To the top

Page Manager: Webmaster
Last update: 9/11/2012 3:13 PM

Tell a friend about this page
Print version

Modelling living fluids w… - University of Gothenburg, Sweden Till startsida
Sitemap
To content Read more about how we use cookies on gu.se

Modelling living fluids with the subdivision into the components in terms of probability distributions

Journal article
Authors Magnus Willander
Eugen Mamontov
Zackary Chiragwandi
Published in Math. Models Methods Appl. Sci.
Volume 14
Issue 10
Pages 1495-1520
ISSN 0218-2025
Publication year 2004
Published at Department of Physics (GU)
Pages 1495-1520
Language en
Links dx.doi.org/10.1142/S021820250400370...
Keywords multicomponent fluid of living cells and related macromolecules, generalized kinetic theory, stochastic differential equation, probability distribution of parameters of the fluid particles, mode of probability distribution and multimodal distributions
Subject categories Mathematical Analysis, Applied mathematics, Mathematical physics, Statistical physics, Non-linear dynamics, chaos, Cell and molecular biology, Microbiology, Bioinformatics and Systems Biology

Abstract

As it follows from the results of C. H. Waddigton, F. E. Yates, A. S. Iberall, and other well-known bio-physicists, living fluids cannot be modelled within the frames of the fundamental assumptions of the statistical-mechanics formalism. One has to go beyond them. The present work does it by means of the generalized kinetics (GK), the theory enabling one to allow for the complex stochasticity of internal properties and parameters of the fluid particles. This is one of the key features which distinguish living fluids from the nonliving ones. It creates the disparity of the particles and hence breaks the each-fluid-component-uniformity requirement underlying statistical mechanics. The work deals with the corresponding modification of common kinetic equations which is in line with the GK theory and is the complement to the latter. This complement allows a subdivision of a fluid into the fluid components in terms of nondiscrete probability distributions. The treatment leads to one more equationthat describes the above internal parameters. The resulting model is the system of these two equations. It appears to be always nonlinear in case of living fluids. In case of nonliving fluids, the model can be linear. Moreover, the living-fluid model, as a whole, cannot have the thermodynamic equilibrium, only partial equilibriums (such as the motional one) are possible. In contrast to this, in case of nonliving fluids, the thermodynamic equilibrium is, of course, possible. The number of the fluid components is treated as the number of the modes of the particle-characteristic probability density. In so doing, a fairly general extension of the notion of the mode from the one-dimensional case to the multidimensional case is proposed. The work also discusses the variety of the time-scales in a living fluid, the simplest quantum-mechanical equation relevant to living fluids, and the non-equilibrium nonlinear stochastic hydrodynamics option. The latter is simpler than, but conceptually comparable to, stochastickinetic equations. A few directions for future research are suggested. The work notes a cohesion of mathematical physics and fluid mechanics with the living-fluid-related fields as a complex interdisciplinary problem.

Page Manager: Webmaster|Last update: 9/11/2012
Share:

The University of Gothenburg uses cookies to provide you with the best possible user experience. By continuing on this website, you approve of our use of cookies.  What are cookies?