Related papers: Coarsening dynamics in one dimension: The phase di…
We consider the dynamics of diffusing particles in one space dimension with annihilation on collision and nucleation (creation of particles) with constant probability per unit time and length. The cases of nucleation of single particles and…
The motivation of this work is to produce an integrated formulation for material response due to detonation wave loading. Here, we focus on elastoplastic structural response. In particular, we are interested to capture miscible and…
We present a systematic analysis of diffusion-controlled evolution and collapse of two identical spatially separated $d$-dimensional $A$-particle islands in the $B$-particle sea at propagation of the sharp reaction front $A+B\to 0$ at equal…
We compute the diffusion coefficient and the Lyapunov exponent for a diffusive intermittent map by means of cycle expansion of dynamical zeta functions. The asymptotic power law decay of the coefficients of the relevant power series are…
The swelling dynamics of polymer gels are characterized by the (collective) diffusion coefficient $D$ of the polymer network. Here, we measure the temperature dependence of $D$ of polymer gels with controlled homogeneous network structures…
The paper addresses the single-file diffusion in the presence of an absorbing boundary. The emphasis is on an interplay between the hard-core interparticle interaction and the absorption process. The resulting dynamics exhibits several…
We performed a thorough investigation of the drying dynamics of a charged colloidal dispersion drop in a confined geometry. We developed an original methodology based on Raman micro-spectroscopy to measure spatially-resolved colloids…
This paper considers the Dirichlet problem $$ -\mathrm{div}(a\nabla u_a)=f \quad \hbox{on}\,\,\ D, \qquad u_a=0\quad \hbox{on}\,\,\partial D, $$ for a Lipschitz domain $D\subset \mathbb R^d$, where $a$ is a scalar diffusion function. For a…
The paper considers parabolic equations in non-divergent form with discontinuous coefficients at higher derivatives. Their investigation is most complicated because, in general, in the case of discontinuous coefficients, the uniqueness of a…
We introduce a new measure of coarseness for characterizing phase separation processes such as those described by Cahn--Hilliard equations. An advantage of our measure is that it remains consistent throughout the evolution, including for…
The coarsening process in a class of driven systems is studied. These systems have previously been shown to exhibit phase separation and slow coarsening in one dimension. We consider generalizations of this class of models to higher…
We derive diffusive macroscopic equations for the particle and energy density of a system whose time evolution is described by a kinetic equation for the one particle position and velocity function f(r,v,t) that consists of a part that…
A scheme is developed for estimating state-dependent drift and diffusion coefficients in a stochastic differential equation from time-series data. The scheme does not require to specify parametric forms for the drift and diffusion…
The coarsening exponents describing the growth of long-range order in systems quenched from a disordered to an ordered phase are discussed in terms of the decay rate, omega(k), for the relaxation of a distortion of wavevector k applied to a…
Identification of nonlinear dynamical systems is crucial across various fields, facilitating tasks such as control, prediction, optimization, and fault detection. Many applications require methods capable of handling complex systems while…
A novel D-model of wave turbulence is presented which allows to reproduce in a single frame various nonlinear wave phenomena such as intermittency, formation and direction of energy cascades, possible growth of nonlinearity due to direct…
We consider nonlinear partial differential equations (PDEs) for advection-diffusion processes which are augmented by an auxiliary parameter $\delta$ such that $\delta=0$ corresponds to linear advection-diffusion. We derive potentially…
The variance of the local density of the pair contact process with diffusion (PCPD) is investigated in a bosonic description. At the critical point of the absorbing phase transition (where the average particle number remains constant) it is…
For the first time the phenomenon of cellular structure coarsening are consistently analysed from the positions of kinetic, hydrodynamic and stochastodynamic theories of nonequilibrium statistical systems. Thereby micro-, meso- and…
In this paper, we propose a dynamically low-dimensional approximation method to solve a class of time-dependent multiscale stochastic diffusion equations. A dynamically bi-orthogonal (DyBO) method was developed to explore low-dimensional…