antioxidants. This combination may be of value in the treatment of cardiovascular disease.

Natural rocks are highly heterogeneous due to various geological processes that constantly alter their properties. The accumulation, deposition, and cementation of mineral and organic particles continuously modify the spatial characteristics of rock properties. Property variability or anisotropy is commonly observed in most rock types and influences strength, transport, and thermal conductivity behavior. This unpredictability presents a significant challenge for laboratory testing. Binder-jet additive manufacturing (3D printing) has emerged as a valuable technology for characterizing rock properties in geoscience and engineering. This study proposes a methodology to evaluate the variability and repeatability of mechanical properties of 3D-printed sandstones during binder-jet additive manufacturing. The mechanical properties were analyzed statistically for samples located in various parts of the 3D printer build volume. The results showed that the 3D-printed sandstones exhibited significant variations in their strength and stiffness properties when measured from samples produced within the same build volume during binder-jet additive manufacturing. The Uniaxial Compressive Strength (UCS) varied from 23 to 38 MPa, with an average value of 29 MPa. The Young's modulus, on the other hand, ranged from 1.5 to 4.05 GPa, with an average value of 2.33 GPa. The variability of the mechanical properties, quantified by the standard deviation, decreased when the entire population of 3D-printed sandstones was divided into smaller samples situated at different elevations of the build platform.

The lay-up of cross laminated timber (CLT) leads to significant differences in properties over its cross-section. Particularly the out-of-plane shear behavior of CLT is effected by the changes in shear moduli over the cross-section. Results from laboratory shear tests are used to evaluate the shear stiffness of 3- and 5-layer CLT panels in their major and minor strength direction. The results are compared to calculated shear stiffness values on evaluated single-layer properties as well as commonly used property ratios using the Timoshenko beam theory and the shear analogy method. Differences between the two calculation approaches are pointed out. The shear stiffness is highly sensitive to the ratio of the shear modulus parallel to the grain to the shear modulus perpendicular to the grain. The stiffness values determined from two test measurements are compared with the calculated results. The level of agreement is dependent on the number of layers in CLT and the property axis of the CLT panels.

We show that one of the two important uncertainty principles derived by Maccone and Pati \textit{[Phys. Rev. Lett., 2014]} can be derived for arbitrary maps defined on subsets of $\mathcal{L}^p$ spaces for $1< p<\infty$. Our main tool is the Clarkson inequalities. We also derive a nonlinear uncertainty principle for weak parallelogram spaces and Type-p Banach spaces.

According to our current understanding of quantum mechanics, a `measurement' violates unitarity. In other words as the act of measurement `resets' the probabilities described by the Schrödinger equation, in the very `moment' of the collapse of the wavefunction, conservation of probability does not hold. To make progress in our understanding of the measurement problem it is thus expected that one must encompass in a single equation both otherwise mutually-exclusive processes of measurement and unitary evolution. In this light, turning to the continuity equation, we realize the possibility that if we allow for existence of sources and sinks in the `fluid of probability' we get closer to such a theory by arriving at nonlinear generalizations of Schrödinger and Klein-Gordon equations. The generalized equations derived are then shown to satisfy all conditions that are expected from a proper generalization: simplification to their linear counterparts by a well-defined dynamical condition, and Galilean and Lorentz invariance.

Continuation methods are presented that are capable of treating frequency-domain flutter equations including multiple nonlinearities represented by describing functions. A small problem demonstrates how a series of continuation processes can find all limit-cycle oscillations within a specified region with a reasonable degree of confidence. Curves of the limit-cycle amplitude variation with velocity, indicating regions of stability and instability with colors give a compact view of the nonlinear behavior throughout the flight regime. A continuation technique for reducing limit-cycle amplitudes by adjusting various system parameters is presented. These processes are economical enough to be a routine part of aircraft design and certification.

The study of different forms of preconditioners for solving a system of nonlinear equations, by using Newton’s method, is presented. The preconditioners provide numerical stability and rapid convergence with reasonable computation cost, whenever chosen accurately. Different families of iterative methods can be constructed by using a different kind of preconditioners. The multi-step iterative method consists of a base method and multi-step part. The convergence order of base method is quadratic and each multi-step add an additive factor of one in the previously achieved convergence order. Hence the convergence of order of an m-step iterative method is m + 1. Numerical simulations confirm the claimed convergence order by calculating the computational order of convergence. Finally, the numerical results clearly show the benefit of preconditioning for solving system of nonlinear equations.

The purpose of this study was to determine the effects of aerobic exercise on carotid to femoral pulse wave velocity (cf-PWV), cell adhesion molecules (intracellular adhesion molecules (ICAM-1), vascular cell adhesion molecules (VCAM-1), and endothelial selectin (E-selectin), and oxidized-LDL in elderly women aged 70–85 years, and to identify the effect of and correlation with vascular stiffness. Forty participants were recruited and divided into three groups; vascular stiffness (VSG, n=14), obesity (OG, n=14), and normal (NG, n=12). All groups were given a 16-week intervention of aerobic exercise, and the data collected before and after exercise were analyzed using SPSS Ver. 23.0. Two-way repeated-measures ANOVA was used to evaluate between-group and time-dependent interaction effects. One-way ANOVA was used to evaluate between-group variations. In addition, the significance was tested using a post-hoc test (Scheffe). The within-group variations by time before and after exercise were examined using a paired t-test, and correlation analysis was performed using Pearson correlation coefficients. Simple regression analysis was performed for variables showing significant differences. The results indicated interaction effects for cf-PWV (p<.001), VCAM-1 (p<.01), E-selectin (p<.05) and oxidized LDL (p<.001). The rate of change of cf-PWV was positively correlated with that of VCAM-1 (r=.352, p<.05) and that of oxidized-LDL (r=.325, p<.05) with statistical significance. To determine the effect of the rate of change of cf-PWV on the rate of change of VCAM-1, the variables were tested, and the coefficient of determination in the regression analysis was .124, indicating that 12.4% of the tested variables fit the standard regression line. The variables for the effect of the rate of change of cf-PWV on the rate of change of oxidized LDL were also tested, and the coefficient of determination in the regression analysis was .106, indicating that 10.6% of the tested variables fit the standard regression line. Thus, the 16-week regular and consistent aerobic exercise program had significant effects on the cf-PWV, ICAM-1, VCAM-1, E-selectin, and oxidized-LDL in elderly Korean women with vascular stiffness, suggesting improvements in vascular stiffness, based on which the intervention is predicted to contribute to the prevention of vascular dysfunction by lowering the risk of cardiovascular disease due to atherosclerosis, as well as having a positive effect in the prevention of impairment of vascular endothelial cells.

Variable Angle Tow (VAT) laminates offer a promising alternative to classical straight fiber composites in terms of design and performance. However, analyzing these structures can be more complex due to the introduction of new design variables. Carrera's Unified Formulation (CUF) has been successful in previous works for buckling, vibrational, and stress analysis of VAT plates. Typically, one-dimensional (1D) and two-dimensional (2D) CUF models are used, with a linear law describing the fiber orientation variation in the main plane of the structure. The objective of this article is to expand the CUF 2D plate finite elements family to perform free vibration analysis of composite laminated plate structures with curvilinear fibers. The primary contribution is the application of Reissner's Mixed Variational Theorem (RMVT) to a CUF finite element model. The Principle of Virtual Displacements (PVD) and RMVT are both used as variational statements for the study of monolayer and multilayer VAT plates dynamic behavior. The proposed approach is compared to Abaqus three-dimensional (3D) reference solutions, classical theories and literature results to investigate the effectiveness of the developed models. Results demonstrate that mixed theories provide the best approximation of the reference solution in all cases.

