Related papers: Kinetic equation for spatially averaged molecular …
We propose a mathematical kinetic framework to investigate interactions between tumor cells and the immune system, focusing on the spatial dynamics of tumor progression and immune responses. We develop two kinetic models: one describes a…
Kinetic equations for the stationary state distribution function of ions moving through narrow pores are solved for a number of one-dimensional models of single ion transport. Ions move through pores of length $L$, under the action of a…
Recently, a new connection between density functional theory and kinetic theory has been proposed. In particular, it was shown that the Kohn-Sham (KS) equations can be reformulated as a macroscopic limit of the steady-state solution of a…
This paper aims to improve existing results about using averaging method for analysis of dynamic systems on time scales. We obtain a more accurate estimate for proximity between solutions of original and averaged systems regarding…
In many environmental applications involving spatially-referenced data, limitations on the number and locations of observations motivate the need for practical and efficient models for spatial interpolation, or kriging. A key component of…
We propose a novel measure valued process which models the behaviour of chemical reaction networks in spatially heterogeneous systems. It models reaction dynamics between different molecular species and continuous movement of molecules in…
A new idea for the quantization of dynamic systems, as well as space time itself, using a stochastic metric is proposed. The quantum mechanics of a mass point is constructed on a space time manifold using a stochastic metric. A stochastic…
A kinetic equation is derived for the phase density of a system of point particles, generating a system of integro-differential equations for distribution functions that have a deterministic meaning. The derivation took into account the…
We obtain exact analytic expressions for a class of functions expressed as integrals over the Haar measure of the unitary group in d dimensions. Based on these general mathematical results, we investigate generic dynamical properties of…
The kinetic spherical model with long-range interactions is studied after a quench to $T < T_c$ or to $T = T_c$. For the two-time response and correlation functions of the order-parameter as well as for composite fields such as the energy…
Difference Kinetic Equations are derived quantum mechanically in a plane wavelets representation with account of two-particle correlations. It is shown that the set of plane wavelet orthonormal functions is complete. The set of ket vectors…
In this paper we introduce and discuss kinetic equations for the evolution of the probability distribution of the number of particles in a population subject to binary interactions. The microscopic binary law of interaction is assumed to be…
In this paper, a new efficient and generalized consistency correction method for weakly-compressible smoothed particle hydrodynamics is proposed and successfully implemented in the simulation of violent free-surface flow exhibiting breaking…
This paper concerns space-sphere point processes, that is, point processes on the product space of $\mathbb R^d$ (the $d$-dimensional Euclidean space) and $\mathbb S^k$ (the $k$-dimen\-sional sphere). We consider specific classes of models…
We extend ring-polymer molecular dynamics (RPMD) to allow for the direct simulation of general, electronically non-adiabatic chemical processes. The kinetically constrained (KC) RPMD method uses the imaginary-time path-integral…
We derive a new constructive procedure to rapidly generate ensembles of phase-covariant dynamical maps that may be associated to the individual spins of a closed quantum system. We do this by first computing the single-spin dynamical maps…
We study the dynamics of synthetic molecules whose architectures are generated by space transformations from a point group acting on seed resonators. We show that the dynamical matrix of any such molecule can be reproduced as the left…
Kinetically constrained models (KCM) generically have trivial thermodynamics and yet manifest rich glassy dynamics. In order to resolve the thermodynamics-dynamics disconnect in KCMs, we derive a KCM by coarse-graining a non-trivial…
We introduce a simple and straight-forward averaging procedure, which is a generalization of one which is commonly used in electrodynamics, and show that it possesses all the characteristics we require for linearized averaging in general…
The kinetics of the deposition of colloidal particles onto a solid surface is analytically studied. We take into account both the diffusion of particles from the bulk as well as the geometrical aspects of the layer of adsorbed particles. We…