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 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 impacts of inflation on international finance are generally reflected in the decline of buying power, risks of investment and deposit loss from currency devaluation. For the purpose of optimized allocation and management of asset values, i.e., annual income or research grants, a framework of a three-level model for static financial management is presented to maximize banking interests, bonuses, and the remaining balance after spending necessary expenditures. Meanwhile, in retrospect to higher-level financial inflation, strategies of dynamic investment, i.e., posing regular tests of flipping coins, exploiting variations of the currency exchange rate, as well as applying the theory of broad money, are presented to increase the appreciation rate of net assets in and post the era of COVID-19. Quantitative evaluations in case studies verify the feasibility of improving the financial situation, indicating broader applications for budgeting and investing when US inflation rate is below 3.0%. Besides, combining approaches of static and dynamic strategies, the expected annual growth rate of individual zero-risk asset investment is predicted as within the range of 8.30~9.62% according to budgeted appreciation on net assets in 12 months, which is capable of overcoming negative impacts from higher level annual inflation, i.e., those as highest as 8.01% in the Year 2022.

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 research on the excavation mechanical properties of underpass tunnels has already had certain results, but fewer of them consider the effects of dynamic and static loads on the excavation mechanical properties of underground tunnels at the same time, especially the lack of research cases of double-line highway tunnels with angled underpasses of existing railway tunnels. In this paper, based on the tunnel project of the new double-line Shiqian Highway Tunnel passing under the Hurong Railway at an oblique angle, the mechanical parameters of the rock body in the cross-tunneling area under the influence of static and dynamic load coupling are obtained by using the disturbance quantification coefficients and the Hoek-Brown criterion based on the method of over-advanced geological prediction and the investigation of the surrounding rock on the palisade face, and the engineering-scale finite element model is constructed and the mechanical characteristics of the excavation in the tunnel of the double-lane highway tunnel passing under the existing railroad under the influence of the static and dynamic loads are analyzed. The results show that: the new tunnel rock movement law for the top of the arch sinking, bottom plate bulging, side wall to move outward, the height and width of the arch and bottom plate arch with the tunnel excavation and increase, the side wall rock displacement effect is smaller; left and right lines of the tunnel disturbed area of the rule of change is similar; the existing tunnel bottom plate displacement is more than the top plate and the left and right side walls by the excavation of the time step influence is larger. Typical profile displacement is mainly determined by the distance from the excavation surface; the new tunnel in the four types of calculation conditions of the rock disturbance angle is the same; the existing tunnel roof and side wall Von Mises stress extreme occurs in the tunnel structure, the bottom plate there are pressure relief and pressure-bearing areas; based on the displacement control criteria, the recommended upper and lower step blasting method.

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.

Waterbomb structures are origami-inspired deformable structural components used in new types of robots. They have a unique radially deployable ability that enables robots to better adapt to their environment. In this paper, we propose a series of new waterbomb structures with square, rectangle, and parallelogram base units. Through quasi-static axial and radial compression experiments and numerical simulations, we prove that the parallelogram waterbomb structure has a twist displacement mode along the axial direction. Compared with the square waterbomb structure, the proposed optimal design of the parallelogram waterbomb structure reduces the critical axial buckling load-to-weight ratio by 55.4% and increases the radial stiffness-to-weight ratio by 67.6%. The significant increase in the radial stiffness-to-weight ratio of the waterbomb structure and decrease in the critical axial buckling load-to-weight ratio make the proposed origami pattern attractive for practical robotics applications.

The static formation temperature (SFT) is required to determine the thermophysical properties and production parameters in geothermal and oil reservoirs. However, the SFT is not easy to be obtained by both experimental and physical methods. In this paper, a mathematical approach to predicting SFT based on a new model describing the relationship between bottom hole temperature (BHT) and shut-in time was proposed. The unknown coefficients of the model were derived from least squares fit by Particle Swarm Optimization (PSO) algorithm. Besides, the ability to predict SFT based on a few BHT data (such as first 3, 4, or 5 ones of a data set) was evaluated. The accuracy of the proposed method to predict SFT was testified with a deviation percentage less than ±4% and high values of regression coefficient R² (>0.98). The proposed method could be used as a practical tool to predict SFT in both geothermal and oil wells.

A semi–numerical approach proposed many years ago for describing gravitational collapse in the post–quasi–static approximation , , , , is modified in order to avoid the numerical integration of the basic differential equations the approach is based upon. For doing that we have to impose some restrictions on the fluid distribution. More specifically, we shall assume the vanishing complexity factor condition, which allows for analytical integration of the pertinent differential equations and leads to physically interesting models. Instead, we show that neither the homologous nor the quasi–homologous evolution are acceptable since they lead to geodesic fluids, which are unsuitable for being described in the post–quasi–static approximation. Also, we prove that, within this approximation, adiabatic evolution also leads to geodesic fluids and therefore we shall consider exclusively dissipative systems. Besides the vanishing complexity factor condition, additional information is required for a full description of models. We shall propose different strategies for obtaining such an information, which are based on observables quantities (e.g. luminosity and redshift), and/or heuristic mathematical ansatz. To illustrate the method, we present two models. One model is inspired in the well known Schwarzschild interior solution, and another one is inspired in Tolman VI solution.

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.