In this paper, we have shown the electronic circuit equivalence of a mechanical system consists of two oscillators coupled with each other. The mechanical design has the effects of the magnetic, resistance forces and the spring constant of the system is periodically varying. We have shown that the system’s state variables, such as the displacements and the velocities, under the effects of different forces, lead to some nonlinear behaviors, like a transition from the fixed point attractor to the chaotic attractor through the periodic and quasi-periodic attractors. We have constructed the equivalent electronic circuit of this mechanical system and have verified the numerically obtained behaviors using the electronic circuit.

The principles of causality and unitarity are studied within rational nonlinear electrodynamics proposed earlier. We investigate dyonic and magnetized black holes and show that in the self-dual case, when the electric charge equals the magnetic charge, corrections to Coulomb's law and Reissner-Nordstrom solutions are absent. In the case of the magnetic black hole, the Hawking temperature, the heat capacity and the Helmholtz free energy are calculated. It is shown that there are second-order phase transitions and it was demonstrated that at some range of parameters the black holes are stable.

Background: Myocardial infarction is increasing at a young age. New tools are needed to evaluate the risk population of young patients. GDF-15 has been implicated in several key mechanisms of atherogenesis and also is associated with increased mortality and cardiovascular events in patients with coronary artery disease. Arterial stiffness parameters, including pulse wave velocity, can also be measured using peripheral arterial tonometry and can indicate the presence or progression of atherosclerotic changes. The aim of this study is to evaluate the GDF-15 level and arterial stiffness parameters in patients with premature myocardial infarction Method: Thirty patients who recovered from a myocardial infarction were consecutively included. Fifteen age-sex-matched subjects were included as controls. The patients’ serum GDF-15 concentration levels were measured using relevant kits. Measurements of arterial stiffness [pulse-wave velocity (PWV) and augmentation index (AIx)] were performed using a Mobil-O-Graph arteriography system. Results: GDF-15 concentration levels were significantly higher in the patients with premature myocardial infarction when compared to controls. PWV and AIx were similar between the groups. GDF-15 level was negatively correlated with high-density cholesterol (HDL) and positively correlated with uric acid levels in all study populations. Conclusions: GDF-15 levels may be a risk factor for patients with premature myocardial infarction. This pilot study may trigger further studies to elucidate the central role of GDF-15 in the pathophysiology of early atherosclerosis in the young population.

The subject of the research is the investigation of the behavior of railway tracks in locations with a significant change in the stiffness of the track. These locations can be designed from various structural elements and their materials, and this mainly results in a height change of the track level during its operation. These transition zones are monitored and expertly examined in order to detect undesirable deformations of the geometrical position of the track caused by the trains running. The transition zones are at the points where the fixed track transitions to the classic track bed, in our case it is their combination with bridge structures, especially at their supports. In Slovakia, under the conditions of the Railways of the Slovak Republic, the issue is topical within the framework of the modernization of trans-European railway corridors. The results of experimental measurements and their analysis will provide relevant data for subsequent research solutions for their new numerical modeling, which will ensure a smooth passage through these points of change without height fluctuations, vibrations, and shocks from the wheels of train sets.

This study presents a platform for ex-vivo detection of cancer nodules, addressing automation of medical diagnoses in surgery and associated histological analyses. The proposed approach takes advantage of the property of cancer to alter the mechanical and acoustical properties of tissues, because of changes in stiffness and density. A force sensor and an ultrasound probe were combined to detect such alterations during force-regulated indentations. To explore the specimens, regardless of their orientation and shape, a scanned area of the test sample was defined using shape recognition applying optical background subtraction to the images captured by a camera. The motorized platform was validated using seven phantom tissues, simulating the mechanical and acoustical properties of ex-vivo diseased tissues, including stiffer nodules that can be encountered in pathological conditions during histological analyses. Results demonstrated the platform’s ability to automatically explore and identify the inclusions in the phantom. Overall, the system was able to correctly identify up to 90.3% of the inclusions by means of stiffness in combination with ultrasound measurements, paving pathway towards robotic palpation during intraoperative examinations.

Aiming at the problem that soft robots are challenging to take into account both flexibility and bearing capacity, Using the software Pneu-Net driver as the deformation mode, magnetorheological fluid material phase transformation to achieve variable stiffness, A pneumatic modular soft joint structure with dynamically adjustable deformation and stiffness in all directions is proposed. In this paper, mathematical models of deformation and variable stiffness are established. The correspondence between gas pressure and deformation and applied current and joint stiffness is obtained. The finite element analysis method was used to simulate the deformation characteristics and variable stiffness characteristics of modular joints based on the Yeoh model. Finally, the theoretical and simulation results are verified by deformation and variable stiffness tests. It is proved that the modular joint has good rigid-flexible coupling characteristics.

We show that Universe inflation occurs when Einstein's gravity couples to nonlinear electromagnetic fields with cosmic stochastic magnetic fields background. Nonlinear electrodynamics with two parameters is used. The strength of magnetic fields to have the Universe inflation is obtained. It is shown that singularities of the energy density and pressure are absent for any scale factors. At large scale factors one arrives at equation of state for ultra-relativistic case. It is demonstrated that the curvature invariants do not have singularities. By computing the deceleration parameter we show that graceful exit takes place with reasonable e-folding number. The duration of Universe inflation as a function of model parameters is obtained. The classical stability and causality are analyzed by calculating the speed of the sound.

We derive an uncertainty principle for Lipschitz maps acting on subsets of Banach spaces. We show that this nonlinear uncertainty principle reduces to the Heisenberg-Robertson-Schrodinger uncertainty principle for linear operators acting on Hilbert spaces.

The article analyzes existing materials and structures with quadratic-nonlinear optical properties that can be used to generate a difference frequency in the terahertz and sub-terahertz frequency ranges. The principle of constructing a nonlinear optical-radio converter, based on an optical focon (a focusing cone), is proposed. Based on the assumption that this focon can be implemented from the metal-organic framework (MOF), we propose a technique for modeling its parameters. The mathematical model of the process of propagation and nonlinear interaction of waves inside the focon is based on a simplification of the nonlinear wave equation. Within the framework of the developed model, the following parameters are approximately determined: the 3D gradient of the linear refractive index and the function determining the geometric profile of the focon, which provide a few-mode-based generation of the difference frequency.

The nonlinear deformation and stress analysis of a circular torus is a difficult undertaking due to its complicated topology and the variation of the Gauss curvature. A nonlinear deformation (only one term in strain is omitted) of Mindlin torus was formulated in terms of the generalized displacement, and a general Maple code was written for numerical simulations. Numerical investigations show that the results obtained by nonlinear Mindlin, linear Mindlin, nonlinear Kirchhoff-Love, and linear Kirchhoff-Love models are close to each other. The study further reveals that the linear Kirchhoff-Love modeling of the circular torus gives good accuracy and provides assurance that the nonlinear deformation and stress analysis (not dynamics) of a Mindlin torus can be replaced by a simpler formulation, such as a linear Kirchhoff-Love theory of the torus, which has not been reported in the literature.

