1,720,983 research outputs found
On the onset of non-linearity for diffusion models of binary mixtures of biological materials by asymptotic analysis
No full textOn the mathematical kinetic theory of active particles with discrete states. The derivation of macroscopic equations
No full textMathematical methods and tools of kinetic theory towards modelling complex biological systems
No full textThis 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
On the derivation of macroscopic hyberbolic equations for binary multicellular growing mixtures
No full textAbstractThis paper presents an asymptotic theory, based on the hyperbolic scaling, for a large class of Boltzmann-type equations suitable to model the evolution of a binary mixture of multicellular systems in biology. The modelling approach is that of the kinetic theory for active particles. Time scaling related to cell movement and biological activity are shown to play a crucial role in determining the macroscopic equations corresponding to each case. Applications are focused on the immune competition
From the mathematical kinetic theory for active particles on the derivation of hyperbolic macroscopic tissue models
No full textFrom a class of kinetic models to the macroscopic equations for multicellular systems in biology,
No full textThe modelling of the immune competition by generalized kinetic (Boltzmann) models; review and research perspectives
No full text
Asymptotic limits of a discrete kinetic theory model of vehicular traffic
No full textAbstractThe paper proposes a rigorous method to construct the hyperbolic asymptotic limit of the discrete Kinetic Theory model of vehicular traffic proposed in [8]. A second-order macroscopic model of the Payne–Whitham type is derived and the coefficients of the equations are obtained from the detailed description of the microscopic interactions developed in the kinetic model
Mathematical topics on the modelling complex multicellular systems and tumor immune cells competition
No full textThis paper deals with a critical analysis and some developments related to the mathema-
tical literature on multiscale modelling of multicellular systems involving tumor immune
cells competition at the cellular level. The analysis is focused on the development of
mathematical methods of the classical kinetic theory to model the above physical sys-
tem and to recover macroscopic equation from the microscopic description. Various hints
are given toward research perspectives, with special attention on the modelling of the
interplay of microscopic (at the cellular level) biological and mechanical variables on the
overall evolution of the system. Indeed the nal aim of this paper consists of organizing
the various contributions available in the literature into a mathematical framework
suitable to generate a mathematical theory for complex biological systems
- …
