Search results for "Kinetic equation"
showing 10 items of 11 documents
Generalized transport coefficients in a gas with large shear rate
1987
We get a solution of the Bhatnagar-Gross-Krook (BGK) model kinetic equation by means of a perturbative expansion of a temperature gradient to study the transport properties in a gas with large shear rate. The irreversible fluxes are evaluated exactly to first order in the expansion for Maxwell molecules. The transport coefficients obtained are highly nonlinear functions of the shear rate. This dependence on shear rate is analysed and compared with previous results for several transport coefficients. Finally, we have found a solution for a simple model of constant collision frequency for which a large shear rate coexists with an arbitrary temperature gradient.
Unstable massive tau-neutrinos and primordial nucleosynthesis
1998
The impact of unstable Majorana tau neutrinos on primordial nucleosynthesis is considered. The mass and lifetime of nu_tau are taken in the intervals 0.1-20 MeV and 0.001-400 sec respectively. The studied decay modes are nu_tau -> nu_mu + phi and nu_tau -> nu_e + phi, where phi is a massless (or light) scalar. Integro-differential kinetic equations are solved numerically without any simplifying assumptions. Our results deviate rather strongly from earlier calculations. Depending on mass, lifetime, and decay channels of the nu_tau, the number of effective neutrino species (found from He4), in addition to the 3 standard ones, varies from -2 to +2.5. The abundances of H2 and Li7 are also…
Invariant density and time asymptotics for collisionless kinetic equations with partly diffuse boundary operators
2018
This paper deals with collisionless transport equationsin bounded open domains $\Omega \subset \R^{d}$ $(d\geq 2)$ with $\mathcal{C}^{1}$ boundary $\partial \Omega $, orthogonallyinvariant velocity measure $\bm{m}(\d v)$ with support $V\subset \R^{d}$ and stochastic partly diffuse boundary operators $\mathsf{H}$ relating the outgoing andincoming fluxes. Under very general conditions, such equations are governedby stochastic $C_{0}$-semigroups $\left( U_{\mathsf{H}}(t)\right) _{t\geq 0}$ on $%L^{1}(\Omega \times V,\d x \otimes \bm{m}(\d v)).$ We give a general criterion of irreducibility of $%\left( U_{\mathsf{H}}(t)\right) _{t\geq 0}$ and we show that, under very natural assumptions, if an …
The interplay between genetic and bioelectrical signaling permits a spatial regionalisation of membrane potentials in model multicellular ensembles
2016
AbstractThe single cell-centred approach emphasises ion channels as specific proteins that determine individual properties, disregarding their contribution to multicellular outcomes. We simulate the interplay between genetic and bioelectrical signals in non-excitable cells from the local single-cell level to the long range multicellular ensemble. The single-cell genetic regulation is based on mean-field kinetic equations involving the mRNA and protein concentrations. The transcription rate factor is assumed to depend on the absolute value of the cell potential, which is dictated by the voltage-gated cell ion channels and the intercellular gap junctions. The interplay between genetic and ele…
A supramolecular system that strictly follows the binding mechanism of conformational selection
2020
Induced fit and conformational selection are two dominant binding mechanisms in biology. Although induced fit has been widely accepted by supramolecular chemists, conformational selection is rarely studied with synthetic systems. In the present research, we report a macrocyclic host whose binding mechanism is unambiguously assigned to conformational selection. The kinetic and thermodynamic aspects of this system are studied in great detail. It reveals that the kinetic equation commonly used for conformational selection is strictly followed here. In addition, two mathematical models are developed to determine the association constants of the same guest to the two host conformations. A “confo…
Catastrophic process of coherence degradation
2018
We predict a catastrophic process of coherence degradation characterized by a virtually unlimited spectral broadening of the waves. This effect is described by self-similar solutions of the kinetic equations inherent to the wave turbulence theory.
Particle models for kinetic equations: an introduction and some rigorous results
2011
We shall give an introduction to the validity problem for kinetic equations and we shall review some convergence theorems concerning the derivation from a microscopic dynamics of systems of partial differential equations describing, at the mesoscopic scale, collections of particles interacting through various (collisions and mean field) type of interaction.
Testing of a kinetics equation of mechanical degradation
1987
A modification of the kinetics equation of mechanical degradation of Harrington and Zimm is proposed to fit experimental data taken on a molten polystyrene. This equation is applied to each molecular weight of the discretized molecular weight distribution curve, and the limiting molecular weight is determined for each molecular weight. With this modification the theoretical curves fit both Mw and Mn curves well.
Relativistic transport equations with generalized mass shell constraints
1999
We reexamine the derivation of relativistic transport equations for fermions when conserving the most general spinor structure of the interaction and Green function. Such an extension of the formalism is needed when dealing with {\it e.g.} spin-polarized nuclear matter or non-parity conserving interactions. It is shown that some earlier derivations can lead to an incomplete description of the evolution of the system even in the case of parity-conserving, spin-saturated systems. The concepts of kinetic equation and mass shell condition have to be extended, in particular both of them acquire a non trivial spinor structure which describe a rich polarization dynamics.
Theory of non-equilibrium critical phenomena in three-dimensional condensed systems of charged mobile nanoparticles.
2014
A study of 3d electrostatic self-assembly (SA) in systems of charged nanoparticles (NPs) is one of the most difficult theoretical problems. In particular, the limiting case of negligible or very low polar media (e.g. salt) concentration, where the long-range NP interactions cannot be reduced to commonly used effective short-range (Yukawa) potentials, remains unstudied. Moreover, the present study has demonstrated that unlike the Debye–Huckel theory, a complete screening of the charges in SA kinetics (dynamic SA) is not always possible. Generally speaking, one has to take into account implicitly how each NP interacts with all other NPs (the true long-range interactions). Traditional theoreti…