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We present a non-variational, kinetic energy operator approach to the solution of quantum three-body problem with Coulomb interactions, based on the utilization of symmetries intrinsic to the kinetic energy operator, i.e., the three-body Laplacian operator with the respective masses. Through a four-step reduction proc...
The feasibility of using a thermomagnetically pumped ferrofluid to enhance the performance of a natural convection cooling loop is investigated. First, a simplified analytical estimate for the thermomagnetic pumping action is derived, and then design rules for optimal solenoid and ferrofluid are presented.
We introduce a novel explicit and stable numerical algorithm to solve the spatially discretized heat or diffusion equation. We compare the performance of the new method with analytical and numerical solutions.
Particle-laden flows occur in a wide range of disciplines, from atmospheric flows to renewable energy to turbomachinery. They generally pose a challenging environment for the numerical prediction of particle-induced phenomena due to their often complex geometry and highly instationary flow field which covers a wide ra...
We describe a method for coupling an embedded domain in a magnetohydrodynamic (MHD) simulation with a particle-in-cell (PIC) method. In this two-way coupling we follow the work of Daldorff et al. in which the PIC domain receives its initial and boundary conditions from MHD variables (MHD to PIC coupling) while the MHD...
The (py)LIon package is a set of tools to simulate the classical trajectories of ensembles of ions in electrodynamic traps. Molecular dynamics simulations are performed using LAMMPS, an efficient and feature-rich program.
Anisotropic core-shell model of a nano-grained polycrystal, proposed recently for nanocrystalline copper, is applied to estimate elastic effective properties for a set of crystals of cubic symmetry. Materials selected for analysis differ in the lattice geometry (face-centered cubic vs. body-centered cubic) as well as ...
Accurate estimation of the run time of computational codes has a number of significant advantages for scientific computing. It is required information for optimal resource allocation, improving turnaround times and utilization of science gateways.
We present a fully pseudo-spectral scheme to solve axisymmetric hyperbolic equations of second order. With the Chebyshev polynomials as basis functions, the numerical grid is based on the Lobbato (for two spatial directions) and Radau (for the time direction) collocation points.
The crack onset and propagation at the fibre-matrix interface in a composite under tensile/compressive remote biaxial transverse loads is studied by a new linear elastic - (perfectly) brittle interface model. In this model the interface is represented by a continuous distribution of springs which simulates the presenc...
A more accurate, stable, finite-difference time-domain (FDTD) algorithm is developed for simulating Maxwell's equations with isotropic or anisotropic dielectric materials. This algorithm is in many cases more accurate than previous algorithms (G. R. Werner et. al., 2007; A. F. Oskooi et. al., 2009), and it remedie...
In scientific computing, the acceleration of atomistic computer simulations by means of custom hardware is finding ever growing application. A major limitation, however, is that the high efficiency in terms of performance and low power consumption entails the massive usage of low-precision computing units.
In this work, we propose a positivity-preserving scheme for solving two-dimensional advection-diffusion equations including mixed derivative terms, in order to improve the accuracy of lower-order methods. The solution to these equations, in the absence of mixed derivatives, has been studied in detail, while positivity...
The Full Configuration Interaction Quantum Monte Carlo (FCIQMC) method has proved able to provide near-exact solutions to the electronic Schrödinger equation within a finite orbital basis set, without relying on an expansion about a reference state. However, a drawback to the approach is that being based on an expansi...
Nested sampling provides an estimate of the evidence of a Bayesian inference problem via probing the likelihood as a function of the enclosed prior volume. However, the lack of precise values of the enclosed prior mass of the samples introduces probing noise, which can hamper high-accuracy determinations of the eviden...
The solution of the geodesic problem for an oblate ellipsoid is developed in terms of series. Tables are provided to simplify the computation.
In certain naturally aged aluminum alloys, significant strengthening can be obtained due to the decomposition of a super-saturated solid solution into clusters. The origins of such strengthening remain unclear due to the challenge of differentiating solute cluster strengthening from solid solution or precipitate stren...
