Related papers: Analytical solutions for precipitation size distri…
The problem of ballistically controlled annihilation is revisited for general initial velocity distributions and arbitrary dimension. An analytical derivation of the hierarchy equations obeyed by the reduced distributions is given, and a…
A model accounting for finite spatial dimensions of the deposit patterns in the evaporating sessile drops of colloidal solution on a plane substrate is proposed. The model is based on the assumption that the solute particles occupy finite…
Due to complex physical phenomena, the distribution of heavy rainfall events is difficult to model spatially. Physically based numerical models can often provide physically coherent spatial patterns, but may miss some important…
We study the long-time regime of the Kardar-Parisi-Zhang (KPZ) equation in $1+1$ dimensions for the Brownian and droplet initial conditions and present a simple derivation of the tail of the large deviations of the height on the negative…
A new class of integro-partial differential equation models is derived for the prediction of granular flow dynamics. These models are obtained using a novel limiting averaging method (inspired by techniques employed in the derivation of…
Clouds are important components of the atmosphere. Since it is usually not possible to treat them as ensembles of huge numbers of particles, parameterizations on the basis of averaged quantities (mass and/or number concentration) must be…
The aim of this paper is to discuss the appropriate modelling of in- and outflow boundary conditions for nonlinear drift-diffusion models for the transport of particles including size exclusion and their effect on the behaviour of…
Fractional calculus allows one to generalize the linear, one-dimensional, diffusion equation by replacing either the first time derivative or the second space derivative by a derivative of fractional order. The fundamental solutions of…
The methods for parameter estimation under assumption of agreement between observation and model are reviewed. The distribution parameters are obtained for one set of experimental data by using different estimation methods under assumption…
Stable distributions is an interesting and important class of probability distributions. They were discovered explicitly by Paul L\'{e}vy in 1925 \cite{lk}. They possess many interesting properties, most importantly they are by definiton…
We use probabilistic methods to study properties of mean-field models, arising as large-scale limits of certain particle systems with mean-field interaction. The underlying particle system is such that $n$ particles move forward on the real…
A general reaction-diffusion equation with spatiotemporal delay and homogeneous Dirichlet boundary condition is considered. The existence and stability of positive steady state solutions are proved via studying an equivalent…
We numerically study the finite-size droplet condensation-evaporation transition in two dimensions. We consider and compare two orthogonal approaches, namely at fixed temperature and at fixed density, making use of parallel multicanonical…
This Article presents a nonequilibrium thermodynamic theory for the mean-field precipitation, aggregation and pattern formation of colloidal clusters. A variable gradient energy coefficient and the arrest of particle diffusion upon…
The Langer-Schwartz equations for precipitation are formulated to calculate nucleation, growth and coarsening of second phase precipitates under non-isothermal situations. A field-theoretic steady-state nucleation rate model is used in the…
A new stochastic model for daily precipitation occurrence processes observed at multiple locations is developed. The modeling concept is to use the indicator function and the elliptical shape of multivariate Gaussian distribution to…
We provide a numerical algorithm for the model characterizing anomalous diffusion in expanding media, which is derived in [F. Le Vot, E. Abad, and S. B. Yuste, Phys. Rev. E {\bf96} (2017) 032117]. The Sobolev regularity for the equation is…
We study scaling properties of stochastic aggregation processes in one dimension. Numerical simulations for both diffusive and ballistic transport show that the mass distribution is characterized by two independent nontrivial exponents…
Two models of binary fragmentation are introduced in which a time dependent transition size produces two regions of fragment sizes above and below the transition size. In the models we consider a fixed rate of fragmentation for the largest…
We propose a method to derive the stationary size distributions of a system, and the degree distributions of networks, using maximisation of the Gibbs-Shannon entropy. We apply this to a preferential attachment-type algorithm for systems of…