Related papers: A Modified Walk-on-sphere Method for High Dimensio…
A method is given to obtain the Green's function for the Poisson equation in any arbitrary integer dimension under periodic boundary conditions. We obtain recursion relations which relate the solution in d-dimensional space to that in…
We present a new technique to apply finite element methods to partial differential equations over curved domains. A change of variables along a coordinate transformation satisfying only low regularity assumptions can translate a Poisson…
Random walks on five-dimensional potential-energy surfaces were recently found to yield fission-fragment mass distributions that are in remarkable agreement with experimental data. Within the framework of the Smoluchowski equation of…
We use the method of images to present a worldsheet derivation of the sphere partition function for the dilaton in half-space to leading order in $\apr$ with Neumann boundary conditions. We use Tseytlin's sphere prescription to obtain the…
The Fourier-Bessel expansion of a function on a circular disc yields a simple series representation for the end-to-end probability distribution function w(R,phi) encountered in a planar persistent random walk, where the direction taken in a…
Fractional diffusion equations replace the integer-order derivatives in space and time by their fractional-order analogues. They are used in physics to model anomalous diffusion. This paper develops strong solutions of space-time fractional…
An unsteady problem is considered for a space-fractional diffusion equation in a bounded domain. A first-order evolutionary equation containing a fractional power of an elliptic operator of second order is studied for general boundary…
The time-fractional Fokker-Planck equation is a key model for characterizing anomalous diffusion, stochastic transport, and non-equilibrium statistical mechanics with applications in finance, chaotic dynamics, optical physics, and…
We propose a new least squares finite element method to solve the Poisson equation. By using a piecewisely irrotational space to approximate the flux, we split the classical method into two sequential steps. The first step gives the…
We present an efficient sampling method for computing a partition function and accelerating configuration sampling. The method performs a random walk in the $\lambda$ space, with $\lambda$ being any thermodynamic variable that characterizes…
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…
We introduce a simulation-based, amortised Bayesian inference scheme to infer the parameters of random walks. Our approach learns the posterior distribution of the walks' parameters with a likelihood-free method. In the first step a graph…
There has recently been considerable interest in using a nonstandard piecewise approximation to formulate fractional order differential equations as difference equations that describe the same dynamical behaviour and are more amenable to a…
In this paper, we develop a sliding method for the fractional Laplacian. We first obtain the key ingredients needed in the sliding method either in a bounded domain or in the whole space, such as narrow region principles and maximum…
We analyze the quantum walk on a cycle using discrete Wigner functions as a way to represent the states and the evolution of the walker. The method provides some insight on the nature of the interference effects that make quantum and…
A scheme for implementing the discrete-time quantum walk on the Bloch sphere is proposed, which is closely related to the SU(2) group. A spin cluster serves as the walker, whereas its location on the Bloch sphere is described by the spin…
The diffuse-domain, or smoothed boundary, method is an attractive approach for solving partial differential equations in complex geometries because of its simplicity and flexibility. In this method the complex geometry is embedded into a…
In this paper we study probabilistic and neural network approximations for solutions to Poisson equation subject to Holder data in general bounded domains of $\mathbb{R}^d$. We aim at two fundamental goals. The first, and the most…
We consider random flights in $\mathbb{R}^d$ reflecting on the surface of a sphere $\mathbb{S}^{d-1}_R,$ with center at the origin and with radius $R,$ where reflection is performed by means of circular inversion. Random flights studied in…
Walk on stars (WoSt) has shown its power in being applied to Monte Carlo methods for solving partial differential equations, but the sampling techniques in WoSt are not satisfactory, leading to high variance. We propose a guiding-based…