In this paper, quasi-static axial compression tests are performed on the nodal Moso bamboos to study the size effect on energy absorption of the bamboos and the damage pattern of the multiple bamboo columns. Experimental results show that under the same moisture content, growth age and growing environment, the specific energy absorption (SEA) of the test samples increases with the increase of the out-diameter and thickness of the bamboo columns, indicating that size effect exists for energy absorption of the Moso Bamboos. For the multiple bamboo columns, there are mainly three failure modes for the constituent single bamboo columns: splitting above the node, splitting below the node and splitting through the node. Also, the tensile tests are conducted on three kinds of dog-bone shaped bamboo samples to investigate the macroscopic tensile fracture mode in the longitudinal direction of Moso bamboos. Results show that there is no direct relationship between the fracture pattern and moisture content of the bamboos, as well as the growth age of the bamboos. However, the tensile loading rate and the shape of the dog-bone shaped bamboo sample could affect the macroscopic fracture pattern of the bamboos in some cases.

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.

Hydrostatic bearings for liquid rocket engine turbopumps provide distinctive advantages including high load capacity even with low viscosity cryogenic fluid and extending a life span by minimizing friction and wear between rotor and bearing surfaces. Application of hydrostatic bearings into turbopumps demands reliable test data base with well-quantified operating parameters and experimentally validated accurate performance predictive tools. The present paper shows the comprehensive experimental data and validation of predicted static load characteristics of hydrostatic journal bearings lubricated with air, water, and liquid nitrogen. Extensive experiments for static load characteristics of hydrostatic bearings are conducted using a turbopump rotor-bearing system simulator while increasing supply pressure (Ps) into the test bearings. The test results demonstrate notable effects of the test fluids and their temperatures, as well as Ps, on the bearing performance. In general, the measured bearing flow rate, rotor displacement, and stiffness of the test bearings steadily increase with Ps. The static load bearing characteristics predictions considering flow turbulence and compressibility matched well with the experimental results. The work with an independent test data and engineering computational programs will further the implementation of hydrostatic bearings in high performance turbopump shaft systems with improved efficiency and enhanced reusability of liquid rocket engine sub-systems.

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.

Hand gestures are an essential part of human-to-human communication and interaction, and therefore for technical applications, the aim is increasingly to achieve interaction between humans and computers that is as natural as possible, for example by means of natural language or hand gestures. In the context of human-machine interaction research, these methods are consequently being explored more and more. However, the realization of natural communication between humans and computers is a major challenge. In the field of hand gesture recognition, research approaches are being pursued that use additional hardware such as special gloves to classify gestures with high accuracy. Recently, deep learning techniques using artificial neural networks have been increasingly proposed for the problem of gesture recognition without using such tools. In this context, in our approach convolutional neural network (CNN) will be explored in detail for the task of hand gesture recognition. CNN is a deep neural network that can be used in the field of visual object processing and classification. The goal of this work is to recognize ten types of static hand gestures in front of complex backgrounds and different hand sizes based on raw images without the use of extra hardware. We achieved good results with a CNN network architecture consisting of seven layers. Through data augmentation and skin segmentation, a significant increase of the model accuracy was achieved. On public benchmarks the ten gestures have been classified almost perfectly with a testing accuracy of 96.5%

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.

Compliant amplifying mechanisms are used widely in high-precision instruments driven by piezoelectric actuators, and the dynamic and static characteristics of these mechanisms are closely related to instrument performance. Although the majority of existing research has focused on analysis of their static characteristics, the dynamic characteristics of the mechanisms affect their response speeds directly. Therefore, this paper proposes a comprehensive theoretical model of compliant amplifying mechanisms based on the multi-body system transfer matrix method to analyze the dynamic and static characteristics of these mechanisms. The effects of the main amplifying mechanism parameters on the displacement amplification ratio and the resonance frequency are analyzed comprehensively using the control variable method. An iterative optimization algorithm is also used to obtain specific parameters that meet the design requirements. Finally, simulation analyses and experimental verification tests are performed. The results indicate the feasibility of using the proposed theoretical compliant amplifying mechanism model to describe the mechanism’s dynamic and static characteristics, which represents a significant contribution to the design and optimization of compliant amplifying mechanisms.

Software defect prediction models enable test managers to predict defect-prone modules and assist with delivering quality products. A test manager would be willing to identify the attributes that can influence defect prediction and should be able to trust the model outcomes. The objective of this research is to create software defect prediction models with a focus on interpretability. Additionally, it aims to investigate the impact of size, complexity, and other source code metrics on the prediction of software defects. This research will also assess the reliability of cross-project defect prediction. Well-known machine learning techniques such as support vector machines, k-nearest neighbors, random forest classifiers, and artificial neural networks were applied to publicly available PROMISE datasets. The interpretability of this approach has been demonstrated by SHapley Additive exPlanations (SHAP) and local interpretable model-agnostic explanations (LIME) techniques. The developed interpretable software defect prediction models showed reliability on independent and cross-project data. Finally, the results demonstrate that static code metrics can contribute to the defect prediction models, and the inclusion of explainability assists in establishing trust in the developed models.

The proliferation of ransomware poses a significant threat to global cybersecurity. This study presents a comprehensive review of the methodologies employed in the detection and analysis of ransomware, emphasizing the dichotomy between static and dynamic analysis approaches. It introduces the historical context and the necessity for robust cybersecurity measures, followed by an outline of the methodological framework used to evaluate existing ransomware analysis techniques. The results detail the effectiveness and limitations of various analysis strategies, identifying key features and patterns that aid in the detection and classification of ransomware threats. The study concludes by summarizing the primary achievements, including the identification of gaps in current research and proposing future research directions aimed at enhancing ransomware detection and mitigation strategies. The synthesis provided in this survey offers a consolidated view of the state-of-the-art in ransomware threat analysis and serves as a resource for cybersecurity professionals and researchers.

