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This paper presents a decomposition method for solving elliptic boundary value problems in one-dimension. The method is an improvement to an existing technique for approximating elliptic systems. It is demonstrated to be computationally…
By the use of homotopy perturbation method-Pad\'e (HPM-Pad\'e) technique, a new analytical approximation of luminosity distance in the flat universe is proposed, which has the advantage of significant improvement for accuracy in…
We study the special point in the phase diagram of a semi-infinite system, where the bulk transition is in the three-dimensional Ising universality class. To this end we perform a finite size scaling study of the improved Blume-Capel model…
We study the finite volume approximation of strong solutions to nonlinear systems of conservation laws. We focus on time-explicit schemes on unstructured meshes, with entropy satisfying numerical fluxes. The numerical entropy dissipation is…
The phase transition temperature for the Bose-Einstein condensation (BEC) of weakly-interacting Bose gases in three dimensions is known to be related to certain non-universal properties of the phase transition of three-dimensional O(2)…
We study the 3D Edwards-Anderson model with binary interactions by Monte Carlo simulations. Direct evidence of finite-size scaling is provided, and the universal finite-size scaling functions are determined. Using an iterative extrapolation…
We present a massively parallel quantum Monte Carlo based implementation of real-space dynamical mean-field theory for general inhomogeneous correlated fermionic lattice systems. As a first application, we study magnetic order in a binary…
We present detailed Monte Carlo results for the two-dimensional melting transition of various systems up to N=65536 hard disks. The simulations are performed in the NVT ensemble, using a new updating scheme. In the isotropic phase the bond…
To date, the comparison of Statistical Shape Models (SSMs) is often solely performance-based, carried out by means of simplistic metrics such as compactness, generalization, or specificity. Any similarities or differences between the actual…
A simple-to-implement weak-sense numerical method to approximate reflected stochastic differential equations (RSDEs) is proposed and analysed. It is proved that the method has the first order of weak convergence. Together with the Monte…
High-dimensional distributions, especially those with heavy tails, are notoriously difficult for off-the-shelf MCMC samplers: the combination of unbounded state spaces, diminishing gradient information, and local moves results in…
Solid-solid collapse transition in open framework structures is ubiquitous in nature. The real difficulty in understanding detailed microscopic aspects of such transitions in molecular systems arises from the interplay between different…
Tensor network contraction is a fundamental computational challenge underlying quantum many-body physics, statistical mechanics, and machine learning. Belief propagation (BP) provides an efficient approximate solution, but introduces…
We describe a simulation method for the accurate study of the equilibrium freezing properties of polydisperse fluids under the experimentally relevant condition of fixed polydispersity. The approach is based on the phase switch Monte Carlo…
Density shift plays one of the major roles in the uncertainty of optical lattice clock, thus has attracted lots of theoretical and experimental studies. However, most of the theoretical research considered the single-band and collective…
We consider the order of convergence for linear and nonlinear Monte Carlo approximation of compact embeddings from Sobolev spaces of dominating mixed smoothness defined on the torus $\mathbb{T}^d$ into the space $L_{\infty}(\mathbb{T}^d)$…
This chapter is devoted to the computation of equilibrium (thermodynamic) properties of quantum systems. In particular, we will be interested in the situation where the interaction between particles is so strong that it cannot be treated as…
We study the sample-to-sample fluctuations of the overlap probability densities from large-scale equilibrium simulations of the three-dimensional Edwards-Anderson spin glass below the critical temperature. Ultrametricity, Stochastic…
Standard molecular dynamics (MD) and Monte Carlo (MC) simulation deals with spherical particles. Extending these standard simulation methodologies to the non-spherical cases is non-trivial. To circumvent this problem, non-spherical bodies…
The one-dimensional asymmetric simple exclusion process (ASEP), where $N$ hard-core particles hop forward with rate $1$ and backward with rate $q<1$, is considered on a periodic lattice of $L$ site. Using KPZ universality and previous…