Offshore Wind Turbines (OWT) with increasingly higher energy output are being developed to meet energy demand, posing challenges for their foundation design. Several foundation types are used to support these turbines with monopiles (MP) accounting for 80% of the installed capacity. In this study, three-dimensional (3D) nonlinear finite element models (FEM) were employed to investigate the behaviour of monopile foundation supporting a 5MW wind turbine when subjected to lateral loading. Results indicate that the MP behavior depending on the pile length to diameter (L/D) ratio and the soil shear strength. Inspection of bending moment profiles at the lateral ultimate capacity indicated the monopiles can behave in flexible manner even with low L/D ratio. The L/D ratio affected the MP normalized lateral ultimate capacity at varying degrees and the biggest effect was for soft clays, amounting to around 5 folds increase for L/D values of 3.33 to 13.33. Lesser effects were found for stiff clays.

We present three reduced integrable hierarchies of nonlocal integrable NLS type equations from a vector integrable hierarchy associated with a matrix Lie algebra, not being A type. Three similarity transformations are taken to keep the invariance of the transformed zero curvature equations. The key step is to formulate a solution to a reduced stationary zero curvature equation so that the zero curvature formulation works for a reduced case.

Hypertension and arterial stiffness are the main factors contributing to cardiovascular disease. L-citrulline, a nitric oxide precursor, has been proposed as a blood pressure-lowering intervention. This study aimed to investigate the impact of L-citrulline on central and peripheral blood pressure, arterial stiffness, and muscle oxygenation at rest and during an isometric knee extension exercise protocol. Twelve older males received 6 g of L-citrulline or a placebo for six days using a double-blind crossover design. Blood hemodynamics parameters (i.e., arterial and brachial systolic and diastolic blood pressure, mean arterial pressure, pulse pressure, heart rate), arterial stiffness (i.e., augmented pressure, augmentation index, forward, backward wave pressure and carotid-femoral pulse wave velocity) and muscle oxygenation [i.e., oxyhemoglobin (Δ[O2Hb]) and deoxyhemoglobin (Δ[HHb]), total hemoglobin concentration (Δ[tHb]) and tissue saturation index (TSI%)], were measured at baseline, post-supplementation and during isometric exercise. No significant effects of L-citrulline supplementation were observed at rest or during exercise on blood pressure, arterial stiffness, and muscle blood flow. Both central and peripheral blood pressure were increased during the exercise, which is consistent with isometric contractions. The results of the present study question the efficacy of short-term L-citrulline in decreasing blood pressure at rest or attenuating blood pressure increases during isometric exercise.

Mechanical properties of tumor cytoskeleton are extremely vital for any phases of cancer, especially in tumor invasion and metastasis. However, in current category of anticancer drugs, the cytoskeleton-targeting drugs are limited and its role in tumor progression is unclear. Here, we present the mechanical characteristics of tumor stiffness are tightly regulated by cancer cytoskeleton including actin filaments and microtubule during tumor initiation, growth and metastasis, and review the natural drugs that target cancer cytoskeleton. We define cytoskeleton dynamics as target mechanisms for anticancer drug, and summary the plant, microbial and marine sources of natural products. Furthermore, the material approaches to active cancer mechanics are supplied in this review. We aim to promote the development of anticancer drugs that target tumor mechanics by using those material approaches in future and find its pharmacological application.

In this study, we focus on an abstract form of summation equations, which can be regarded as a particular class of nonlinear difference equations. We investigate sufficient conditions for the existence of discrete almost automorphic solutions by appealing to the fixed point theory and establish a linkage between the existence of discrete almost automorphic solutions and the existence of bounded solutions for the nonlinear difference equations in the spotlight. Consequentially, we propose a discrete counterpart of the Bohr-Neugebauer theorem for the qualitative theory of difference equations.

Ambient vibration energy is widely being harnessed as a source of electrical energy to drive low-power devices. The vibration energy harvester (VEH) of interest employs an electromagnetic transduction mechanism, whereby ambient mechanical vibration is converted to electrical energy. The limitations affecting the performance of VEHs, with an electromagnetic transduction structure, include its operational bandwidth as well as the enclosure-size constraint. In this study, an analysis and design of a nonlinear VEH system is conducted, using the Output Frequency Response Function (OFRF) representations of the actual system model. However, the OFRF representations are determined from the Generalised Associated Linear Equation (GALE) decompositions of the system of interest. The effect of both nonlinear damping and stiffness characteristics, to respectively extend the average power and operational bandwidth of the VEH device, is demonstrated.

Background: This study aimed to contribute to the standardization of elastography by comparing stiffness values obtained from ultrasound elastography (US-E) and magnetic resonance elastography (MR-E) of the testicular parenchyma in healthy subjects. Methods: A total of 22 healthy volunteers (44 testes) were included in this study. Of the 26 cases analyzed, four were excluded from the study due to the exclusion criteria. The testicular parenchyma of the included patients was evaluated using MR-E and Shear-Wave Ultrasound Elastography (SW-E) examinations. Pearson's correlation test was used to calculate the correlation between age and stiffness values, testicular volumes and stiffness values, and stiffness values from both examinations. Results: The mean US-E stiffness of the right testes was 5.560 ± 3.1 kPa and the mean US-E stiffness of the left testes was 5.361 ± 2.9 kPa. The mean MR-E stiffness of the right testes was 6960.11 ± 460 Pa and the mean MR-E stiffness of the left testes was 6560.19 ± 310 Pa. There was no significant correlation between US-E and MR-E stiffness values (p=0.096). There was also no significant statistical correlation between US-E and MR-E stiffness values and testicular volumes (p=0.17 and p=0.093). Conclusions: No statistical correlation was found between the stiffness values obtained by SW-E and those obtained by MR-E in the normal testicular parenchyma. Additionally, no conclusive relationship between stiffness levels, age, or testicular volume was discovered.

Cells actively sense differences in topology, matrix elasticity and protein composition of the extracellular microenvironment and adapt their function and morphology. In this study, we focus on the cross-talk between matrix stiffness and protein coating density that regulate morphology and proliferation dynamics of single myocytes. For this, C2C12 myocytes were monitored on L-DOPA functionalized hydrogels of 22 different elasticity and fibronectin density compositions. Static images were recorded and statistically analyzed to determine morphological differences and to identify the optimized extracellular matrix (ECM). Using that information, selected ECMs were used to study the dynamics before and after cell proliferation by statistical comparison of distinct cell states. We observed a fibronectin density independent increase of the projected cell area until 12 kPa. Additionally, changes in the fibronectin density led to an area optimum at about 2.6 μg/cm, which was confirmed by an independent F-actin analysis, revealing a maximum actin filament to cell area ratio of 7.5 %. The proliferation evaluation showed an opposite correlation between cell spreading duration and speed to the matrix elasticity and protein density, which did not affect the cell cycle duration. In summary, we identified an optimized ECM composition, while independent matrix properties regulate distinct cell characteristics.

The widespread integration and growing dependence among currency, stock and commodity markets make these markets often very vulnerable to shocks and at risk of collapse at the same time. As a result, these trends threaten the sustainability of the entire financial system. In this study, we explore the spillovers and nonlinear dependences between the seven major foreign ex-change rates, crude oil and gold prices, a global stock price index, and oil and stock implied volatility indices as proxy variables for global risk factors by em-ploying directional spillover network approach. We also use multi-scale de-composition method and nonlinear causality test between these variables to capture multi-level relationships at short and long horizons. Major findings are summarized as follows. First, from the multi-scale decomposition analysis, we identify that Granger causality test results and the direction and strength of return spillovers change with the level of decomposition. Second, the results of nonlinear causality tests show variation in both the significance and direction of Granger causality relationships between the decomposed currency and other series at different timescales, especially for the decomposed oil, gold, and OVX series. Third, the measured directional spillover indices identify the EUR as the largest contributor of connectedness to the other series. The central role of the EUR is a net transmitter of connectedness to gold, oil, the GBP, JPY, and CHF.