Retailers must have accurate sales forecasts to operate their businesses efficiently and effectively and to remain competitive in the marketplace. Global forecasting models like RNNs can be a powerful tool for forecasting in retail settings, where multiple time series are often interrelated and influenced by a variety of external factors. By including covariates in a forecasting model, we can better capture the various factors that can influence sales in a retail setting. This can help improve the accuracy of our forecasts and enable better decision-making for inventory management, purchasing, and other operational decisions. In this study we investigate how the accuracy of global forecasting models is affected by the inclusion of different potential demand covariates. To ensure the significance of the study's findings, we used the M5 forecasting competition's openly accessible and well-established dataset. The results obtained from the DeepAR models, which were trained on various combinations of features including time, price, events, and IDs, suggest that individually only the features corresponding to IDs improve the baseline model. However, when all the features are used together, the best performance is achieved, indicating that the individual relevance of each feature is emphasized when the information is given jointly. Comparing the model with features to the model without features, there is an improvement of 1.76\% for MRMSSE and 6.47\% for MMASE.

Background: Previous investigations have found a correlation between abnormal curvatures and a variety of patient complaints such as cervical pain and disability. However, no study has shown that loss of the cervical curve is a direct result of exposure to a motor vehicle collision (MVC). This investigation presents a retrospective consecutive case series of patients with both a pre-injury cervical lateral radiograph (CLR) and a post-injury CLR after exposure to a MVC. Computer analysis of digitized vertebral body corners on CLRs was performed to investigate the possible alterations in the geometric alignment of the sagittal cervical curve. Methods: Three spine clinic records were reviewed, over a 2-year period, looking for patients where both an initial lateral cervical x-ray and an examination were performed prior to the patient being exposed to a MVC; afterwards an additional exam and radiographic analysis were required. A total of 41 patients met the inclusion criteria. Examination records of pain intensity on numerical pain rating scores (NPRS) and neck disability index (NDI), if available, were analyzed. The CLRs were digitized and modeled in the sagittal plane using curve fitting and the least squares error approach. Radiographic variables included total cervical curve (ARA C2-C7), Chamberlain’s line to horizontal (skull flexion), horizontal translation of C2 relative to C7, segmental translations (retrolisthesis and anterolisthesis), and circular modelling radii. Results: There were 15 males and 26 females with an age range of 8-65 years. Most participants were drivers (28) involved in rear end impacts (30). The pre-injury NPRS was 2.7 while the post injury was 5.0; p < 0.001. The NDI was available on 24 /41 (58.5%) patients and was found to increase following exposure to the MVC: 15.7% to 32.8%, p < 0.001. An altered cervical curvature was identified following exposure to MVC, characterized by an increase in radius of curvature and an approximate 8° reduction of lordosis from C2-C7; p < 0.001. The mid cervical spine (C3-C5) showed the greatest curve reduction with localized mild kyphosis at these levels on average. Several participants developed segmental translations that approached the instability value of translation > 3.5mm. Conclusions: Abnormalities of cervical lordosis occurred following exposure to a MVC. The average loss of cervical curvature was 8° from C2-C7, with mild flexion of the mid cervical segments. Snap through type or dynamic buckling during the MVC may explain our findings. The primary contribution of this study to the motor vehicle collision literature is that altered cervical lordosis may result from MVC exposures and the consequences of an altered cervical alignment, in turn, may lead to future pain, disability and decreased health-related quality of life.

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.

A large set of undrained compression triaxial tests was carried out on different types of cohesionless soils, from sands to silty-sands and silts. Shear wave velocity measurements were carried out alongside. These tests exhibited distinct state transitions ranging from flow liquefaction to strain softening or strain hardening. With the purpose of defining a framework to assess soil liquefaction, it was found that the ratio between the shear wave velocity (VS0) and the peak undrained deviatoric stress, qpeak, VS0/qpeak, could be accurately used to define a boundary between liquefaction and strain hardening for sands, and between strain softening and strain hardening for silty-sands and silts. Since this ratio is a function of the tested material, it was also discovered that the prediction of these boundaries could be made as a function of soil grading, namely via the coefficient of uniformity, CU. Despite not being regarded as a strong geomechanical parameter, CU is easily determined from a grain-size distribution test and it has an empirically proven correlation with critical state parameters.

Many applications in the context of Industry 4.0 require precise localization. However, indoor localization remains an open problem, especially in complex environments such as industrial environments. In recent years, we have seen the emergence of Ultra WideBand (UWB) localization systems. The aim of this article is to evaluate the performance of a UWB system to estimate the position of a person moving in an indoor environment. To do so, we implemented an experimental protocol to evaluate the accuracy of the UWB system both statically and dynamically. The UWB system is compared to a ground truth obtained by a motion capture system with a millimetric accuracy.

In a series of recent papers we developed a formulation of general relativity in which spacetime and the dynamics of matter evolve with a Poincaré invariant parameter τ. In this paper we apply the formalism to derive the metric induced by a `static’ event evolving uniformly along its t-axis at the spatial origin x=0. The metric is shown to vary with t and τ, as well as spatial distance r, taking its maximum value for a test particle at the retarded time τ=t−r/c. In the resulting picture, an event localized is space and time produces a metric field similarly localized, where both evolve in τ. We first derive this metric as a solution to the wave equation in linearized field theory, and discuss its limitations by studying the geodesic motion it produces for an evolving event. By then examining this solution in the 4+1 formalism, which poses an initial value problem for the metric under τ-evolution, we clarify these limitations and indicate how they may be overcome in a solution to the full nonlinear field equations.

