Related papers: Global random walk solvers for fully coupled flow …
Discrete-time quantum walks (DTQWs) in random artificial electric and gravitational fields are studied analytically and numerically. The analytical computations are carried by a new method which allows a direct exact analytical…
The Richards equation, a nonlinear elliptic parabolic equation, is widely used to model infiltration in porous media. We develop a finite element method for solving the Richards equation by introducing a new bounded auxiliary variable to…
Increasing concerns on the security and quality of water distribution systems (WDS), call for computational tools with performance guarantees. To this end, this work revisits the physical laws governing water flow and provides a hierarchy…
Physical systems with complex unsteady dynamics, such as fluid flows, are often poorly represented by a single mean solution. For many practical applications, it is crucial to access the full distribution of possible states, from which…
Graph-limit theory focuses on the convergence of sequences of graphs when the number of nodes becomes arbitrarily large. This framework defines a continuous version of graphs allowing for the study of dynamical systems on very large graphs,…
In this paper, we introduce a mathematical model to describe the nanoparticles transport carried by a two-phase flow in a porous medium including gravity, capillary forces and Brownian diffusion. Nonlinear iterative IMPES scheme is used to…
Random walks describe diffusion processes, where movement at every time step is restricted to only the neighbouring locations. We construct a quantum random walk algorithm, based on discretisation of the Dirac evolution operator inspired by…
Random walks are studied on disordered cellular networks in 2-and 3-dimensional spaces with arbitrary curvature. The coefficients of the evolution equation are calculated in term of the structural properties of the cellular system. The…
In this paper, we propose a local-global multiscale method for highly heterogeneous stochastic groundwater flow problems under the framework of reduced basis method and the generalized multiscale finite element method (GMsFEM). Due to…
This paper is about the construction of displacement interpolations on a discrete metric graph. Our approach is based on the approximation of any optimal transport problem whose cost function is a distance on a discrete graph by a sequence…
We propose random walks on suitably defined graphs as a framework for finescale modeling of particle motion in an obstructed environment where the particle may have interactions with the obstructions and the mean path length of the particle…
Functional limit theorem for continuous-time random walks (CTRW) are found in general case of dependent waiting times and jump sizes that are also position dependent. The limiting anomalous diffusion is described in terms of fractional…
Continuous Time Random Walks (CTRW) are widely used to coarse-grain the evolution of systems jumping from a metastable sub-set of their configuration space, or trap, to another via rare intermittent events. The multi-scaled behavior typical…
In this paper, we develop a universal method that identifies the (non-local) governing evolution equations for Continuous Time Random Walks' (CTRWs) limit processes. Given one of these processes, our method provides the form of a non-local…
We introduce the quantum stochastic walk (QSW), which determines the evolution of generalized quantum mechanical walk on a graph that obeys a quantum stochastic equation of motion. Using an axiomatic approach, we specify the rules for all…
Random walk neural networks (RWNNs) have emerged as a promising approach for graph representation learning, leveraging recent advances in sequence models to process random walks. However, under realistic sampling constraints, RWNNs often…
Based on studies on four specific networks, we conjecture a general relation between the walk dimensions $d_{w}$ of discrete-time random walks and quantum walks with the (self-inverse) Grover coin. In each case, we find that $d_{w}$ of the…
This paper is concerned with numerical solution of transport problems in heterogeneous porous media. A semi-discrete continuous-in-time formulation of the linear advection-diffusion equation is obtained by using a mixed hybrid finite…
Distribution of loops in a one-dimensional random walk (RW), or, equivalently, neutral segments in a sequence of positive and negative charges is important for understanding the low energy states of randomly charged polymers. We investigate…
This work deals with the stationary analysis of two-dimensional partially homogeneous nearest-neighbour random walks. Such type of random walks are characterized by the fact that the one-step transition probabilities are functions of the…