Related papers: The continuous version of the generalized exchange…
We study the existence of a solution for a one-dimensional generalized backward stochastic differential equation with two reflecting barriers (GRBSDE for short) under assumptions on the input data which are weaker than that on the current…
A Markov evolution of a system of point particles in $\mathbb{R}^d$ is described at micro-and mesoscopic levels. The particles reproduce themselves at distant points (dispersal) and die, independently and under the influence of each other…
A generalization of the ABC model, a one-dimensional model of a driven system of three particle species with local dynamics, is introduced, in which the model evolves under either (i) density-conserving or (ii) nonconserving dynamics. For…
We present several models to describe the stochastic evolution of stocks that show some strong resistance at some level and generalize to this situation the evolution based upon geometric Brownian motion. If volatility and drift are related…
Fluctuations of cell state, e.g., abundances of some proteins, have attracted much attention both theoretically and experimentally. The distribution of such state over cells, however, is not only a result of intracellular stochastic…
We consider a diffusion process on an evolving surface with a piecewise Lipschitz-continuous boundary from an energetic point of view. We employ an energetic variational approach with both surface divergence and transport theorems to derive…
In the context of an exactly soluble out of equilibrium (quenched) model, we study an extension of the fluctuation-dissipation relation. This involves a modified differential form of this relation, with an effective temperature which may…
We propose a new approach to models of general compressible viscous fluids based on the concept of dissipative solutions. These are weak solutions satisfying the underlying equations modulo a defect measure. A dissipative solution coincides…
In this work, we propose a theory for the kinetics of emulsions in which a continuous supply of matter feeds droplet growth. We consider cases where growth is either limited by bulk diffusion or the transport through the droplets'…
A generalized master equation (GME) governing quantum evolution of modular exciton density (MED) is derived for large scale light harvesting systems composed of weakly interacting modules of multiple chromophores. The GME-MED offers a…
In this manuscript, we study a nonlinear model of tumor growth, described by a coupled hyperbolic-elliptic system of partial differential equations. In this model, the compressible flow of tumor cells is modeled by a transport equation for…
Diffusion models have emerged as powerful generative tools with applications in computer vision and scientific machine learning (SciML), where they have been used to solve large-scale probabilistic inverse problems. Traditionally, these…
One-dimensional non-equilibrium models of particles subjected to a coagulation-diffusion process are important in understanding non-equilibrium dynamics, and fluctuation-dissipation relation. We consider in this paper transport properties…
We present a class of tractable non-equilibrium dynamical quantum systems which includes combinations of injection, detection and extraction of particles interspersed by unitary evolution. We show how such operations generate a hierarchy of…
In particle systems, flocking refers to the phenomenon where particles' individual velocities eventually align. The Cucker-Smale model is a well-known mathematical framework that describes this behavior. Many continuous descriptions of the…
Continual learning models for stationary data focus on learning and retaining concepts coming to them in a sequential manner. In the most generic class-incremental environment, we have to be ready to deal with classes coming one by one,…
By considering the master equation of asymmetric exclusion process on a one-dimensional lattice, we obtain the most general boundary condition of the multi-species exclusion processes in which the number of particles is constant in time.…
While inflation gives an appealing explanation of observed cosmological data, there are a wide range of different inflation models, providing differing predictions for the initial perturbations. Typically models are motivated either by…
We formulate dynamical rate equations for physical processes driven by a combination of diffusive growth, size fragmentation and fragment coagulation. Initially, we consider processes where coagulation is absent. In this case we solve the…
Using the analogy with inelastic granular gasses we introduce a model for wealth exchange in society. The dynamics is governed by a kinetic equation, which allows for self-similar solutions. The scaling function has a power-law tail, the…