This paper presents a comprehensive study and the analysis of a topology of a no isolated DC-DC intituled Double Quadratic Boost converter with high static gain. This converter has the main advantage of high static gain and low voltage stress on its switches. The article will first present the theoretical analysis of the converter operating in an open loop. The objective of the work is the mathematical modeling and the control strategy of the converter, as well as the validation through closed-loop experimental results. Besides, we presented the practice test results to demonstrate the operation of the converter, such as the static gain experimental curve, the practice efficiency of the converter, and the control of the output voltage, as well as the capacitor voltage balance control. The authors designed a prototype for 1 kW, with a switching frequency of fs=50kHz, with FPGA-based command and modulation.

Static standing postural stability has been measured by multiscale entropy (MSE), which is used to measure complexity. In this study, we used the average entropy (AE) to measure the static standing postural stability, as AE is a good measure of disorder. The center of pressure (COP) trajectories were collected from 11 subjects under four kinds of balance situation, from stable to unstable: bipedal with open eyes, bipedal with closed eyes, unipedal with open eyes, and unipedal with closed eyes. The AE, entropy of entropy (EoE), and MSE methods were used to analyze these COP data, and EoE was found to be a good measure of complexity. The AE of the 11 subjects sequentially increased by 100%as the balance situations progressed from stable to unstable, but the results of EoE and MSE did not follow this trend. Therefore, AE, rather than EoE or MSE, is a good measure of static standing postural stability. Furthermore, the comparison of EoE and AE plots exhibited an inverted U curve, which is another example of a complexity versus disorder inverted U curve.

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 Sei Dareh Bridge is a cable-stayed bridge located in West Sumatra Province, Indonesia. The bridge, which crosses the Batanghari River, has a main span of 123 meters long and 9 meters wide. Traffic load is transmitted through 24 prestressed cables to a 42.4-meter-high pylon made of concrete. The bridge deck and traffic loads are directly supported by steel box girders as main beams that are reinforced laterally with cross beams IWF 800.300.16.24 and stringers IWF 350.350.12.19. This paper discusses static and dynamic testing on the bridge which aims to assess its feasibility before it is opened to the public. Based on the test, it was concluded that a static load of 73% could not be achieved because the deflection that occurred was beyond the allowable deflection. This is exacerbated by a loud clanging sound on the ST2-X1 prestressed cable when loading to 240 tons or 58% of the targeted load. In addition, this bridge is included in the "lazy bridge" category because it takes 24 hours to return to an undeformed condition after loading. As a recommendation for this bridge, it is necessary to carry out a structural health monitoring system (SHMS) regularly on bridge slabs and cables.

It is well known that the photon trajectories follow a curved path in a gravitational field. We explore here the gravitational bending of electric field lines. It seems that the electric field lines of a charge, supported in a gravitational field, follow exactly the trajectories of photons emitted isotropically from a source situated at the charge location. From a detailed examination of the electrostatic field of a charge accelerated uniformly in the instantaneous rest frame, exploiting the strong principle of equivalence, one can determine the bending of the electric field lines of a charge in a gravitational field. The fraction of electric field lines crossing a surface, stationary above or below the charge in the gravitational field, is shown to be exactly similar to the fraction of photon trajectories, emitted from a source placed at the charge location, intersecting that surface. On the other hand, for a freely falling charge in the gravitational field there is no such bending of electric field lines. The field lines continue to extend in radial straight lines from the instantaneous 'present' position of the charge, as do the trajectories of photons streaming away from the instantaneous position of a freely falling source in the gravitational field. The electric field configuration of a freely falling charge in the gravitational field is shown to be exactly the same as that of a charge moving uniformly in an inertial frame with velocity equal to the instantaneous ``present'' velocity of the freely falling charge.

The Sei Dareh Bridge is a cable-stayed bridge located in West Sumatra Province, Indonesia. The bridge, has a main span of 123 meters length and 9 meters wide, crosses the Batanghari River. Traffic load is transmitted through 4 prestressed cables to a 42.4 meter high pylon made of concrete. Bridge deck and traffic loads are directly supported by steel box girders as main beams that are reinforced laterally with cross beams IWF 800.300.16.24 and stringers IWF 350.350.12.19. This paper discusses static and dynamic testing on the bridge which aims to assess the feasibility before it is opened for public. Based on the test, it was concluded that the 73% static load could not be achieved because the deflection that occurred was beyond the allowable deflection. This is exacerbated by the sound of a loud clanging sound on the ST2-X1 prestressed cable when loading to 240 tons or 58% of the targeted load. In addition, this bridge is included in the "lazy bridge" category because it takes 24 hours to return to an undeformed condition after loading. As a recommendation for this bridge, it is necessary to carry out a structural health monitoring system (SHMS) regularly on the vehicle floor and cables.

Forest fire is a major ecological disaster, which has economic, social and environmental impacts on humans and also causes the loss of biodiversity. Forest officials issue the warnings to the public on the basis of fire danger index classes. There is no fire danger index for the country India due to the sparsely distributed meteorological stations. Previous studies suggest that Static Fire Danger Index (SFDI) as well as Dynamic Fire Danger Index (DFDI) have been derived from the satellite datasets. In this study, we have made an attempt to integrate both the Static and Dynamic fire danger indices and also used the Near Real Time (NRT) data sets that can be available for download through NASA FTP server after one hour of the satellite overpass. In this study, DFDI has been calculated from the MODIS Terra NRT Land Surface Temperature (MOD11_L2) and MODIS TERRA NRT surface reflectance MOD09. Finally, The Forest Fire Danger Index (FFDI) has been developed from the static and dynamic fire danger indices by the additive model and the overall accuracy was around 81.27%. Thus, the FFDI has been useful to predict the fire danger accurately and can be useful anywhere, where the meteorological stations are un-available.

