Version 1
: Received: 24 December 2020 / Approved: 26 December 2020 / Online: 26 December 2020 (10:45:47 CET)
Version 2
: Received: 27 February 2021 / Approved: 1 March 2021 / Online: 1 March 2021 (13:13:47 CET)
How to cite:
Carvalho, J.; Carrondo, M.; Bonilla, L. Biofilm Early Stages of Growth and Accumulation Theoretical Model. Preprints2020, 2020120673. https://doi.org/10.20944/preprints202012.0673.v2
Carvalho, J.; Carrondo, M.; Bonilla, L. Biofilm Early Stages of Growth and Accumulation Theoretical Model. Preprints 2020, 2020120673. https://doi.org/10.20944/preprints202012.0673.v2
Carvalho, J.; Carrondo, M.; Bonilla, L. Biofilm Early Stages of Growth and Accumulation Theoretical Model. Preprints2020, 2020120673. https://doi.org/10.20944/preprints202012.0673.v2
APA Style
Carvalho, J., Carrondo, M., & Bonilla, L. (2021). Biofilm Early Stages of Growth and Accumulation Theoretical Model. Preprints. https://doi.org/10.20944/preprints202012.0673.v2
Chicago/Turabian Style
Carvalho, J., Manuel Carrondo and Luis Bonilla. 2021 "Biofilm Early Stages of Growth and Accumulation Theoretical Model" Preprints. https://doi.org/10.20944/preprints202012.0673.v2
Abstract
A theoretical model to translate the evolution over time, in early stages, of growth and accumulation of biofilm bacterial mass is introduced. The model implies the solution of a system of differential-difference master equations. The application of an algorithm like Miller´s tree term recurrence, already known for Bessel functions of first kind, allows an exact calculation of the solutions of such equations, for a wide range of parameters values and time. For biofilm model a five term recurrence is deduced and applied in a backwards computation. A suitable normalisation condition completes the reach of the solution.
Keywords
biofilm; Miller recurrent algorithm; Bessel functions; differential-difference master equations
Subject
Engineering, Automotive Engineering
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received:
1 March 2021
Commenter:
José Carvalho
Commenter's Conflict of Interests:
Author
Comment:
New sections were included: 1. More detailed initial description of the model 2. A section of numerical examples 3. A conclusions section 4. A future work section
Commenter: José Carvalho
Commenter's Conflict of Interests: Author
1. More detailed initial description of the model
2. A section of numerical examples
3. A conclusions section
4. A future work section