The article is devoted to issues related to the propagation and transformation of vortexes in the optical range of frequency. Within the framework of the traditional and modified model of slowly varying envelope approximation (SVEA), the process of converting vortex beams of the optical domain into vortex beams of the terahertz radio range based on nonlinear generation of a difference frequency in a medium with a second-order susceptibility is considered. The modified SVEA splits a slowly varying amplitude into two factors, which makes it possible to more accurately describe the three-wave mixing process. The theoretical substantiation of the rule of vortex beams topological charges conversion is given – the topological charge of the output radio-vortex beam is equal to the difference between the topological charges of the input optical vortex beams. A numerical simulation model of the processes under consideration has been implemented and analyzed.

The particulars of stimulus-response experiments done on dynamic biosystems clearly limit what one can learn and validate about their structural interconnectivity (topology), even when collected kinetic output data are perfect (noise-free). As always, available access ports and other data limitations rule. For linear systems, exponential modes, visible and hidden, play an important role in understanding data limitations, embodied in what we call dynamical signatures in the data. We show here how to circumscribe and analyze modal response data in compartmentalizing model structures – so that modal analysis can be used constructively in systems biology model building – for nonlinear (NL) as well as linear biosystems. We do this by developing and exploiting the modal basis for dynamical signatures in hypothetical (perfect) input-output data associated with a structural model – one that includes inputs and outputs explicitly – and for NL as well as linear biosystems. The methodology establishes model dimensionality (size, complexity) from particular data sets; helps select among multiple candidate models (model distinguishability); helps in designing new experiments to extract “hidden” structure; and helps to simplify (reduce) models to their essentials. For NL biosystems, results are not as comprehensive, similarly informative about their dominant dynamical properties, and unified with linear models on invariant 2-dimensional manifolds in phase space. Some automation of these highly technical aspects of biomodeling is also introduced.

An algorithm for the treatment of images affected by both blurring and salt&pepper noise is proposed with a cost only proportional to the number of pixels. The methodology uses a discretization scheme for the Laplace operator multiplied by a suitable nonlinear term depending on the gradient. Even if this approach resembles a diffusion type algorithm, only one step of the procedure is applied, leading to significant time savings. The procedure is successfully tested on some standard black&white natural images.

DGJ (Daftardar-Gejii-Jafaris) method is used to obtain numerical solution of the third order fractional differential equation. Providing the DGJ method converges, the approximate solution is a good and effective numerical result which is close to the exact solution or the exact solution. For this,the examples of the explaning the method are presented. The proposed method is implemented for the approximation solution of the third order nonlinear fractional partial differential equations. The method was shown to be unsuitable and inconsistent for an example of a nonlinear fractional partial differential equation depend on initial-boundary value conditions. The fact that these numerical results are not consistent can be explained by the fact that the method is not convergent.

Reliable fatigue design rules affect the proactive identification of safety parameters in aerospace industry. Numerous fatigue crack initiation and propagation models, linear and nonlinear, have been developed for designing purposes or estimation of the remaining life of aging airplanes. Depending on the adopted assumptions, the accuracy varies for different loading histories, loading types, and materials. Semi empirical models are simple but yield significant inaccuracies. Models with better theoretical basis provide better accuracy, but implementation in real conditions is problematic. In the present work, a review of author’s recent fatigue crack initiation and propagation models based on physical mechanisms is presented and improvements are proposed. Verification of the models on test results is provided and discussed.

Since the introduction of Cross-laminated Timber (CLT) in Austria in the early 1990s, the adoption of this 90°-crosswise-laminated product has seen exponential growth worldwide. Compared to traditional laminated timber products (e.g. glulam), CLT provides improved dimensional stability, but with reduced out-of-plane bending stiffness. To improve the bending stiffness, while maintaining relative dimensional stability, a modified orientation of the inner layers in a diagonal direction can be used. This novel product is Diagonal-Cross-laminated Timber (DCLT), a composite timber product, consisting of inner layers which are rotated at different angle-ply orientations between 0 and 90 degrees to the outer layers. To properly model the out-of-plane bending behavior of the DCLT, analytical models and Finite Element Analysis (FEA) were used and the results were validated by third-point bending tests performed on DCLT panels with angle-ply orientations of 10°, 20°, 40°, 70°, and a conventional CLT 90° panel. The results indicate that DCLT panels with angle-ply cross-layers have a structural advantage in out-of-plane bending over traditional CLT (90°) panels. The development of DCLT and its introduction to the industry could enable the use of lower-quality timber that would not otherwise satisfy structural requirements for CLT.

Arthroscopic capsular release (ACR) is used for persistent shoulder stiffness after an index surgery. No cases of post-ACR humeral head osteonecrosis have been reported to date. A 56-year-old male patient underwent open reduction and internal fixation using a hook plate for acromioclavicular joint dislocation. Despite hardware removal, the patient presented with unresolved shoulder pain and range-of-motion (ROM) limitation. He had a history of hypertension, chronic hepatitis B infection, and alcohol consumption. Preoperative ROM was forward flexion 90°and internal rotation sacral level. Preoperative functional status was visual analog scale (VAS) score 4, American Shoulder and Elbow Surgeons (ASES) score 51, and Constant–Murley (CMS) score 48, and normal radiography and magnetic resonance imaging. Standard ACR was performed with 360° release of the joint capsule via electrocautery ablation. Six-months post-ACR, ROM (forward flexion: 135°, abduction: 135°, external rotation: 70°, internal rotation: T10 vertebra) and functional outcomes (VAS 2; ASES79; CMS 75) were significantly improved, without interval change in radiographic assessment. However, 21 months later, he had recurrent shoulder pain and decreased ROM. Radiography revealed humeral head osteonecrosis. Patients with intrinsic or extrinsic risk factors related to humeral head circulation disturbance should be monitored for humeral head osteonecrosis post-ACR.

Background: We aimed to determine the splenic stiffness (SS) values in healthy individuals as measured by 3 Tesla magnetic resonance elastography (3T MRE) and to investigate the possible effects of parameters such as age, sex, spleen volume, diameter, and parenchyma thickness on SS.Methods: A total of 54 healthy volunteers were included in this cross-sectional study. Participants' age and sex information were recorded, in addition to spleen craniocaudal and anteroposterior diameter, cortical thickness, spleen volume, and SS, which were measured using 3T magnetic resonance imaging and MRE. Results: Twenty-nine male and 25 female subjects with a mean age of 54.78±15.40 years were included in the study. Mean cradiocaudal diameter was 10.46±1.16 cm, anteroposterior diameter was 9.88±1.29 cm, parenchyma thickness was 4.08±0.67 cm, SS was 3721.94±709.69 Pascal (Pa), and median spleen volume was 292.54 (239.40-311.00) cm³. A significant positive correlation was observed between age and SS (r=0.779, p<0.001). The SS values were not associated with sex, craniocaudal diameter, anteroposterior diameter, parenchymal thickness, or volume.Conclusion:Age should be considered when using SS in the diagnosis and staging of relevant diseases such as portal hypertension and esophageal varices. Our results should be confirmed by future studies using 3T MRE in larger populations.

