Related papers: On the Modified Random Walk for Monte-Carlo Radiat…
The implementation and reliability of a quadratic diffusion Monte Carlo method for the study of ground-state properties of atoms are discussed. We show in the simple yet non-trivial calculation of the binding energy of the Li atom that the…
We calculate the diffusion coefficients of persistent random walks on cubic and hypercubic lattices, where the direction of a walker at a given step depends on the memory of one or two previous steps. These results are then applied to study…
An indirect, hybrid Monte Carlo discretization of general relativistic kinetic theory suitable for the development of numerical schemes for radiation transport is presented. The discretization is based on surface flux estimators obtained…
We present a novel quasi-Monte Carlo mechanism to improve graph-based sampling, coined repelling random walks. By inducing correlations between the trajectories of an interacting ensemble such that their marginal transition probabilities…
We discuss the efficiency of Monte Carlo methods in solving continuum radiative transfer problems. The sampling of the radiation field and convergence of dust temperature calculations in the case of optically thick clouds are both studied.…
We investigate ways of accurately simulating the propagation of energetic charged particles over small times where the standard Monte Carlo approximation to diffusive transport breaks down. We find that a small-angle scattering procedure…
Diffusive random walks feature the surprising property that the average length of all possible random trajectories that enter and exit a finite domain is determined solely by the domain boundary. Changes in the diffusion constant or the…
Propagation in quantum walks is revisited by showing that very general 1D discrete-time quantum walks with time- and space-dependent coefficients can be described, at the continuous limit, by Dirac fermions coupled to electromagnetic…
We consider the recently introduced Transformation-based Markov Chain Monte Carlo (TMCMC) (Dutta and Bhattacharya (2014)), a methodology that is designed to update all the parameters simultaneously using some simple deterministic…
This paper considers the problem of optimizing the average tracking error for an elliptic partial differential equation with an uncertain lognormal diffusion coefficient. In particular, the application of the multilevel quasi-Monte Carlo…
In this paper, we derive the distribution of a two-dimensional (complex) random walk in which the angle of each step is restricted to a subset of the circle. This setting appears in various domains, such as in over-the-air computation in…
In network embedding, random walks play a fundamental role in preserving network structures. However, random walk based embedding methods have two limitations. First, random walk methods are fragile when the sampling frequency or the number…
The random walk with choice is a well known variation to the random walk that first selects a subset of $d$ neighbours nodes and then decides to move to the node which maximizes the value of a certain metric; this metric captures the number…
We present an efficient Monte Carlo method to simulate reaction-diffusion processes with spatially varying particle annihilation or transformation rates as it occurs for instance in the context of motor-driven intracellular transport. Like…
The computational cost of a Monte Carlo algorithm can only be meaningfully discussed when taking into account the magnitude of the resulting statistical error. Aiming for a fixed error per particle, we study the scaling behavior of the…
We consider an alternative to the Monte Carlo method for dust continuous radiative transfer simulations: the Quasi-Monte Carlo method. We briefly discuss what it is, its history, and possible implementations. We compare the Monte Carlo…
We present an extensive Monte Carlo study on light transport in optically thin slabs, addressing both axial and transverse propagation. We completely characterize the so-called ballistic-to-diffusive transition, notably in terms of the…
Current digital computers are about to hit basic physical boundaries with respect to integration density, clock frequencies, and particularly energy consumption. This requires the application of new computing paradigms, such as quantum and…
In this paper the multi-dimensional random walk models governed by distributed fractional order differential equations and multi-term fractional order differential equations are constructed. The scaling limits of these random walks to a…
Quantitative photoacoustic tomography aims at estimating optical parameters from photoacoustic images that are formed utilizing the photoacoustic effect caused by the absorption of an externally introduced light pulse. This optical…