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 electrification of rural areas of the planet has become one of the greatest challenges for sustainability. In fact, it would be the key to guaranteeing development for the poorest of the planet, but from which most of the raw material for the food market derives. The paradigm of centralized production is not applicable in these territories, because the distribution network would involve unjustifiable costs. For this reason, studies have multiplied to ensure the energy supply, especially electricity, of off-grid utilities, to guarantee energy autonomy while reducing the dependence on specialist assistance for the management of the system. In this work, a hybrid system (HRES) is proposed that combines the exploitation of solar energy with that of the wind through the use of static devices, in order to improve the system's availability and limit the cost of operation and maintenance.

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.

Using graph theory, computer aided motion, static force and power flow analysis of planetary gear mechanism is realized. The motion, static force and efficiency calculations of 6HP26 automatic transmission are carried out. Based on kinematic and static force analysis model, related matrices are acquired. Hence, kinematic and static force analysis of planetary gear mechanism is achieved. The link power can be determined by the link speed and torque. Power flow diagrams of each gear are acquired. The efficiency is calculated by transmission ratio method.

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.

This article explores matter collineations (MCs) of static plane-symmetric spacetimes, considering the stress-energy tensor in its contravariant and mixed forms. We solve the MC equations in two cases: when the energy-momentum tensor is nondegenerate and degenerate. For the case of degenerate energy-momentum tensor, we employ a direct integration technique to solve the MC equations, which leads to an infinite-dimensional Lie algebra. On the other hand, when considering the nondegenerate energy-momentum tensor, the contravariant form results in a finite-dimensional Lie algebra with dimensions of either 4 or 10. However, in the case of the mixed form of the energy-momentum tensor, the dimension of the Lie algebra is infinite. Moreover, the obtained MCs are compared with those already found for covariant stress-energy.

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.

We study the problem of a spherically-symmetric distribution of a perfect relativistic fluid accreting onto a (potentially spinning) black hole within a fully discrete spacetime setting. This problem has previously been studied extensively in the context of continuum spacetimes, beginning with the purely analytic work of Bondi in the spherically-symmetric Newtonian case, Michel in the spherically-symmetric general relativistic case, and Petrich, Shapiro and Teukolsky in the axially-symmetric general relativistic case relevant for spinning black holes. However, the purpose of the present work is to determine the effect of discretization of the underlying spacetime upon the mass/energy and momentum accretion rates, the overall morphology and characteristics of the accretion flow, and the drag force exerted on the black hole in the case of non-zero spin. In order to achieve this, we first develop a novel formulation of the equations of general relativistic hydrodynamics that is more directly amenable to rigorous analysis within a discrete spacetime setting, and we then proceed to implement this formulation into the \textsc{Gravitas} computational general relativity framework. Through a combination of mathematical analysis and explicit numerical simulation in \textsc{Gravitas}, we discover that the mass/energy and momentum accretion rates both decrease monotonically as functions of the underlying spacetime discretization scale, with this effect becoming more pronounced for higher values of the black hole spin parameter, higher fluid temperatures, and stiffer equation of state parameters. We also find that the exerted drag force is highly sensitive to the value of the underlying discretization scale in the case of spinning black hole spacetimes, with certain instabilities becoming significantly more pronounced at certain critical values of the discretization parameter. We discuss some potentially observable consequences of these results, as well as some directions for future theoretical investigation.

We classify all the topologically non-equivalent phase portraits of the quadratic polynomial differential system dx/dt = (1-2x)(y-x), dy/dt =y (2-g y-(5g-4)x/(g-1)), in the Poincaré disc for all the values of the parameter g in R\{1}. The differential system dx/dt = y-x, dy/dt =y (2-g y-(5g-4)x/(g-1))/(1-2x), when the parameter g in (1,2] models the structure equations of a static star in general relativity in the case of the existence of a homologous family of solutions, being x = m(r)/r where m(r)>= 0 is the mass inside the sphere of radius r of the star, y = 4pi r^2 rho where rho is the density of the star, and t = ln (r/R) where R is the radius of the star. We classify the possible values of m(r)/r and 4pi r^2 rho when r-->0.

The damage evolution rules of coal under true triaxial combined static-dynamic loads are important to understand and reveal the mechanism of rockburst in coal mines. The numerical simulation was carried out using FLAC3D to explore the coupling effect of static and dynamic stress, especially the influence of dynamic load parameters. The results show that the increase of dynamic load amplitude not only makes the plastic zone grow exponentially and shorten the damage development time, but also decreases the residual strength of the coal sample, which leads to a much more violent of the dynamic failure. The stress wave can propagate more stable in the coal sample with the increase of dynamic load frequency and the development time of the plastic zone also show synchronous fluctuating features, and when the frequency is like the intrinsic frequency of the coal sample, the dynamic load has a significant stimulate effect. The static and dynamic loads have different damage effect to the coal sample under true triaxial stress path, the weight decreases in order of the minimum principal stress, the maximum principal, the amplitude of the dynamic load and at last the dynamic stress frequency by the entropy weight method analysis.

In this paper, we study the deflection angle for wormhole-like static aether solution by using Gibbons and Werner technique in non-plasma, plasma and dark matter mediums. For this purpose, we use optical spacetime geometry to calculate the Gaussian optical curvature, then implement the Gauss-Bonnet theorem in weak field limits. Moreover, we compute the deflection angle by using a technique known as Keeton and Petters technique. Furthermore, we analyze the graphical behaviour of the bending angle ψ with respect to the impact parameter b, mass m as integration constant and parameter q in non-plasma and plasma mediums. We examine that deflection angle is exponentially increasing as direct with charge. Also, we observe that for small values of b, ψ increases and for large values of b the angle deceases. We also considered an analysis to the shadow cast of the wormhole relative to an observer at various locations. Comparing it the the Schwarzschild shadow, shadow cast is possible for wormhole as r<2m. At r>2m, the Schwarzschild is larger. As r → ∞, we have seen that the behavior of the shadow, as well as the weak deflection angle, approaches that of the Schwarzschild black hole. Overall, the effect of plasma tends to decrease the value of the observables due to the wormhole geometry.

