Related papers: Smoothness of the diffusion coefficients for parti…
We consider random walks on quasi one dimensional lattices, as introduced in \cite{FS}. This mathematical setting covers a large class of discrete kinetic models for non-cooperative molecular motors on periodic tracks. We derive general…
We prove the existence of solutions of a cross-diffusion parabolic population problem. The system of partial differential equations is deduced as the limit equations satisfied by the densities corresponding to an interacting particles…
In the paper the flow in a thin tubular structure is considered. The velocity of the flow stands for a coefficient in the diffusion-convection equation set in the thin structure. An asymptotic expansion of solution is constructed. This…
We introduce a model of self-propelled particles carrying out a Brownian motion with a diffusion coefficient which depends on the local density of particles within a certain finite radius. Numerical simulations show that in a range of…
A particle with internal unobserved states diffusing in a force field will generally display effective advection-diffusion. The drift velocity is proportional to the mobility averaged over the internal states, or effective mobility, while…
In some estimation problems, especially in applications dealing with information theory, signal processing and biology, theory provides us with additional information allowing us to restrict the parameter space to a finite number of points.…
An exact discretization method is being developed for solving linear systems of ordinary fractional-derivative differential equations with constant matrix coefficients (LSOFDDECMC). It is shown that the obtained linear discrete system in…
Asymptotic representations for large values of the hyperradius are constructed for the scattering wave function of a system of $ N $ particles considered as a generalized function of angular variable coordinates. The coefficients of the…
In this paper, uniformly unconditionally stable first and second order finite difference schemes are developed for kinetic transport equations in the diffusive scaling. We first derive an approximate evolution equation for the macroscopic…
In this paper, we prove some a priori estimates for a system of partial differential equations arising in the nonstationary flow of a nonhomogeneous incompressible asymmetric fluid in a bounded domain with smooth boundary. The unknowns of…
We study a second order scheme for spatial fractional differential equations with variable coefficients. Previous results mainly concentrate on equations with diffusion coefficients that are proportional to each other. In this paper, by…
Systems are studied in which transport is possible due to large extension with open boundaries in certain directions but the particles responsible for transport can disappear from it by leaving it in other directions, by chemical reaction…
We obtain the hydrodynamic limit of one-dimensional interacting particle systems describing the macroscopic evolution of the density of mass in infinite volume from the microscopic dynamics. The processes are weak pertubations of the…
Self-similar, spherically symmetric cosmological models with a perfect fluid and a scalar field with an exponential potential are investigated. New variables are defined which lead to a compact state space, and dynamical systems methods are…
A mathematical smooth function means that the function has continuous derivatives to a certain degree C(k). We call it a k-smooth function or a smooth function if k can grow infinitively. Based on quantum physics, there is no such smooth…
We propose a class of nonlocal diffusion systems on time-varying domains, and fully characterize their asymptotic dynamics in the asymptotically fixed, time-periodic and unbounded cases. The kernel is not necessarily symmetric or compactly…
Propulsion of otherwise passive objects is achieved by mechanisms of active driving. We concentrate on cases in which the direction of active drive is subject to spontaneous symmetry breaking. In our case, this direction will be maintained,…
The diffusion coefficient of a circular shaped inclusion in a liquid membrane is investigated by taking into account the interaction between membranes and bulk solvents of arbitrary thickness. As illustrative examples, the diffusion…
We propose a simple deterministic dynamic equation and reveal the mechanism of large-scale endless evolvement of spatial density inhomogeneity in active nematic. We determine the phase regions analytically. The interplay of density,…
Nonlinear waves are a robust phenomenon observed in complex systems ranging from mechanics to ecology. Fronts are fundamental due to their robustness against perturbations and capacity to propagate one state over another. Controlling and…