Mathematical Modeling of Bio-Macromolecule Dynamics in Living Cells: A Continuum Mechanics Approach

2007 ◽  
Author(s):  
Kouroush Sadegh Zadeh ◽  
Hubert J Montas ◽  
Adel Shirmohammadi
Keyword(s):  
Mathematical Modeling ◽  
Continuum Mechanics ◽  
Living Cells

Mathematical Modeling in Continuum Mechanics

2001 ◽  
Vol 54 (4) ◽  
pp. B57-B57 ◽  
Author(s):  
R Temam, ◽  
A Miranville, ◽  
P Gremaud,
Keyword(s):  
Mathematical Modeling ◽  
Continuum Mechanics

scholarly journals Experimental and theoretical researches of high-speed interaction of thin obstacles with a metal fragment

2019 ◽  
Vol 221 ◽  
pp. 01043
Author(s):  
Svetlana Afanasyeva ◽  
Viktor Burkin ◽  
Aleksey Dyachkovsky ◽  
Alexandr Ishchenko ◽  
Konstantin Rogaev ◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Titanium Alloy ◽  
Continuum Mechanics ◽  
High Speed ◽  
Interaction Process ◽  
Actual Problem ◽  
Cost Weight ◽  
Ballistic Resistance ◽  
Protective Structures ◽  
Metal Fragment

The development of lightweight protective structures of increased ballistic resistance is not an easy task, since often there are conflicting requirements in terms of cost, weight, thickness, materials availability, processability, etc. To assess the effectiveness of protective structures one should use methods that allow to research the obstacles destruction when collided with high-speed particles. The paper is devoted to the actual problem of studying the ballistic stability of thin barriers made of various protective materials (steel, titanium alloy, ceramics, metal ceramics) when interacting with a metal fragment simulator a spherical steel drummer in the range of interaction speeds of about 2500 m/s. An experimental technique has been developed to study the most important indicators: the depth of a crater in an obstacle, a fragment’s velocity drop when interacting with protection, the obstacle’s and splinter’s fragments scattering in overgraded space. Mathematical modeling was carried out within the framework of continuum mechanics, which adequately describes the interaction process of the drummer and the obstacle under various impact conditions.

scholarly journals Diffusion–reaction compartmental models formulated in a continuum mechanics framework: application to COVID-19, mathematical analysis, and numerical study

2020 ◽  
Vol 66 (5) ◽  
pp. 1131-1152 ◽  
Author(s):  
Alex Viguerie ◽  
Alessandro Veneziani ◽  
Guillermo Lorenzo ◽  
Davide Baroli ◽  
Nicole Aretz-Nellesen ◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Continuum Mechanics ◽  
Mathematical Analysis ◽  
Numerical Study ◽  
Interdisciplinary Collaboration ◽  
Compartmental Models ◽  
Diffusion Reaction ◽  
Pde Model ◽  
Fundamental Equations ◽  
Detailed Derivation

Abstract The outbreak of COVID-19 in 2020 has led to a surge in interest in the research of the mathematical modeling of epidemics. Many of the introduced models are so-called compartmental models, in which the total quantities characterizing a certain system may be decomposed into two (or more) species that are distributed into two (or more) homogeneous units called compartments. We propose herein a formulation of compartmental models based on partial differential equations (PDEs) based on concepts familiar to continuum mechanics, interpreting such models in terms of fundamental equations of balance and compatibility, joined by a constitutive relation. We believe that such an interpretation may be useful to aid understanding and interdisciplinary collaboration. We then proceed to focus on a compartmental PDE model of COVID-19 within the newly-introduced framework, beginning with a detailed derivation and explanation. We then analyze the model mathematically, presenting several results concerning its stability and sensitivity to different parameters. We conclude with a series of numerical simulations to support our findings.

scholarly journals Mathematical Modeling of the Impact Produced by Magnetic Disks on Living Cells

2016 ◽  
Vol 9 (4) ◽  
pp. 432-442 ◽  
Author(s):  
Valery V. Denisenko ◽  
◽  
Vladimir M. Sadovskiiy ◽  
Keyword(s):  
Mathematical Modeling ◽  
Living Cells ◽  
Magnetic Disks ◽  
The Impact

scholarly journals Application Of More Complex Rheological Models In Continuum Mechanics

2015 ◽  
Vol 15 (2) ◽  
Author(s):  
Mária Minárová ◽  
Jozef Sumec
Keyword(s):  
Mathematical Modeling ◽  
Relaxation Process ◽  
Rheological Properties ◽  
Continuum Mechanics ◽  
Rheological Behavior ◽  
Constitutive Equations ◽  
Structural Materials ◽  
Rheological Models ◽  
Complex Models ◽  
Maxwell Models

Abstract The paper deals with mathematical modeling of the structural materials representing their rheological properties. The materials are modeled by more complex models (enhancement of Voigt and Maxwell models). The constitutive equations are derived; the relationships within the creep and relaxation process are developed. The rheological behavior of the materials is introduced.

scholarly journals Unstable Modes and Order Parameters of Bistable Signaling Pathways at Saddle-Node Bifurcations: A Theoretical Study Based on Synergetics

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Till D. Frank
Keyword(s):  
Mathematical Modeling ◽  
Signaling Pathways ◽  
Cell Fate ◽  
Theoretical Study ◽  
Living Cells ◽  
Order Parameters ◽  
Self Organization ◽  
Memory Functions ◽  
Bifurcation Points ◽  
Saddle Node

Mathematical modeling has become an indispensable part of systems biology which is a discipline that has become increasingly popular in recent years. In this context, our understanding of bistable signaling pathways in terms of mathematical modeling is of particular importance because such bistable components perform crucial functions in living cells. Bistable signaling pathways can act as switches or memory functions and can determine cell fate. In the present study, properties of mathematical models of bistable signaling pathways are examined from the perspective of synergetics, a theory of self-organization and pattern formation founded by Hermann Haken. At the heart of synergetics is the concept of so-called unstable modes or order parameters that determine the behavior of systems as a whole close to bifurcation points. How to determine these order parameters for bistable signaling pathways at saddle-node bifurcation points is shown. The procedure is outlined in general and an explicit example is worked out in detail.

Mathematical Modeling in Continuum Mechanics

2005 ◽  
Author(s):  
Roger Temam ◽  
Alain Miranville
Keyword(s):  
Mathematical Modeling ◽  
Continuum Mechanics
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