FROM THE MATHEMATICAL KINETIC THEORY TO MODELLING COMPLEX SYSTEMS IN APPLIED SCIENCES

2004 ◽  
Vol 18 (04n05) ◽  
pp. 487-500 ◽  
Author(s):  
NICOLA BELLOMO
Keyword(s):  
Applied Sciences ◽  
Kinetic Theory ◽  
Statistical Mechanics ◽  
Complex Systems ◽  
Nonequilibrium Statistical Mechanics ◽  
Classical Mechanics ◽  
Large Complex ◽  
Large Systems

This paper deals with the design of a nonequilibrium statistical mechanics theory developed to model large systems of interacting individuals. Interactions being ruled, not only by laws of classical mechanics, but also by some intelligent or organized behaviour. The paper technically shows, also by reasoning on specific examples, how the theory can be applied to model large complex systems in natural and applied sciences.

HYBRID TWO SCALES MATHEMATICAL TOOLS FOR ACTIVE PARTICLES MODELLING COMPLEX SYSTEMS WITH LEARNING HIDING DYNAMICS

2007 ◽  
Vol 17 (02) ◽  
pp. 171-187 ◽  
Author(s):  
C. CATTANI ◽  
A. CIANCIO
Keyword(s):  
Applied Sciences ◽  
Kinetic Theory ◽  
Differential Equations ◽  
Complex Systems ◽  
Ordinary Differential Equations ◽  
Preliminary Analysis ◽  
Mathematical Structures ◽  
Active Particles ◽  
Model Complex ◽  
Large Systems

This paper deals with the derivation of hybrid mathematical structures to describe the behavior of large systems of active particles by ordinary differential equations with stochastic coefficients whose evolution is modelled by equations of the mathematical kinetic theory. A preliminary analysis shows how the above tools can be used to model complex systems of interest in applied sciences, with special attention to the immune competition.

LOOKING FOR NEW PARADIGMS TOWARDS A BIOLOGICAL-MATHEMATICAL THEORY OF COMPLEX MULTICELLULAR SYSTEMS

2006 ◽  
Vol 16 (07) ◽  
pp. 1001-1029 ◽  
Author(s):  
NICOLA BELLOMO ◽  
GUIDO FORNI
Keyword(s):  
Kinetic Theory ◽  
Complex Systems ◽  
Critical Analysis ◽  
Mathematical Theory ◽  
Classical Mechanics ◽  
Biological Functions ◽  
Living Matter ◽  
Research Perspectives ◽  
Active Particles ◽  
Large Systems

This paper deals with the development of new paradigms based on the methods of the mathematical kinetic theory for active particles to model the dynamics of large systems of interacting cells. Interactions are ruled, not only by laws of classical mechanics, but also by a few biological functions which are able to modify the above laws. The paper technically shows, also by reasoning on specific examples, how the theory can be applied to model large complex systems in biology. The last part of the paper deals with a critical analysis and with the indication of research perspectives concerning the challenging target of developing a biological-mathematical theory for the living matter.

scholarly journals Necessary and Sufficient Condition for Stability of Generalized Expectation Value

2011 ◽  
Vol 2011 ◽  
pp. 1-7 ◽  
Author(s):  
Aziz El Kaabouchi ◽  
Sumiyoshi Abe
Keyword(s):  
Probability Distribution ◽  
Statistical Mechanics ◽  
Complex Systems ◽  
Nonequilibrium Statistical Mechanics ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Expectation Value ◽  
Necessary And Sufficient ◽  
Small Deformations ◽  
Generalized Expectation

A class of generalized definitions of expectation value is often employed in nonequilibrium statistical mechanics for complex systems. Here, the necessary and sufficient condition is presented for such a class to be stable under small deformations of a given arbitrary probability distribution.

ON THE MATHEMATICAL THEORY OF THE DYNAMICS OF SWARMS VIEWED AS COMPLEX SYSTEMS

2012 ◽  
Vol 22 (supp01) ◽  
pp. 1140006 ◽  
Author(s):  
N. BELLOMO ◽  
J. SOLER
Keyword(s):  
Complex System ◽  
Kinetic Theory ◽  
Statistical Mechanics ◽  
Complex Systems ◽  
Modeling And Simulation ◽  
Mathematical Theory ◽  
Stochastic Games ◽  
Microscopic Scale

This paper deals with the modeling and simulation of swarms viewed as a living, hence complex, system. The approach is based on methods of kinetic theory and statistical mechanics, where interactions at the microscopic scale are nonlinearly additive and modeled by stochastic games.

MATHEMATICAL METHODS AND TOOLS OF KINETIC THEORY TOWARDS MODELLING COMPLEX BIOLOGICAL SYSTEMS

2005 ◽  
Vol 15 (11) ◽  
pp. 1639-1666 ◽  
Author(s):  
ABDELGHANI BELLOUQUID ◽  
MARCELLO DELITALA
Keyword(s):  
Kinetic Theory ◽  
Evolution Equations ◽  
Classical Mechanics ◽  
Mathematical Framework ◽  
Mathematical Approach ◽  
Biological Functions ◽  
Mathematical Methods ◽  
Research Perspectives ◽  
Large Systems ◽  
The One

This paper develops a variety of mathematical tools to model the dynamics of large systems of interacting cells. Interactions are ruled not only by laws of classical mechanics, but also by some biological functions. The mathematical approach is the one of kinetic theory and non-equilibrium statistical mechanics. The paper deals both with the derivation of evolution equations and with the design of specific models consistent with the above-mentioned mathematical framework. Various hints for research perspectives are proposed in the last part of the paper.

scholarly journals Nonlinearity-generated resilience in large complex systems

2021 ◽  
Vol 103 (2) ◽  
Author(s):  
S. Belga Fedeli ◽  
Y. V. Fyodorov ◽  
J. R. Ipsen
Keyword(s):  
Complex Systems ◽  
Large Complex
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