The evidence is presented for the long-range previtreous changes of two static properties: dielectric constant ( ) and its strong electric field related counterpart - the nonlinear dielectric effect (NDE). Notable is the evidence for the functional characterizations of (T) temperature changes by the ‘Mossotti Catastrophe’ formula, and NDE vs. T evolution by the relations resembling one developed for critical liquids. The analysis of dynamic properties based on the activation energy index excluded the Vogel-Fulcher-Tammann (VFT) relation as a validated tool for portraying the evolution of the primary relaxation time. Such a result questions the commonly applied ‘Stickel operator’ routine as the reliable tool for determining the dynamic crossover temperature. It is worth stressing that the strong electric field radically affects the distribution of relaxation times, the form of the evolution of the primary relaxation time as well as the fragility. Obtained results support the concept of a possible semi-continuous phase transition hidden below Tg. Studies were carried out in supercooled squalene, the material with extremely low electric conductivity, strongly elongated molecule, and vitally important for biology and medicine related issues.

In this paper, a metal cutting machine position control have been designed and simulated using Matlab/Simulink Toolbox successfully. The open loop response of the system analysis shows that the system needs performance improvement. Static output feedback and full state feedback H₂ controllers have been used to increase the performance of the system. Comparison of the metal cutting machine position using static output feedback and full state feedback H₂ controllers have been done to track a set point position using step and sine wave input signals and a promising results have been analyzed.

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.

One of the important issues being explored in Industry 4.0 is a collaborative mobile robots. This collaboration requires precise navigation systems, especially indoor navigation systems where GNSS (Global Navigation Satellite System) cannot be used. To enable precise localization of robots, different variations of navigation systems are being developed, mainly based on trilateration and triangulation methods. Triangulation systems are distinguished by the fact that they allow precise determination of an object’s orientation, which is important for mobile robots. An important feature of positioning systems is the frequency of position updates based on measurements. For most systems it is 10-20 Hz. In our work, we propose a high-speed 50 Hz positioning system based on the triangulation method with infrared transmitters and receivers. In addition, our system is completely static, i.e. it has no moving/rotating measurement sensors, which makes it more resistant to disturbances (caused by vibrations, wear and tear of components, etc.). In this paper we describe the principle of the system as well as its design. Finally, we present tests of the built system, which show centimeter positioning accuracy with a position update frequency of 50 Hz.

Human-to-human communication via the computer is mainly done using a keyboard or microphone. In the field of Virtual Reality (VR), where the most immersive experience possible is desired, the use of a keyboard contradicts this goal, while the use of a microphone is not always desirable (e.g. silent commands during task force training) or simply not possible (e.g. if the user has a hearing loss). Data gloves help to increase immersion within the VR as they correspond to our natural interaction. At the same time, they offer the possibility to accurately capture hand shapes, such as those used in non-verbal communication (e.g. thumbs up, okay gesture, ...) and in sign language. In this paper, we present a hand shape recognition system using Manus Prime X data gloves, including data acquisition, data preprocessing, and data classification to enable nonverbal communication within VR. We investigate the impact on accuracy and classification time of using an Outlier Detection and a Feature Selection approach in our data preprocessing. To obtain a more generalized approach, we also studied the impact of artificial Data Augmentation, i.e., we create new artificial data from the recorded and filtered data to augment the training dataset. With our approach, 56 different hand shapes could be distinguished with an accuracy of up to 93.28%. With a reduced number of 27 hand shapes, an accuracy of up to 95.55% could be achieved. Voting Meta-Classifier (VL2) has proven to be the most accurate, albeit slowest, classifier. A good alternative is Random Forest (RF), which was even able to achieve better accuracy values in a few cases and was generally somewhat faster. Outlier Detection has proven to be a effective approach, especially in improving classification time. Overall, we have shown that our hand shape recognition system using data gloves is suitable for communication within VR.

Soccer is the most played sport worldwide, with over 265 million participants. It is an incredibly demanding sport, with many different technical skills and physical loads placed on the body. This makes post-match recovery strategies amongst high level soccer players of great importance. The aim of this review is to summarize the existing literature on stretching for post-match recovery, examining its relation to injury prevention, Delayed Onset Muscle Soreness (DOMS), and performance. Scientific evidence of the highest quality and relevance was extracted and reviewed. Despite its common practice, evidence does not support static stretching as a modality to improve recovery post-match amongst soccer players. Larger trials with important outcome measures are needed to determine if a post-match stretching regimen to facilitate recovery exists.

A new attack against the Kirchhoff-Law-Johnson-Noise (KLJN) key distribution system is introduced. The attack is based on 1) Utilizing the dc-voltage-source - which we put at Alice’s end in our mathematical modeling of the attack-that could exist due to errors, imbalances, Electromagnetic interference and etc.2) On studying the number of samples per bit in the security key that the measured Alice/Bob voltages exceeds or falls below a threshold voltage, respectively. The threshold voltage is the average between dc voltages across low and high resistors- generated by a dc-voltage source. We count the number of samples the voltage at Bob’s end (containing both the noise and dc components) exceeds the threshold voltage and how many times it falls below the threshold to judge whether the resistor can be guessed as low or high for every cycle. Also for a pre-specified key-length we count the number of high resistance estimations per bit –at Bob’s end-according to the previous criterion and the non-successful estimations per bit to judge the final guessed resistor value at Alice’s end and Bob’s end, where if we have more bits with most of its measured samples are above the threshold voltage then we will predict Bob’s resistance as high resistance, otherwise we predict Bob’s resistance to be low resistance. The Simulation was conducted and the attack proved that it is successful unless the temperature increased dramatically to ranges more than a threshold temperature ~ Kelvin that increases when the number of samples per bit increases.

