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A new solution to the mono-dimensional diffusion equation for time-variable first kind boundary condition is presented where the time-variable function at the surface is derived proposing a surface saturation model. This solution may be…

Materials Science · Physics 2022-12-08 Guglielmo Macrelli

Stochastic dynamical systems often contain nonlinearities which make it hard to compute probability density functions or statistical moments of these systems. For the moment computations, nonlinearities in the dynamics lead to unclosed…

Optimization and Control · Mathematics 2017-03-28 Khem Raj Ghusinga , Mohammad Soltani , Andrew Lamperski , Sairaj Dhople , Abhyudai Singh

We introduce a class of partial differential equations on metric graphs associated with mixed evolution: on some edges we consider diffusion processes, on other ones transport phenomena. This yields a system of equations with possibly…

Analysis of PDEs · Mathematics 2021-03-29 Amru Hussein , Delio Mugnolo

Many features of physical systems, both qualitative and quantitative, become sharply defined or tractable only in some limiting situation. Examples are phase transitions in the thermodynamic limit, the emergence of classical mechanics from…

Mathematical Physics · Physics 2024-02-16 Lauritz van Luijk , Alexander Stottmeister , Reinhard F. Werner

We establish conditions for uniform $r$-th moment bound of certain $\R^d$-valued functions of a discrete-time stochastic process taking values in a general metric space. The conditions include an appropriate negative drift together with a…

Probability · Mathematics 2011-07-26 Arnab Ganguly , Debasish Chatterjee , John Lygeros , Heinz Koeppl

We give Hoeffding and Bernstein-type concentration inequalities for the largest eigenvalue of sums of random matrices arising from a Markov chain. We consider time-dependent matrix-valued functions on a general state space, generalizing…

Probability · Mathematics 2025-07-01 Joe Neeman , Bobby Shi , Rachel Ward

In the setting of abstract Markov maps, we prove results concerning the convergence of renormalized Birkhoff sums to normal laws or stable laws. They apply to one-dimensional maps with a neutral fixed point at 0 of the form…

Dynamical Systems · Mathematics 2007-05-23 Sebastien Gouezel

As model problem we consider the prototype for flow and transport of a concentration in porous media in an interior domain and couple it with a diffusion process in the corresponding unbounded exterior domain. To solve the problem we…

Numerical Analysis · Mathematics 2018-10-22 Christoph Erath , Günther Of , Francisco-Javier Sayas

Typically, aggregation-diffusion is modeled by parabolic equations that combine linear or nonlinear diffusion with a Fokker-Planck convection term. Under very general suitable assumptions, we prove that radial solutions of the evolution…

Analysis of PDEs · Mathematics 2021-12-15 Jose A. Carrillo , David Gómez-Castro , Juan Luis Vázquez

Solutions of the Dirichlet and Robin boundary value problems for the multi-term variable-distributed order diffusion equation are studied. A priori estimates for the corresponding differential and difference problems are obtained by using…

Numerical Analysis · Mathematics 2014-01-31 A. A. Alikhanov

We present an adaptation of Stein's method of normal approximation to the study of both discrete- and continuous-time dynamical systems. We obtain new correlation-decay conditions on dynamical systems for a multivariate central limit…

Probability · Mathematics 2017-01-12 Olli Hella , Juho Leppänen , Mikko Stenlund

This paper provides new summation inequalities in both single and double forms to be used in stability analysis of discrete-time systems with time-varying delays. The potential capability of the newly derived inequalities is demonstrated by…

Optimization and Control · Mathematics 2016-06-02 Le Van Hien , Hieu Trinh

We investigate the asymptotic properties of the large deviation function of the integrated particle current in systems, in or out of thermal equilibrium, whose dynamics exhibits anomalous diffusion. The physical systems covered by our study…

Statistical Mechanics · Physics 2011-11-29 Vivien Lecomte , Uwe C. Tauber , Frederic van Wijland

We evaluate the percolation threshold values for a realistic model of continuum segregated systems, where random spherical inclusions forbid the percolating objects, modellized by hard-core spherical particles surrounded by penetrable…

Disordered Systems and Neural Networks · Physics 2009-11-13 N. Johner , C. Grimaldi , T. Maeder , P. Ryser

In this paper, we consider the approximate controllability of partial differential equations with time derivatives of non-integer order via boundary control. We first show the unique existence of the solution under smooth boundary…

Optimization and Control · Mathematics 2015-01-07 Kenichi Fujishiro

In this paper, we prove a central limit theorem and estabilish a moderate deviation principle for stochastic models of incompressible second fluids. The weak convergence method inreoduced by [4] plays an important role.

Probability · Mathematics 2016-08-01 Jianliang Zhai , Tusheng Zhang , Wuting Zheng

We provide an explicit rigorous derivation of a diffusion limit - a stochastic differential equation with additive noise - from a deterministic skew-product flow. This flow is assumed to exhibit time-scale separation and has the form of a…

Dynamical Systems · Mathematics 2015-05-27 I. Melbourne , A. M. Stuart

The global existence and boundedness of solutions to volume-surface reaction diffusion systems with a mass control condition are investigated. Such systems arise typically in e.g. cell biology, ecology or fluid mechanics, when some…

Analysis of PDEs · Mathematics 2024-12-18 Juan Yang , Bao Quoc Tang

We propose a computational method to simulate anomalous self-diffusion in a simple liquid. The method is based on a molecular dynamics simulation on which we impose the following two conditions: firstly, the inter-particle interaction is…

Statistical Mechanics · Physics 2010-04-07 Simon Standaert , Jan Ryckebusch , Lesley De Cruz

We consider a system of random walks in a random environment interacting via exclusion. The model is reversible with respect to a family of disordered Bernoulli measures. Assuming some weak mixing conditions, it is shown that, under…

Probability · Mathematics 2007-05-23 Jeremy Quastel