Background: We aimed to determine the splenic stiffness (SS) values in healthy individuals as measured by 3 Tesla magnetic resonance elastography (3T MRE) and to investigate the possible effects of parameters such as age, sex, spleen volume, diameter, and parenchyma thickness on SS. Methods: A total of 54 healthy volunteers were included in this cross-sectional study. Participants' age and sex information were recorded, in addition to spleen craniocaudal and anteroposterior diameter, cortical thickness, spleen volume, and SS, which were measured using 3T magnetic resonance imaging and MRE. Results: Twenty-nine male and 25 female subjects with a mean age of 54.78±15.40 years were included in the study. Mean cradiocaudal diameter was 10.46±1.16 cm, anteroposterior diameter was 9.88±1.29 cm, parenchyma thickness was 4.08±0.67 cm, SS was 3721.94±709.69 Pascal (Pa), and median spleen volume was 292.54 (239.40-311.00) cm3. A significant positive correlation was observed between age and SS (r=0.779, p<0.001). The SS values were not associated with sex, craniocaudal diameter, anteroposterior diameter, parenchymal thickness, or volume Conclusion:Age should be considered when using SS in the diagnosis and staging of relevant diseases such as portal hypertension and esophageal varices. Our results should be confirmed by future studies using 3T MRE in larger populations.

In this paper, a modular wire-actuated robotic arm was designed to improve the safety and adaptability of service robots during human-robot interaction. To raise the stiffness adjustment range of the robotic arm, a symmetric variable-stiffness unit was designed based on flexure, which had compact and simple structure, and lowly nonlinear stiffness-force relationship. In this paper, we focused on the research of the symmetric 1-DOF joint module. Based on the kinematics and stiffness analysis, the pose of the joint module could be adjusted by controlling the length of the wires, and the stiffness of the joint module could be adjusted by controlling the tension of the wires. Because of the actuation redundancy, the pose and stiffness of the joint module could be controlled synchronously. Furthermore, a directly method was proposed for the stiffness-oriented wire tension distribution problem of the 1-DOF joint module. A simulation was carried out to verify the proposed method.

Chronic hemodialysis (HD) patients have very high cardiovascular risk. Acute vascular changes during dialysis mediated by factors of the endothelium may have a crucial role in this. Aim: To study acute vascular changes during HD. In 29 consecutive chronic HD patients (age: 65.6±10.4 years) pre-, mid-, and post-HD plasma syndecan-1 (SDC-1) and endothelin-1 (ET-1) levels were measured. Applanation tonometry was performed before HD. SDC-1 levels increased during HD (p=0.004). Males had higher ET-1 levels. Patients were divided into 2 groups based on pulse wave velocity (PWV): PWV≥12 m/s and PWV<12 m/s. Pre-HD and mid-HD SDC-1 levels were higher in the group with PWV≥12 m/s (10.174±2.568 vs. 7.928±1.794 ng/ml, p=0.013, and 10.319±3.482 vs. 8.248±1.793 ng/ml, p=0.044, respectively). Post-HD ET-1 levels were higher in the patient group having PWV≥12 m/s (10.88±3.00 vs. 8.05±3.48 pg/l, p=0.027). Patients having PWV≥12 m/s had higher pre-HD peripheral and aortic systolic blood pressure (p<0.05). Total cholesterol correlated with the SDC-1 decrease during HD (r=0.539; p=0.008). Pre-, mid-, and post-HD SDC-1 correlated with the ultrafiltration (r=0.432, p=0.019; r=0.377, p=0.044; and r=0.401, p=0.012, respectively). SDC-1 and ET-1 contribute to vascular changes observed during HD, and they have correlations with some cardiovascular risk factors.

Although it’s been some forty years since we started to teach combined modified Fault Tree / Event Tree acyclic digraphs, as much simpler Bow Tie diagrams, their popularity seems undimmed; as their pictorial and focussed discussion prompts, fulfil a valuable function in the safe design and operation of hazardous plants and installations. An excellent review of the current state of the art and an authoritative treatise on the terminology and issues involved has been produced as an internationally recognised standard for using the approach. But just as this model has augmented and helped formalise previous pictorial tools, (such as “Dominoes” and holey “Cheese” slices), this paper suggests and sets out to show how we can build on even this current cornerstone of practice and augment its versatility; with the ability to obtain, what engineers rely on, some more quantitative insights from these pictures. “Layers Of Protection Analysis” (LOPA), has already demonstrated a way of pulling together more quantitative predictions from the pictures. This paper would go further and by concentrating on the function not the physicality of a barrier, outlines a methodology that can extend, not just the quantification ability of the LOPA extension, but present a much more holistic view of how the Barriers, as functions, need to work together, interact and interdepend; often in nonlinear, unexpected ways, to give system designers and operators a much clearer view of actual performance predictions.

In this paper we introduce an ODE system to model the interaction between nature resources and human exploitation in a rich consumeristic society. In this model the rate of change of population depends on wealth per capita, and the rate of consumption has a quadratic growth with respect to population and wealth. As in our previous work \cite{BaCra_1}, we distinguish between renewable and non renewable resources, and we introduce a replenishment term for non renewable resources. We first get some information on the asymptotic behaviour of wealth and population, then we compute all the equilibria of the system and we study their stability when the parameter of exploitation of resources is small. Some numerical simulations confirm the theoretical results, and give suggestions for future research.

We introduce the linear subgroup of volume-preserving diffeomorphism as the underlying symmetry to construct an action within the effective field theory framework and the Schwinger-Keldish formalism. The formulated action is posited to effectively incorporate dissipative effects into the Navier-Stokes equations.

As a rapidly expanding family of two-dimensional (2D) materials, MXenes have recently gained considerable attention due to their appealing properties. Here, by developing a solution-based coating method that enables transfer-free and layer-by-layer film coating, we investigate the layer-dependent nonlinear optical absorption of Ti₃C₂T_x films ‒ an important member of the MXene family. By using the Z-scan technique, we characterize the nonlinear absorption of the prepared MXene films consisting of different numbers of monolayers. The results show that there is a strong and layer-dependent nonlinear absorption behavior, transitioning from revisable saturable absorption (RSA) to saturable absorption (SA) as the layer number increases from 5 to 30. Notably, the nonlinear absorption coefficient β varies significantly within this range, changing from ~7.13 × 10² cm/GW to ~-2.69 × 10² cm/GW. We also characterize the power-dependent nonlinear absorption of the MXene films at various incident laser intensities, and a decreasing trend in β is observed for increasing laser intensity. These results reveal the intriguing layer-dependent nonlinear optical properties of 2D MXene films, highlighting their versatility and potential for implementing high-performance nonlinear photonic devices.

Soft tactile sensors based on piezoresistive materials have various large-area sensing applications. However, their accuracy is often affected by hysteresis, a phenomenon that poses a significant challenge during operation. This paper introduces a novel approach that employs a backpropagation (BP) neural network to address the hysteresis nonlinearity in conductive fibre-based tactile sensors. To assess the effectiveness of the proposed method, four sensor units with different layer configurations (1, 3, 6, and 12) were designed. These sensor units underwent force sequences to collect corresponding output resistances. A backpropagation network was trained using these force sequences, thereby correcting the resistance values. The training process exhibited excellent convergence, effectively adjusting the network's parameters to minimize the error between predicted and actual resistance values. As a result, the trained BP network accurately predicted the output resistances. Several validation experiments were conducted to highlight the primary contribution of this research. The proposed method reduced the maximum hysteresis error from 24.2% of the sensor's full-scale output to 13.5%. This improvement establishes the approach as a promising solution for enhancing the accuracy of soft tactile sensors based on piezoresistive materials. By effectively mitigating hysteresis nonlinearity, the capabilities of soft tactile sensors in various applications can be enhanced. These sensors become more reliable and more efficient tools for force measurement and control, particularly in the fields of soft robotics and wearable technology. Consequently, their widespread applications extend to robotics, medical devices, consumer electronics, and gaming. Notably, the complete elimination of hysteresis in tactile sensors may not be feasible. Nevertheless, the proposed method effectively modifies the hysteresis nonlinearity, leading to improved sensor output accuracy.