Particulate Stokesian flows describe the hydrodynamics of rigid or deformable particles in Stokes flows. Due to highly nonlinear fluid-structure interaction dynamics, moving interfaces, and multiple scales, numerical simulations of such flows are challenging and expensive.
This project models and studies the `head-on' collision of liquid helium nanodroplets within a vacuum, using molecular dynamics simulation techniques. Programs written in MATLAB and C are utilized in tandem to facilitate computer experimentation that achieves this goal.
Machine learning force fields (MLFFs) are an increasingly popular choice for atomistic simulations due to their high fidelity and improvable nature. Here, we propose a hybrid small-cell approach that combines attributes of both offline and active learning to systematically expand a quantum mechanical (QM) database whi...
In this paper, we present a parallel algorithm for Monte Carlo simulation of the 2D Ising Model to perform efficiently on a cluster computer using MPI. We use C++ programming language to implement the algorithm.
Chau et al. [New J. Phys. 20, 073003 (2018)] presented a new and straight-forward derivation of a fourth-order approximation '$U_7$' of the time-evolution operator and hinted at its potential value as a symplectic integrator.
Within the Correlated Gaussian Method the parameters of the Gaussian basis functions are often chosen stochastically using pseudo-random sequences. We show that alternative low-discrepancy sequences, also known as quasi-random sequences, provide bases of better quality.
The advection-diffusion and wave equations are the fundamental equations governing any physical law and therefore arise in many areas of physics and astrophysics. For complex problems and geometries, only numerical simulations can give insight into quantitative and accurate behavior of the seeked solutions.
Kernel approximation with exponentials is useful in many problems with convolution quadrature and particle interactions such as integral-differential equations, molecular dynamics and machine learning. This paper proposes a weighted balanced truncation to construct an optimal model reduction method for compressing the...
When the flow is sufficiently rarefied, a temperature gradient, for example, between two walls separated by a few mean free paths, induces a gas flow---an observation attributed to the thermo-stress convection effects at microscale. The dynamics of the overall thermo-stress convection process is governed by the Boltzm...
In this study, we employed the non-equilibrium Green's function method combined with density functional theory to investigate the spin transport properties of the actinide sandwich phthalocyanine molecule U(Pc)<a href="http://2.This" rel="external noopener nofollow" class="link-external link-http">this http URL</a>...
We conduct a molecular dynamics simulation of an inelastic gas system utilizing an event-driven algorithm combined with a thermostat mechanism. Initially, the kinetic energy of the system experiences a decay before settling into a non-equilibrium steady state.
Microwave Imaging is an essential technique for reconstructing the electrical properties of an inaccessible medium. Many approaches have been proposed employing algorithms to solve the Electromagnetic Inverse Scattering Problem associated with this technique.
Fermi operator expansion (FOE) methods are powerful alternatives to diagonalization type methods for solving Kohn-Sham density functional theory (KSDFT). One example is the pole expansion and selected inversion (PEXSI) method, which approximates the Fermi operator by rational matrix functions and reduces the computati...
Many steady-state transport problems in condensed matter physics can be reduced to a set of coupled diffusion equations. This is true in particular when relaxation processes are sufficiently fast that the system is in the diffusive --opposite of ballistic-- regime.
A recently developed spectral-element adaptive refinement incompressible magnetohydrodynamic (MHD) code [Rosenberg, Fournier, Fischer, Pouquet, J. Comp. Phys. 215, 59-80 (2006)] is applied to simulate the problem of MHD island coalescence instability (MICI) in two dimensions. MICI is a fundamental MHD process that can...
We study the rotations of a heavy string (helicoseir) about a vertical axis with one free endpoint and with arbitrary density, under the action of the gravitational force. We show that the problem can be transformed into a nonlinear eigenvalue equation, as in the uniform case.