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.

This work presents the results of the experimental and theoretical study of the static pull-in of tilting actuation executed by a hybrid levitation micro-actuator (HLMA) based on the combination of inductive levitation and electrostatic actuation. A semi-analytical model to study such the pull-in phenomenon is developed, for the first time, as a result of using the qualitative technique based on the Lagrangian approach to analyze inductive contactless suspensions presented in work and a recent progress in the calculation of mutual inductance and force between two circular filaments. The obtained non-linear model, accounting for two degrees of freedom of the actuator, allows us to predict accurately the static pull-in displacement and voltage. The results of modelling were verified experimentally and agree well with measurements.

In this work, we experimentally investigate mass and heat transport phenomena in a modular device while converting a solution salinity difference into a temperature difference. Operations occur under fixed total ambient pressure and without mechanical moving parts, thus realizing a fully static conversion. Provided that a constant salinity gradient can be imposed, the proposed device is able to generate a steady cooling capacity. Here, we purposely operate with environmentally benign and easily accessible sodium chloride water solutions only. A numerical model is finally elaborated, validated and used to explore a wider range of possible device configurations and operating conditions.

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.

Abstract—The static and fatigue analysis of plates with holes, made of 2D woven roving composites, is conducted. The parametrization of convex holes is proposed. Experimental results of specimens without holes and with different shapes of notches are discussed. The fatigue behaviour is considered with the use of the low cycle fatigue method. The analysis is supplemented by the numerical finite element modeling. The present work is an extension of the results discussed in the literature. The finite element modeling of plates with holes is presented in details in Ref [1-3] including also the problems of the accuracy. The experimental results and the form of specimens are shown in Ref [4]. Two parametrical description of static and fatigue behaviour of plates with holes characterizes the goal and the novelty of the paper. The fuzzy approach is employed to reduce the number of experimental data [5].

Although Support Vector Machines (SVM) are widely used for classifying human motion patterns, their application in the automatic recognition of dynamic and static activities of daily life in the healthy older adults is limited. Using a body mounted wireless inertial measurement unit (IMU), this paper explores the use of SVM approach for classifying dynamic (walking) and static (sitting, standing and lying) activities of the older adults. Specifically, data formatting and feature extraction methods associated with IMU signals are discussed. To evaluate the performance of the SVM algorithm, the effects of two parameters involved in SVM algorithm—the soft margin constant C and the kernel function parameter $\mathsf{\gamma }$—are investigated. The changes associated with adding white-noise and pink-noise on these two parameters along with adding different sources of movement variations (i.e., localized muscle fatigue and mixed activities) are further discussed. The results indicate that the SVM algorithm is capable of keeping high overall accuracy by adjusting the two parameters for dynamic as well as static activities, and may be applied as a tool for automatically identifying dynamic and static activities of daily life in the older adults.

In this paper, we investigated the trajectory of the massive particle in the vicinity of a general spherical symmetric black hole. Also, in the framework of general sphericalily symmetric black hole, Pseudo-Newtonian potential (PNP) and effective potentials has been investigated. As an example, static spherically symmetric black hole in f(R) gravity is considered and presented the brief discussion on the structure of spacetime and horizons. We calculated energy and angular momentum in the framework of general relativity as well as in Pseudo-Newtonian theory. A graphical comparison of angular momentum in this both framework has been studied.

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.

Vitamin D3 deficiency is a global phenomenon, which can be coped with supplementation and food fortification. However, vitamin D3 bioaccessibility may depend on factors, such as matrix composition and interactions throughout the gastrointestinal tract. This research focused on the effect of different matrices on vitamin D3 content during digestion, and the effect of pH on its bioaccessibility. The INFOGEST protocol was employed to simulate digestion. Three different types of commercial supplements, two foods naturally rich in vitamin D3, and three fortified foods were investigated. High-Performance Liquid Chromatography was used to determine the vitamin D3 initial content in supplements and foods, as well as after each digestion stage. Results indicated that foods exhibited higher bioaccessibility indices compared to supplements, and a higher percentage retention at the end of the gastric phase. The pH study revealed a positive correlation between increased gastric pH and the corresponding content of vitamin D3. Interestingly, exposing the matrix to low pH during the gastric phase resulted in an increased intestinal content of D3. Vitamin D3 is more bioaccessible from foods than supplements, and its bioaccessibility is susceptible to changes in gastric pH. Fasting conditions (i.e. gastric pH=1) enhances vitamin’s bioaccessibility.

Laser shock peening is a process which can reduce stress corrosion cracking and improve fatigue life by forming compressive residual stress on the surface of the material. In a computational FE simulation of laser shock peening, during applying the pressure load generated by the laser pulse to the surface of simulation geometry, the peening is simulated by explicit analysis and then convert to implicit analysis to dissipate the dynamic energy remaining in the geometry. In this study, static damping is applied to dissipate residual dynamic energy without converting it into an implicit analysis. The compressive residual stress distribution is compared between the simulation results for the stainless steel 304 material and the same material subjected to actual laser shock peening. The laser shock peening parameters were 4.2J laser pulse energy, 50% overlap of 3mm diameter of the laser beam and water as a confinement layer. As a result, the compressive residual stress from the surface to the depth direction is similar to both the simulation and the experimental result measured by the hole drilling method.