This paper presents the common methods and corresponding drawbacks concerning nonlinear analysis of fluxgate excitation circuits and emphasizes the importance of nonlinear analysis for these circuits. With regard to the nonlinearity of the excitation circuit, this paper proposes the use of the core-measured hysteresis curve for mathematical analysis and the use of a nonlinear model that considers the coupling effect of the core and winding and influence of the historical magnetic field on the core for simulation analysis. The feasibility of mathematical calculations and simulation for the nonlinear study of fluxgate excitation circuit is verified via experiments. The results demonstrate that, in this regard, the simulation is better than a mathematical calculation. The simulation and experimental results of the excitation current and voltage waveforms under different excitation circuit parameters and structures are essentially consistent with each other, thereby verifying the effectiveness of the nonlinear excitation analysis method.

With correct dynamic system parameters (embodied in self-awareness statements), a controller can provide precise signals for tracking desired state trajectories. If dynamic system parameters are initially guessed incorrectly, a learning method may be used to find the correct parameters. In the deterministic artificial intelligence method, self-awareness statements are formed as mathematical expressions of the governing physics. When the nonlinear, coupled expressions are precisely parameterized as the product of known matrix components and unknown victrix (i.e., a regression form) tracking errors may be projected onto the known matrix to update the unknown victrix in an optimal form (in a two-norm sense). In this work, a modified learning method is proposed and proved to have global convergence of both state error and parameter estimation error. The modified learning method is compared with those in the prequels using simulation experiments of three-dimensional rigid body dynamic rotation motion. The modified approach is two magnitudes better than the methods in the prequels in terms of state error convergence.

Integrated photonic devices operating via optical nonlinearities offer a powerful solution for all-optical information processing, yielding processing speeds that are well beyond that of electronic processing as well as providing the added benefits of compact footprint, high stability, high scalability, and small power consumption. The increasing demand for high-performance nonlinear integrated photonic devices has facilitated the hybrid integration of novel materials to address the limitations of existing integrated photonic platforms, such as strong nonlinear optical absorption or an inadequate optical nonlinearity. Recently, graphene oxide (GO), with its large optical nonlinearity, high flexibility in altering its properties, and facile fabrication processes, has attracted significant attention, enabling many hybrid nonlinear integrated photonic devices with improved performance and novel capabilities. This paper reviews the applications of GO to nonlinear integrated photonics. First, an overview of GO’s optical properties and the fabrication technologies needed for its on-chip integration is provided. Next, the state-of-the-art GO nonlinear integrated photonic devices are reviewed, together with comparisons of the nonlinear optical performance of different integrated platforms incorporating GO. Finally, the challenges and perspectives of this field are discussed.

Cellular Nonlinear Networks (CNN) are a concept introduced in 1988 by Leon Chua and Lin Yang as a bio-inspired architecture, capable of massively parallel computation. Later on, CNN have been enhanced by incorporating designs that incorporate memristors to profit from their processing and memory capabilities. In addition, Stochastic Computing (SC) can be used to optimize the quantity of required processing elements; thus it provides a lightweight approximate computing framework, quite accurate and effective, though. In this work, we propose utilization of SC in designing and implementing a memristor-based CNN. As a proof of the proposed concept, an example of application is presented. This application combines Matlab and a FPGA in order to create the CNN. The implemented CNN has then been used to perform three different real-time applications on a 512x512 gray-scale and a 768x512 color image: storage of the image, edge detection, and image sharpening. It has to be pointed out that the same CNN has been used for the three different tasks, with the sole change of some programmable parameters. Results show an excellent capability with significant accompanying advantages, like the low number of needed elements further allowing for a low cost FPGA-based system implementation, something confirming the system’s ability for real time operation.

Master equations define the dynamics that govern the time evolution of various physical processes on lattices. In the continuum limit, master equations lead to Fokker-Planck partial differential equations that represent the dynamics of physical systems in continuous spaces. Over the last few decades, nonlinear Fokker-Planck equations have become very popular in condensed matter physics and in statistical physics. Numerical solutions of these equations require the use of discretization schemes. However, the discrete evolution equation obtained by the discretization of a Fokker-Planck partial differential equation depends on the specific discretization scheme. In general, the discretized form is different from the master equation that has generated the respective Fokker-Planck equation in the continuum limit. Therefore, the knowledge of the master equation associated with a given Fokker-Planck equation is extremely important for the correct numerical integration of the latter, since it provides a unique, physically motivated discretization scheme. This paper shows that the Kinetic Interaction Principle (KIP) that governs the particle kinetics of many body systems, introduced in [G. Kaniadakis, Physica A 296, 405 (2001)], univocally defines a very simple master equation that in the continuum limit yields the nonlinear Fokker-Planck equation in its most general form.

Backward electromagnetic waves are extraordinary waves with contra-directed phase velocity and energy flux. Unusual properties of the coherent nonlinear optical coupling of the phase-matched ordinary and backward electromagnetic waves with contra-directed energy fluxes are described which enable greatly-enhanced frequency and propagation direction conversion, parametrical amplification, as well as control of shape of the light pulses. Extraordinary transient processes that emerge in such metamaterials in pulsed regimes are described. The results of the numerical simulation of particular plasmonic metamaterials with hyperbolic dispersion are presented, which prove the possibility to match phases of such coupled guided ordinary and backward electromagnetic waves. Particular properties of the outlined processes in the proposed metamaterial are demonstrated through numerical simulations. Potential applications include ultra-miniature amplifiers, frequency changing reflectors, modulators, pulse shapers, and remotely actuated sensors.

In the paper, by virtue of techniques in combinatorial analysis, the authors simplify two families of nonlinear ordinary differential equations in terms of the Stirling numbers of the first kind.

We have investigated the canine of olive flounder in terms of the nonlinear optical signals of two-photon excitation autofluorescence (2PEF) and second harmonic generation (SHG), whereby two kinds of nonlinear microscope images of the canine were obtained using ~140 femtosecond pulses. For increasing excitation power of laser pulses, a photobleaching effect was found to be significant in the red and green ranges of autofluorescence, where a double-exponential decay of the intensity occurs within hundreds of second due to collagen fluorophores in the canine. In the blue range of autofluorescence, the photobleaching is suppressed due to an energy conversion of the incident laser pulse to SHG signal. As a result, the signal in blue range remains constant for long term exposure to laser. We have also found that the SHG intensity depends on the orienta-tion of linearly polarized excitation, and the optical anisotropy of SHG can be attributed to the collagen alignment of canines.

We examine a family of nonlinear q-difference-differential Cauchy problems obtained as a coupling of linear Cauchy problems containing dilation q-difference operators, recently investigated by the author, and quasi-linear Kowalevski type problems that involve contraction q-difference operators. We build up local holomorphic solutions to these problems. Two aspects of these solutions are explored. One facet deals with asymptotic expansions in the complex time variable for which a mixed type Gevrey and q-Gevrey structure is exhibited. The other feature concerns the problem of confluence of these solutions as q tends to 1.