We describe an initial implementation of an electrostatic Particle-in-Cell (ES-PIC) module with adaptive Cartesian mesh in our Unified Flow Solver framework. Challenges of PIC method with cell-based adaptive mesh refinement (AMR) are related to a decrease of the particle-per-cell number in the refined cells with a cor...
First-principles molecular dynamics simulation based on a plane wave/pseudopotential implementation of density functional theory is adopted to investigate atomic scale energy transport for semiconductors (silicon and germanium). By imposing thermostats to keep constant temperatures of the nanoscale thin layers, initia...
Finding proper collective variables for complex systems and processes is one of the most challenging tasks in simulations, which limits the interpretation of experimental and simulated data and the application of enhanced sampling techniques. Here, we propose a machine learning approach able to distill few, physically...
A biconcave particle suspended in a Poiseuille flow is investigated by the multiple-relaxation-time lattice Boltzmann method with the Galilean-invariant momentum exchange method. The lateral migration and equilibrium of the particle are similar to the Segré-Silberberg effect in our numerical simulations.
We have used unbiased global optimization to fit a reactive force field to a given set of reference data. Specifically, we have employed genetic algorithms (GA) to fit ReaxFF to SiOH data, using an in-house GA code that is parallelized across reference data items via the message-passing interface (MPI).
Formation of surface plasmon modes in sodium nanoclusters containing 20-300 atoms was studied using the GW method. It is shown that in the small Na nanoparticles up to 2 nm in size, the loss function $Im[\epsilon^{-1}]$ is dominated by a single peak corresponding to localized surface plasmon resonance (LSPR).
In recent years, researchers have increasingly sought batteries as an efficient and cost-effective solution for energy storage and supply, owing to their high energy density, low cost, and environmental resilience. However, the issue of dendrite growth has emerged as a significant obstacle in battery development.
We introduce a modified SPH approach that is based on discretising the particle density instead of the mass density. This approach makes it possible to use SPH particles with very different masses to simulate multi-phase flows with large differences in mass density between the phases.
We discuss the advantages of parallelization by multithreading on graphics processing units (GPUs) for parallel tempering Monte Carlo computer simulations of an exemplified bead-spring model for homopolymers. Since the sampling of a large ensemble of conformations is a prerequisite for the precise estimation of statis...
We formulate the continuum field equations and constitutive equations that govern deformation, stress, and electric current flow in a Li-ion half-cell. The model considers mass transport through the system, deformation and stress in the anode and cathode, electrostatic fields, as well as the electrochemical reactions ...
In this paper we describe a method for evolving the projected Gross-Pitaevskii equation (PGPE) for a Bose gas in a harmonic oscillator potential. The central difficulty in solving this equation is the requirement that the classical field is restricted to a small set of prescribed modes that constitute the low energy c...
Flexoelectricity phenomenon is the response of electric polarization to an applied strain gradient and is developed as a consequence of crystal symmetry in all materials. In this study, we show that the presence of strain gradient in non-piezoelectric graphene sheet does not only affect the ionic positions, but also t...
We address the role of noise and the issue of efficient computation in stochastic optimal control problems. We consider a class of non-linear control problems that can be formulated as a path integral and where the noise plays the role of temperature.
Realizing large materials models has emerged as a critical endeavor for materials research in the new era of artificial intelligence, but how to achieve this fantastic and challenging objective remains elusive. Here, we propose a feasible pathway to address this paramount pursuit by developing universal materials mode...
Spin-based logic devices could operate at very high speed with very low energy consumption and hold significant promise for quantum information processing and metrology. Here, an in-house developed, experimentally verified, ensemble self-consistent Monte Carlo device simulator with a Bloch equation model using a spin-...
This work proposes an autoencoder neural network as a non-linear generalization of projection-based methods for solving Partial Differential Equations (PDEs). The proposed deep learning architecture presented is capable of generating the dynamics of PDEs by integrating them completely in a very reduced latent space wi...
Analytic continuation is an essential step in extracting information about the dynamical properties of physical systems from quantum Monte Carlo (QMC) simulations. Different methods for analytic continuation have been proposed and are still being developed.
