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A discrete analysis of the phase and dissipation errors of an explicit, semi-Lagrangian spectral element method is performed. The semi-Lagrangian method advects the Lagrange interpolant according the Lagrangian form of the transport…
In this paper, we propose a multiscale empirical interpolation method for solving nonlinear multiscale partial differential equations. The proposed method combines empirical interpolation techniques and local multiscale methods, such as the…
We propose extensions and improvements of the statistical analysis of distributed multipoles (SADM) algorithm put forth by Chipot et al. in [6] for the derivation of distributed atomic multipoles from the quantum-mechanical electrostatic…
Studies of multiphase fluids utilizing the lattice Boltzmann method (LBM) are typically severely restricted by the number of components or chemical species being modeled. This restriction is particularly pronounced for multiphase systems…
Tensor interpolation is an essential step for tensor data analysis in various fields of application and scientific disciplines. In the present work, novel interpolation schemes for general, i.e., symmetric or non-symmetric, invertible…
Machine-Learning Interatomic Potentials (MLIPs) have surged in popularity due to their promise of expanding the spatiotemporal scales possible for simulating molecules with high fidelity. The accuracy of any MLIP is dependent on the data…
We have studied electron correlations in the doped two-dimensional (2D) Hubbard model by using the coupled-cluster method (CCM) to investigate whether or not the method can be applied to correct the independent particle approximations…
We represent an integration algorithm combining the characteristics method and Hopf-Cole transformation. This algorithm allows one to partially integrate a large class of multidimensional systems of nonlinear Partial Differential Equations…
Chemical component design is a computationally challenging procedure that often entails iterative numerical modeling and authentic experimental testing. We demonstrate a novel optimization method, Tensor train Optimization (TetraOpt), for…
In this paper, we present a splitting algorithm to solve multicomponent transport models. These models are related to plasma simulations, in which we consider the local thermodynamic equilibrium and weakly ionised plasma-mixture models that…
Several methods in nonadiabatic molecular dynamics are based on Madelung's hydrodynamic description of nuclear motion, while the electronic component is treated as a finite-dimensional quantum system. In this context, the quantum potential…
Phase transitions of fluid mixtures of the type introduced by Stillinger and Helfand are studied using a continuum version of the invaded cluster algorithm. Particles of the same species do not interact, but particles of different types…
In this work we formulate and test a new procedure, the Multiscale Perturbation Method for Two-Phase Flows (MPM-2P), for the fast, accurate and naturally parallelizable numerical solution of two-phase, incompressible, immiscible…
The analytical solution of the recently proposed ideal chain polymer mean-spherical approximation (Yu.Kalyuzhnyi, Mol.Phys., 94, 735(1998)) is presented for the multicomponent mixture of charged hard-sphere linear chain flexible molecules.…
The ion distribution around charged colloids in solution has been investigated intensely during the last decade. However, few theoretical approaches have included the influence of variation in the dielectric permittivity within the system,…
The multigrid algorithm is an efficient numerical method for solving a variety of elliptic partial differential equations (PDEs). The method damps errors at progressively finer grid scales, resulting in faster convergence compared to…
A method for measuring the pair interaction potential between colloidal particles by extrapolation measurement of collective structure to infinite dilution is presented and explored using simulation and experiment. The method is…
This paper aims to study time periodic solutions for 3D inviscid quasi-geostrophic model. We show the existence of non trivial rotating patches by suitable perturbation of stationary solutions given by generic revolution shapes around the…
An infinite projected entangled-pair state (iPEPS) is a variational tensor network ansatz for 2D wave functions in the thermodynamic limit where the accuracy can be systematically controlled by the bond dimension $D$. We show that for the…
In disordered systems, wave functions in the Schr\"{o}dinger equation may exhibit a transition from the extended phase to the localized phase, in which the states at the boundaries or mobility edges may exhibit multifractality. Meanwhile,…