Gol'denveizer's problem of a torus has been analyzed by Audoly and Pomeau (2002) and Sun (2021). However, all of the investigations of Gol'denveizer's problem of an elastic torus have been linear. In this paper, the finite element method is used to more accurately address this problem. Furthermore, Sun (2021) cannot be solved by nonlinear analysis. We research the nonlinear mechanical properties of Gol'denveizer's problem of circular and elliptic tori, and relevant nephograms are given. We study the buckling of Gol'denveizer's problem of an elastic torus, and propose failure patterns and force-displacement curves of tori in the nonlinear range. Investigations reveal that circular tori have more rich buckling phenomena as the parameter a increases. Gol'denveizer's problem of the buckling of an elliptic torus is analyzed, and we find a new buckling phenomenon called a "skirt." As a/b increases, the collapse load of an elliptic torus of the Gol'denveizer problem is enhanced gradually.

Bayesian nonlinear mixed effects models for data in the form of continuous, repeated measurements from a population, also known as Bayesian hierarchical nonlinear models, are a popular platform for analysis when interest focuses on individual specific characteristics and relevant uncertainty quantification. Due to the limitation of computational power, this framework was relatively dormant until the late 1980s, but in recent years, the statistical research community saw vigorous development of new methodological and computational techniques for these models, the emergence of software, and wide application of the models in numerous industrial and academic fields. This article presents an overview of the formulation, interpretation, and implementation of Bayesian nonlinear mixed effects models and surveys recent advances and applications.

This paper presents sufficient conditions for almost global stability of nonlinear switched systems consisting of both stable and unstable subsystems. Techniques from the stability analysis of switched systems have been combined with the multiple Lyapunov density approach - recently proposed by the authors for the almost global stability of nonlinear switched systems composed of stable subsystems. By using slow switching for stable subsystems and fast switching for unstable subsystems lower and upper bounds for mode-dependent average dwell times are obtained. In addition to that, by allowing each subsystem to perform slow switching and using some restrictions on total operation time of unstable subsystems and stable subsystems, we have obtained a lower bound for an average dwell time.

Principle of memristor presented by Leon Chua and time reversal based non-linear elastic wave spectroscopy (TR-NEWS) which can be applied to acoustic tomography are reviewed. Correlation of acoustic or electromagnetic nonlinear waves and its time reversed wave can produce strong signal. Materials like transducer or biological skin can be assumed to be composed of a large number of small elastic unit: hysteretic elementary unit (HEU), and one can take a HEU as a memristor whose operation depends on time. Relation between TR-NEWS and solitonic wave in fluid, and relation between decomposition of time reversal operator (DORT) and chaotic oscillation are discussed.

Nonlinear rheological properties of chiral crystal cholesteryl oleyl carbonate (COC) in blue phase III are investigated under different shear deformations; large amplitude oscillatory shear, step shear deformation, and continuous shear flow. Rheology of the liquid crystal is significantly affected by structural rearrangement of defects under shear flow. One of the examples on the defect-mediated rheology is the blue phase rheology. Blue phase is characterized by three dimensional network structure of the disclination lines. It has been numerically studied that the rheological behavior of the blue phase is dominated by destruction and creation of the disclination networks. In this study, we find that the nonlinear viscoelasticity of BPIII is characterized by the fracture of the disclination networks. Depending on the degree of the fracture, the nonlinear viscoelasticity is divided into two regimes; the weak nonlinear regime where the disclination network locally fractures but still show elastic response, and the strong nonlinear regime where the shear deformation breaks up the networks, which results in a loss of the elasticity. Continuous shear deformation reveals that a series of the fracture process delays with shear rate. The shear rate dependence suggests that force balance between the elastic force acting on the disclination lines and the viscous force determines the fracture behavior.

For orthopaedic applications, additive manufactured (AM) porous scaffolds made of absorbable metals like magnesium, zinc or iron are of particular interest. They do not only offer the potential to design and fabricate bio-mimetic or rather bone equivalent mechanical properties, they also do not need to be removed in further surgery. Located in a physiological environment, scaffolds made of absorbable metals show a decreasing Young’s modulus over time, due to product dissolution. For WE43 scaffolds, during the first days an increase of the smeared Young's modulus can be observed, which is mainly attributed to a forming substrate layer of degradation products on the struts surfaces. In this study the influence of degradation products on the stiffness properties of metallic scaffolds is investigated. For this, analytical calculations and finite element simulations are performed to study the influence of the substrate layer thickness and Young's modulus for single struts and for a new scaffold geometry with adapted polar f2cc,z unit cells. The finite element model is further validated by compression tests on AM scaffolds made from Zn1Mg. The results show, that even low thicknesses and Young's moduli of the substrate layer increases significantly the smeared Young's modulus under axial compression.

(1) Background: Globally, neck pain is prevalent, affecting around thirty percent of the population annually. To better understand the influence of pain on the myofascial layers, the present study investigated these on the upper trapezius muscle in unilateral, more severe neck pain. (2) Methods: This study was a cross-sectional study. Forty patients (42.2 ± 14.7) with a confirmed diagnosis of unilateral neck pain were examined using durometry and indentometry. The study evaluated stiffness, elasticity, and pressure pain threshold of both sides of the neck (symptomatic side: SS; healthy side: HS). Furthermore, the range of motion of the cervical spine (lateral flexion, rotation) was quantified using a digital goniometer. (3) Results: A significant lateral discrepancy was observed in stiffness between groups (durometry: SS – 33.76 ± 7.78, HS – 29.75 ± 7.45, p&lt;0.001; indentometry: SS – 59.73 ± 33.93, HS – 4.18 ± 12.69, p=0.024). In contrast, no differences were found between the comparison sides of the upper trapezius for the parameter’s elasticity (SS – 0.101 ± 1.09, HS – -0.006 ± 0.29, p=0.416), cervical spine mobility (lateral flexion: SS – 37.08 ± 8.15, HS – 37.73 ± 7.61, p=0.559; rotation: SS – 73.55 ± 12.37, HS – 72.85 ± 11.10, p=0.660) and algometry (SS – 36.41 ± 17.53, HS – 37.22 ± 17.00, p=0.657). (4) Conclusion: Overall, it can be concluded that more severe neck pain unilaterally shows differences in stiffness on the same side. Future research is needed to investigate the links.

We propose a new hierarchy of the vector derivative nonlinear Schr{\"o}dinger equations and consider the simplest multiphase solutions of this hierarchy. The study of the simplest solutions of these equations led to the following results. First, the three-leaf spectral curves $\Gamma=\{(\mu,\lambda)\}$ of the simplest multiphase solutions have a quite simple symmetry. They are invariant with respect to holomorphic involution $\tau$. The type of this involution depends on the genus of the spectral curve. Or the involution has the form $\tau:(\mu,\lambda)\to(\mu,-\lambda)$, or $\tau:(\mu,\lambda)\to(-\mu,-\lambda)$. The presence of symmetry leads to the fact that the dynamics of the solution is determined not by the entire spectral curve $\Gamma$, but by its factor $\Gamma/\tau$, which has a smaller genus. Secondly, it turned out that the dynamics of the two-component vector $\bp=(p_1,p_2)^t$ is determined, first of all, by the dynamics of its length $\abs{\bp}$. Independent equations determine the dependence of the direction of the vector $\bp$ from its length. In cases where the direction of the vector $\bp$ is fixed, the corresponding spectral curve splits into separate components. In conclusion, we note that, as in the case of the Manakov system, the equation of the spectral curve is invariant with respect to the orthogonal transformation of the vector solutions. I.e., the solution can be found from the spectral curve up to the orthogonal transformation. This fact indicates that the spectral curve does not depend on the individual components of the solution, but on their symmetric functions. Thus, the spectral data of multiphase solutions have two symmetries. These symmetries make it difficult to reconstruct signals from their spectral data. The work contains examples illustrating these statements.

