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Monte-Carlo (MC) methods, based on random updates and the trial-and-error principle, are well suited to retrieve particle size distributions from small-angle scattering patterns of dilute solutions of scatterers. The size sensitivity of…
Astronomical data generally consists of 2 or more high-resolution axes, e.g., X,Y position on the sky or wavelength and position-along-one-axis (long-slit spectrometer). Analyzing these multi-dimension observations requires combining 3D…
We analyse a multilevel Monte Carlo method for the approximation of distribution functions of univariate random variables. Since, by assumption, the target distribution is not known explicitly, approximations have to be used. We provide an…
On the base of the diffusion Monte-Carlo method we develop the method allowing to simulate the quantum systems with complex wave function. The method is exact and there are no approximations on the simulations of the module and the phase of…
Monte Carlo simulations are powerful tools for understanding the effects of radiation interactions within detector devices allowing not only to evaluate typical estimates for experimental measurements and to serve as means for designing…
Monte Carlo methods represent the "de facto" standard for approximating complicated integrals involving multidimensional target distributions. In order to generate random realizations from the target distribution, Monte Carlo techniques use…
Using diffusion priors to solve inverse problems in imaging have significantly matured over the years. In this chapter, we review the various different approaches that were proposed over the years. We categorize the approaches into the more…
We introduce a Monte Carlo integration-based Shooting and Bouncing Ray (SBR) algorithm for electromagnetic scattering, specifically targeting complex dielectric materials. Unlike traditional deterministic SBR methods, our approach is the…
Within the magnetar scenario, the "twisted magnetosphere" model appears very promising in explaining the persistent X-ray emission from the Soft Gamma Repeaters and the Anomalous X-ray Pulsars (SGRs and AXPs). In the first two papers of the…
Many problems require to approximate an expected value by some kind of Monte Carlo (MC) sampling, e.g. molecular dynamics (MD) or simulation of stochastic reaction models (also termed kinetic Monte Carlo (kMC)). Often, we are furthermore…
Monte Carlo approaches to radiation transport have several attractive properties such as simplicity of implementation, high accuracy, and good parallel scaling. Moreover, Monte Carlo methods can handle complicated geometries and are…
Monte Carlo simulation is one of the most important tools in the study of diffusion processes. For constant diffusion coefficients, an appropriate Gaussian distribution of particle's steplengths can generate exact results, when compared…
Monte Carlo methods play important part in modern statistical physics. The application of these methods suffer from two main difficulties.The first is caused by the relatively small number of particles that can participate in any numerical…
We review efficient Monte Carlo methods for simulating quantum systems which couple to a dissipative environment. A brief introduction of the Caldeira-Leggett model and the Monte Carlo method will be followed by a detailed discussion of…
Generative diffusion models have recently emerged as a powerful strategy to perform stochastic sampling in Bayesian inverse problems, delivering remarkably accurate solutions for a wide range of challenging applications. However, diffusion…
We use the Monte Carlo method to study the two types of devices used in the technique of single electron spectroscopy and get the C-V curve and I-V curve of them. The results compare well to approximate analytical expressions. Furthermore,…
Recently, a class of efficient spectral Monte-Carlo methods was developed in \cite{Feng2025ExponentiallyAS} for solving fractional Poisson equations. These methods fully consider the low regularity of the solution near boundaries and…
Precision theoretical predictions for high multiplicity scattering rely on the evaluation of increasingly complicated scattering amplitudes which come with an extremely high CPU cost. For state-of-the-art processes this can cause technical…
The efficient evaluation of high-dimensional integrals is of importance in both theoretical and practical fields of science, such as data science, statistical physics, and machine learning. However, exact computation methods suffer from the…
Radiative transfer simulation is an important tool that allows us to generate synthetic images of various astrophysical objects. In the case of complex three-dimensional geometries, a Monte Carlo-based method that simulates photon packages…