Canada's northern boreal forest edge offers considerable potential for climate change mitigation through large-scale tree planting. Afforestation in these sparsely forested regions could assist the natural northward migration of forests while capitalizing on their carbon removal capacity.
In this paper we present the two-level homogenization of the flow in a deformable double-porous structure described at two characteristic scales. The higher level porosity associated with the mesoscopic structure is constituted by channels in a matrix made of a microporous material consisting of elastic skeleton and p...
In electromagnetism, acoustics, and quantum mechanics, scattering problems can routinely be solved numerically by virtue of perfectly matched layers (PMLs) at simulation domain boundaries. Unfortunately, the same has not been possible for general elastodynamic wave problems in continuum mechanics.
When solving compressible multi-material flow problems, an unresolved challenge is the computation of advective fluxes across material interfaces that separate drastically different thermodynamic states and relations. A popular idea in this regard is to locally construct bimaterial Riemann problems, and to apply their...
The Artificial Compressibility Method (ACM) for the incompressible Navier-Stokes equations is (link-wise) reformulated (referred to as LW-ACM) by a finite set of discrete directions (links) on a regular Cartesian mesh, in analogy with the Lattice Boltzmann Method (LBM). The main advantage is the possibility of exploit...
Given the time-evolution of an electron charge density, the local potential in Kohn-Sham time-dependent density functional theory (KS-TDDFT) can be modeled as a sum of instantaneous and dynamic contributions by assuming a certain form of the time-dependent Kohn-Sham (TD-KS) orbitals. The instantaneous part is obtained...
We design three dimensional electromagnetic cloaks, starting from a small region of complex shape instead of a point. We derive the expression of a transformation matrix describing an objet with a surface of revolution and its associated non-singular cloak.
Numerous experiments showed that on cold compression graphite transforms into a new superhard and transparent allotrope. Several structures with different topologies have been proposed for this phase.
Real-time time-dependent density functional theory (rt-TDDFT) with hybrid exchange-correlation functional has wide-ranging applications in chemistry and material science simulations. However, it can be thousands of times more expensive than a conventional ground state DFT simulation, hence is limited to small systems....
Deep learning electronic structures from ab initio calculations holds great potential to revolutionize computational materials studies. While existing methods proved success in deep-learning density functional theory (DFT) Hamiltonian matrices, they are limited to DFT programs using localized atomic-like bases and hea...
Accurately quantifying the increased risks of climate extremes requires generating large ensembles of climate realization across a wide range of emissions scenarios, which is computationally challenging for conventional Earth System Models. We propose GEN2, a generative prediction-correction framework for an efficient...
CELES is a freely available MATLAB toolbox to simulate light scattering by many spherical particles. Aiming at high computational performance, CELES leverages block-diagonal preconditioning, a lookup-table approach to evaluate costly functions and massively parallel execution on NVIDIA graphics processing units using ...
We process snapshots of trajectories of evolution equations with intrinsic symmetries, and demonstrate the use of recently developed eigenvector-based techniques to successfully quotient out the degrees of freedom associated with the symmetries in the presence of noise. Our illustrative examples include a one-dimensio...
We present a generalized network model for simulating capillary-dominated two-phase flow through porous media at the pore scale. Three-dimensional images of the pore space are discretized using a generalized network -- described in a companion paper (<a href="https://doi.org/10.1103/PhysRevE.96.013312" rel="external n...
Volumetric crystal structure indexing and orientation mapping are key data processing steps for virtually any quantitative study of spatial correlations between the local chemistry and the microstructure of a material. For electron and X-ray diffraction methods it is possible to develop indexing tools which compare me...
We present a scale-bridging approach based on a multi-fidelity (MF) machine-learning (ML) framework leveraging Gaussian processes (GP) to fuse atomistic computational model predictions across multiple levels of fidelity. Through the posterior variance of the MFGP, our framework naturally enables uncertainty quantifica...