In the last years, a recent growing line of research has been developed with fruitful results by using fractional and conformable derivatives in the iterative procedures of classical methods for solving nonlinear equations. In that sense, the use of conformable derivatives has shown better behavior than fractional ones, not only in the theory, but also in the practice. In this work, we adapt the approximation of conformable derivatives in order to design the first conformable derivative-free iterative schemes to solve nonlinear equations: a Steffensen’s type method and a Secant type method; the latter with memory. Convergence analysis is made, preserving the order of classical cases, and the numerical performance is studied in order to confirm the results in the theory. It is shown that these methods can present some numerical advantages versus their classical partners, with wide sets of converging initial estimations.

An exact spherically symmetric and magnetically charged black hole solution in 4D Einstein-Gauss-Bonnet gravity coupled to nonlinear electrodynamics (NED) is obtained. The NED Lagrangian is given by ${\cal L}_{NED} = -{\cal F}/(1+\sqrt[4]{2\beta{\cal F}})$, where ${\cal F}$ is the field invariant. We study the thermodynamics calculating the Hawking temperature and the heat capacity of the black hole. The phase transitions take place when the Hawking temperature has an extremum and the heat capacity is singular. We demonstrate that black holes are thermodynamically stable in some range of event horizon radii where the heat capacity is positive. The BH shadow radii are calculated. It is shown that when increasing the nonlinearity parameter $\beta$ the BH shadow radius is decreased.

Our earlier work has tentatively shown that the hierarchy of fermion masses and mixing angles follows from the universal behavior of nonlinear dynamics. In this brief sequel we survey a similar scenario in which the Cabibbo angle arises from the nonlinear dynamics of charged-current interactions.

The necessary and sufficient conditions of existence of the nonlinear operator equations' branches of solutions in the neighbourhood of branching points are derived. The approach is based on reduction of the nonlinear operator equations to finite-dimensional problems. Methods of nonlinear functional analysis, integral equations, spectral theory based on index of Kronecker-Poincare, Morse-Conley index, power geometry and other methods are employed. Proposed methodology enables justification of the theorems on existence of bifurcation points and bifurcation sets in the nonstandard models. Formulated theorems are constructive. For a certain smoothness of the nonlinear operator, the asymptotic behaviour of the solutions is analysed in the neighbourhood of the branch points and uniformly converging iterative schemes with a choice of the uniformization parameter enables the comprehensive analysis of the problems details. General theorems are illustrated on the nonlinear integral equations.

In the present work we study the existence of solutions for hybrid nonlinear fractional integrodifferential equations. We developed an algorithm by using the operator theoretical techniques in order to obtain the approximate solutions. The main results depend on the Dhage iteration method that were incorporated with the modern hybrid fixed point theorems. The approximate solutions were obtained by using Lipschitz conditions and weaker form of mixed partial continuity. Further, we provide some examples to explain the hypotheses and the related results.

Background: Heart failure with preserved ejection fraction (HFpEF) is a major health concern. There is a growing recognition of the causal interplay between arterial stiffness and HFpEF. We recently reported that phosphate retention is a trigger for arterial stiffness. This study focuses on whether arterial stiffness due to phosphate retention could be a predictor for HFpEF. Methods: The study subjects were 158 patients (68 males and 90 females, mean age 74.8±11.2). HFpEF was defined according to the guidelines of the ESC 2019. Pulse wave velocity (PWV) and central systolic blood pressure (CSBP) were used as markers for arterial stiffness and afterload, respectively. We measured serum levels of fibroblast growth factor 23 (FGF23) as a marker of phosphate retention. Results: The serum levels of FGF23 had significant relationship with PWV. PWV had significant relationships with LV mass index, plasma BNP levels, and relative wall thickness, e’ and E/e’ (p<0.001, respectively). Multivariate logistic regression analysis revealed that PWV higher values and hypertension were significant predictors for the dependent factor (HFpEF). Conclusions: Arterial stiffness amplified LV afterload, leading to LV concentric hypertrophy and LV diastolic dysfunction. This study presents that arterial stiffness due to phosphate retention, and hypertension are important predictors of HFpEF.

We study in this work a dilute granular gas immersed in a thermal bath made of smaller particles with nonnegligible masses as compared with the granular ones. The kinetic theory for this system is developed and described by an Enskog--Fokker--Planck equation for the one-particle velocity distribution function. Granular particles are assumed to have inelastic and hard interactions, losing energy in collisions as accounted by a constant coefficient of normal restitution. The interaction with the thermal bath is based on a nonlinear drag force plus a white-noise stochastic force. To get explicit results of the temperature aging and steady states, Maxwellian and first Sonine approximations are developed. The latter takes into account the coupling of the excess kurtosis with the temperature. Theoretical predictions are compared with direct simulation Monte Carlo and event-driven molecular dynamics simulations. While good results for the granular temperature are obtained from the Maxwellian approximation, a much better agreement, especially as inelasticity and drag nonlinearity increase, is found when using the first Sonine approximation. The latter approximation is, additionally, crucial to account for memory effects like Mpemba and Kovacs-like ones.

The Chebyshev collocation method (ChC) implemented as Chebfun is used in order to solve a class of second order one-dimensional singular and genuinely nonlinear boundary value problems. Efforts to solve these problems with conventional ChC have generally failed, and the outcomes obtained by finite differences or finite elements are seldom satisfactory. We try to fix this situation using the new Chebfun programming environment. However, for toughest problems we have to loosen the default Chebfun tolerance in Newton's solver as the ChC runs into trouble with ill-conditioning of the spectral differentiation matrices. Although in such cases the convergence is not quadratic the Newton updates decrease monotonically. This fact, along with the decreasing behaviour of Chebyshev coefficients of solutions, suggests that the outcomes are trustworthy, i.e., the collocation method has exponential (geometric) rate of convergence or at least an algebraic rate. We consider first a set of problems that have exact solutions or prime integrals and then another set of benchmark problems that do not possess these properties. Actually, for each test problem carried out we have determined how Chebfun solution converges, its length, the accuracy of the Newton method and especially how well the numerical results overlap with the analytical ones (existence and uniqueness).

In this paper, we proposed a new model of non-linear electrodynamics with parameter. Firstly, we study the weak limit approximation and by using the Gauss Bonnet theorem, we obtain the deflection angle of photon from magnetized black hole and effect of bnon-linear electrodynamics. In doing so, we find the corresponding optical metric after that we calculate the Gaussian curvature which is used in Gauss Bonnet theorem. Then we show the deflection angle in the leading order terms. We also analyzed that our results reduces into Maxwell's electrodynamics and RN solution with the reduction of parameters. Moreover, we also investigate the graphical behavior of deflection angle w.r.t correction parameter, black hole charge and impact parameter.

We investigate the exact travelling wave solutions of the Tzitzéica-Dodd–Bullough–Mikhailov (TDBM) and Tzitzéica-type (TT) equations, appear in nonlinear optics, using simple ansatz approach. We use the Painlevé and traveling wave transformations to convert the mentioned nonlinear equations into nonlinear ordinary differential equations. Then, the simple ansatz approach has been employed to procure wave solutions, in terms of bright, singular soliton and trigonometric functions, for the Tzitzéica-Dodd–Bullough–Mikhailov (TDBM) and Tzitzéica-type (TT) equations. The study shows that the simple ansatz approach is straightforward and easy to implement for solving nonlinear problems.