There are many welded structures in the world such as bridges and viaducts that are subject to fatigue. These structures, generally made of non-alloy or low-alloy steels, have been put into operation some of them with many years ago and have accumulated a large number of variable load cycles over the time. For this reason the occurrence of fatigue phenomenon is inevitable and consists in the occurrence of failures at stresses applied to the structure, below the yield limit of the material. These stresses under the static loads would not cause the failures to appear..This paper will investigate whether two reconditioning techniques “weld toe grinding” and “WIG remelting weld toe”, influences favorably the behavior of welded structures made from HSLA steel, in static and variable loads and therefore if the application of these techniques is justified in both cases. In the paper will be presented the chemical composition and mechanical properties of the base and filler materials, micro and macrostructures, graphics with the variation of microhardness, static and fatigue tensile tests will be performed, and it will be rised durability curve in case of fatigue tests.

The current work addresses the control of two-input two-output (TITO) Wood and Berry model of a binary distillation column. The controller design problem is formulated in terms of multivariable H_∞ control synthesis. The controller structure takes the form of simplest static output feedback (SOF) control. The controller synthesis is performed using a hybrid approach of blending linear matrix inequalities (LMI) and genetic algorithm (GA). The performance of the static output feedback controller is compared with three other controllers designed for Wood and Berry model available in the literature. The first simulation study is performed for the case of tracking a unit step command in the presence of a step change in output disturbance. A second simulation study is performed for rejecting a change in sinusoidal output disturbance.

The aim of this work was to determine if the development of low-cost or no-cost finite element analysis (FEA) software has advanced to the point where it can be used in place of trusted commercial FEA packages for linear static structural analyses using isotropic material models. Nonlinear structural analysis will be covered in a separate paper. Several suitable packages were identified, these underwent a process of systematic elimination when they were unable to meet the minimum imposed qualitative criteria. Three packages were chosen to be subjected to performance benchmarking, namely: Code_Aster/Salome Meca; Mecway and Z88 Aurora. SimScale, a browser-based analysis package was included as well because it met all the baseline criteria and has the potential to offer a completely cloud-based approach to computer aided engineering, potentially reshaping the way an engineering business views its operational capabilities. This paper presents the test cases and simulation results for packages that fall under the linear static structural analysis type.

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.

Monitoring the dynamic responses of bridge structures has received considerable attention. It is important to synchronously measure both the quasi-static and dynamic displacements of bridge structures. However, the traditional accelerometer method cannot capture the quasi-static displacement component, although it can detect the dynamic displacement component. To this end, a novel composite instrument of a smartstation was proposed to monitor vibration displacements of footbridges. Full-scale experiments were conducted on a footbridge to validate the feasibility of the composite instrument-based monitoring method. A Chebyshev filter and wavelet algorithms were developed to process the composite instrument measurements. It was concluded that the measurement noise of the composite instrument was mainly distributed in a frequency range of 0–0.1 Hz. In two case studies with displacement peaks of 5.7–10.0 mm and 1.3– 2.5 mm, the composite instrument accurately identified the quasi-static and dynamic displacements. The composite instrument will be a potential tool for monitoring structural dynamics because of its enhanced overall performance.

This study aimed to solve the problems of sealing and tearing failure of packer’s rubber cylinders during CO2 downhole injection. Using the simulation software, Comsol, a rubber cylinder model in a supercritical CO2 (SC-CO2) environment was established. The thermal analogy method was used to simulate the CO2 diffusion and rubber cylinder swelling process, thus we analyzed the deformation and stress of the rubber cylinder caused by temperature, pressure and CO2 as swelling agent. Results showed that, in the SC-CO2 environment, under the influence of CO2 diffusion and the consequent swelling, the rubber cylinder body is prone to large deformation, and the maximum shear stress is significantly increased, leading to shear failure of the rubber cylinder. The reduction of the initial seating pressure can alleviate the impact of deformation, whereas the reduction of the maximum contact pressure could cause the rubber cylinder to lose its seal. We also analyzed the change rules between various factors and the maximum contact pressure of the rubber cylinder, which provides a theoretical basis and technical support for improving the sealing performance of the packer’s rubber cylinder in the SC-CO2 environment.

A reliable finite element procedure to simulate shear-dominated ductile fracture in large-scale, thin-walled steel structures is still evolving due primarily to the challenges in determining the fracture criterion of steel materials under complex stress states. This paper aims to examine the accuracy of the modified Gurson-Tvergaard-Needleman (GTN) model considering the shear failure in simulating ductile fracture of steel plate structures under quasi-static punch loading. The modified GTN damage models are performed by ABAQUS user defined material subroutine (VUMAT). The void related parameters and shear damage parameters of Xue’s and N-H modified GTN models are calibrated from test specimens with various geometries corresponding to different stress triaxiality and shearing conditions. The damage evolution associated with the shearing of voids in the modified GTN models has strong influences on the stress triaxiality versus equivalent plastic strain under complex stress states, especially for the shear dominated loading conditions. Based on the original GTN model, Xue’s model, and N-H modified GTN model with calibrated material parameters, a numerical comparative study examines the ductile fracture of steel non-stiffened plate and stiffened plate under punch loading. Benchmarked against the experimental studies, the numerical simulations demonstrate that the shear driven void evolution in the modified GTN model imposes significant effects on the load-displacement responses, as well as the onset and extension of ductile fracture in steel plates under punch actions. The N-H modified model with calibrated shear damage parameters shows a better correlation with the ductile fractures in steel plates observed in the experiment, than the original GTN model and Xue’s modified GTN model. As a result of this study, the modified GTN model considering the shear failure can be applied for practical applications in the crashworthiness assessment of ship collision and grounding.