Related papers: Nonuniform autonomous one-dimensional exclusion ne…
Mass-conserving reaction-diffusion systems with bistable nonlinearity are useful models for studying cell polarity formation, which is a key process in cell division and differentiation. We rigorously show the existence and stability of…
Theoretical advances in the study of non-equilibrium phenomena are briefly reviewed with emphasis on steady state properties of one-dimensional driven lattice gases. The presentation is focused on the totally asymmetric simple-exclusion…
Mathematical modeling is now used commonly in the analysis of signaling networks. With advances in high resolution microscopy, the spatial location of different signaling molecules and the spatio-temporal dynamics of signaling microdomains…
Extending the famous Model B for the time evolution of a liquid mixture, we derive an approximate expression for the mobility matrix that couples the different mixture components. This approach is based on a single component fluid with…
We study the adsorption and desorption kinetics of interacting particles moving on a one-dimensional lattice. Confinement is introduced by limiting the number of particles on a lattice site. Adsorption and desorption are found to proceed at…
We introduce a two-state non-conserving driven-diffusive system in one-dimension under a discrete-time updating scheme. We show that the steady-state of the system can be obtained using a matrix product approach. On the other hand, the…
We study the one-dimensional asymmetric simple exclusion process on the lattice $\{1, \dots,N\}$ with creation/annihilation at the boundaries. The boundary rates are time dependent and change on a slow time scale $N^{-a}$ with $a>0$. We…
Nonequilibrium statistical models of point vortex systems are constructed using an optimal closure method, and these models are employed to approximate the relaxation toward equilibrium of systems governed by the two-dimensional Euler…
Many biological processes are supported by special molecules, called motor proteins or molecular motors, that transport cellular cargoes along linear protein filaments and can reversibly associate to their tracks. Stimulated by these…
The Lagrange-mesh $R$-matrix method is generalized to inhomogeneous equations. This method is numerically stable and efficient. It can be directly used for transfer reactions with the formalism discussed by Ascuitto and Glendenning [Phys.…
A kinetic description of lattice-gas automaton models for reaction-diffusion systems is presented. It provides corrections to the mean-field rate equations in the diffusion-limited regime. When applied to the two-species Maginu model, the…
We study the spectral properties of a class of random matrices where the matrix elements depend exponentially on the distance between uniformly and randomly distributed points. This model arises naturally in various physical contexts, such…
A unification of characteristic mode decomposition for all method-of-moment formulations of field integral equations describing free-space scattering is derived. The work is based on an algebraic link between impedance and transition…
We introduce a symmetric, gradient exclusion process within the class of non-cooperative kinetically constrained lattice gases, modelling a non-linear diffusivity in which the exchange of occupation values between two neighbouring sites…
An asymptotic limit of a class of Cahn-Hilliard systems is investigated to obtain a general nonlinear diffusion equation. The target diffusion equation may reproduce a number of well-known model equations: Stefan problem, porous media…
We study the transient dynamics of single species reaction diffusion systems whose reaction terms $f(u)$ vary nonlinearly near $u\approx 0$, specifically as $f(u)\approx u^{2}$ and $f(u)\approx u^{3}$. We consider three cases, calculate…
We consider a general class of autocatalytic reactions, that has been shown to display stochastically switching behaviour (Discreteness Induced Transitions) in some parameter regimes. This behaviour was shown to occur when either the…
We present a new method to describe the kinetics of driven lattice gases with particle-particle interactions beyond hard-core exclusions. The method is based on the time-dependent density functional theory for lattice systems and allows one…
The limiting stability of invariant probability measures of time homogeneous transition semigroups for autonomous stochastic systems has been extensively discussed in the literature. In this paper we initially initiate a program to study…
Group classification of systems of two coupled nonlinear reaction-diffusion equation with a diagonal diffusion matrix is carried out. Symmetries of diffusion systems with singular diffusion matrix and additional first order derivative terms…