Related papers: Global random walk solvers for fully coupled flow …
Transport phenomena in porous media are commonplace in our daily lives. Examples and applications include heat and moisture transport in soils, baking and drying of food stuffs, curing of cement, and evaporation of fuels in wild fires. Of…
Open quantum random walks (OQRWs) deal with quantum random motions on the line for systems with internal and orbital degrees of freedom. The internal system behaves as a quantum random gyroscope coding for the direction of the orbital…
A functional approach for the study of the random walks in random sceneries (RWRS) is proposed. Under fairly general assumptions on the random walk and on the random scenery, functional limit theorems are proved. The method allows to study…
In this paper, we study the fundamental problem of random walk for network embedding. We propose to use non-Markovian random walk, variants of vertex-reinforced random walk (VRRW), to fully use the history of a random walk path. To solve…
The path integral for Darcy's law with a stochastic conductivity, which characterizes flow through random porous media, is used as a basis for Wilson renormalization-group (RG) calculations in momentum space. A coarse graining procedure is…
Traffic fluctuation has so far been studied on unweighted networks. However many real traffic systems are better represented as weighted networks, where nodes and links are assigned a weight value representing their physical properties such…
Many important transport phenomena are described by simple mathematical models rooted in the diffusion equation. Geometrical constraints present in such phenomena often have influence of a universal sort and manifest themselves in scaling…
Random walk in random environment (RWRE) is a fundamental model of statistical mechanics, describing the movement of a particle in a highly disordered and inhomogeneous medium as a random walk with random jump probabilities. It has been…
The solution of potential-driven steady-state flow in large networks is required in various engineering applications, such as transport of natural gas or water through pipeline networks. The resultant system of nonlinear equations depends…
Initially developed in the framework of quantum stochastic calculus, the main equations of quantum stochastic filtering were later on derived as the limits of Markov models of discrete measurements under appropriate scaling. In many…
We design strategies in nonlinear geometric analysis to temper the effects of adversarial learning for sufficiently smooth data of numerical method-type dynamics in encoder-decoder methods, variational and deterministic, through the use of…
In this study, we investigate the complexity of two-phase flow (air/water) in a heterogeneous soil sample by using complex network theory, where the supposed porous media is non-deformable media, under the time-dependent gas pressure. Based…
In recent years, graph neural networks (GNNs) have gained increasing popularity and have shown very promising results for data that are represented by graphs. The majority of GNN architectures are designed based on developing new…
Branching processes are used to model diverse social and physical scenarios, from extinction of family names to nuclear fission. However, for a better description of natural phenomena, such as viral epidemics in cellular tissues, animal…
In probability density function (PDF) methods a transport equation is solved numerically to compute the time and space dependent probability distribution of several flow variables in a turbulent flow. The joint PDF of the velocity…
Random walks (RW) of particles adsorbed in the internal walls of porous deposits produced by ballistic-type growth models are studied. The particles start at the external surface of the deposits and enter their pores, in order to simulate…
The Maximal Entropy Random Walk (MERW) is a natural process on a finite graph, introduced a few years ago with motivations from theoretical physics. The construction of this process relies on Perron-Frobenius theory for adjacency matrices.…
Under steady flow conditions, the topological complexity inherent to all random 3D porous media imparts complicated flow and transport dynamics. It has been established that this complexity generates persistent chaotic advection via a…
In this work, a flexible higher-order space-time adaptive finite element approximation of convection-dominated transport with coupled fluid flow is developed and studied. Convection-dominated transport is a challenging subproblem in…
This paper presents a new simulation-based approach to address the stochastic Dynamic Traffic Assignment (DTA) problem, focusing on large congested networks and dynamic settings. The proposed methodology incorporates a random walk model…