In recent years, the 'kirigami' technique has gained significant attention for creating meta-structures and meta-materials with exceptional characteristics, such as unprecedented stretchability. These properties, not typically inherent in the original materials or structures, present new opportunities for appl...
The combination of continuum Many-Body Quantum physics and Monte Carlo methods provide a powerful and well established approach to first principles calculations for large systems. Replacing the exact solution of the problem with a statistical estimate requires a measure of the random error in the estimate for it to be...
Boltzmann machines are physics informed generative models with wide applications in machine learning. They can learn the probability distribution from an input dataset and generate new samples accordingly.
The exchange-correlation energy in Kohn-Sham density functional theory is expressed as a functional of the electronic density and the Kohn-Sham orbitals. An alternative to Kohn-Sham theory is to express the energy as a functional of the reduced first-order density matrix or equivalently the natural orbitals.
The computer processing of images of magnetic force microscopy of cobalt nanodots was performed. The solution of reverse task of magnetic force microscopy is obtained for surface points of samples.
The recently developed Flexible Local Approximation MEthod (FLAME) produces accurate difference schemes by replacing the usual Taylor expansion with Trefftz functions -- local solutions of the underlying differential equation. This paper advances and casts in a general form a significant modification of FLAME proposed...
A spectral element method (SEM) is developed to solve polarized radiative transfer in multidimensional participating medium. The angular discretization is based on the discrete-ordinates approach, and the spatial discretization is conducted by spectral element approach.
A simple and explicit technique for the numerical solution of the two-particle, time-dependent Schrödinger equation is assembled and tested. The technique can handle interparticle potentials that are arbitrary functions of the coordinates of each particle, arbitrary initial and boundary conditions, and multi-dimension...
In the current paper we present a graphical user interface useful for settings input parameter of the Windows precompiled binaries for the Parallel Finite Element Micromagnetics Package (MagPar). The Package is used for magnetization dynamics analysis on a base of the Landau-Lifshitz-Gilbert (LLG) equation.
In this paper, we propose an optimized field/circuit coupling approach for the simulation of magnetothermal transients in superconducting magnets. The approach improves the convergence of the iterative coupling scheme between a magnetothermal partial differential model and an electrical lumped-element circuit.
The boundary integral method for calculating the stationary states of a quantum particle in nano-devices and quantum billiards is presented in detail at an elementary level. According to the method, wave functions inside the domain of the device or billiard are expressed in terms of line integrals of the wave function...
We present a method which allows reduction of a size of a simulated system. The method can be applied to any system where one can define a finite set of possible states of the system and an elementary process which transforms one state of the system to another.
Nowcasting (or short-term weather forecasting) is particularly important in the case of extreme events as it helps prevent human losses. Many of our activities, however, also depend on the weather.
Building on the success of Quantum Monte Carlo techniques such as diffusion Monte Carlo, alternative stochastic approaches to solve electronic structure problems have emerged over the last decade. The full configuration interaction quantum Monte Carlo (FCIQMC) method allows one to systematically approach the exact sol...
This study introduces the FSSH-2 scheme, a redefined and numerically stable adiabatic Fewest Switches Surface Hopping (FSSH) method for mixed quantum-classical dynamics. It reformulates the standard FSSH hopping probability without non-adiabatic coupling vectors and allows for numerical time integration with larger st...
We present a finite-element time-domain (FETD) Maxwell solver for the analysis of body-of-revolution (BOR) geometries based on discrete exterior calculus (DEC) of differential forms and transformation optics (TO) concepts. We explore TO principles to map the original 3-D BOR problem to a 2-D one in the meridian plane ...
In this paper we approximate the radiative transfer equations by the method of moments, constructing mesoscopic approximations of arbitrary order of the otherwise microscopic system. To define the necessary closure a minimum entropy approach is utilized.
Currently, machine learning (ML) methods are widely used to process the results of physical experiments. In some cases, due to the limited amount of experimental data, ML-models can be pre-trained on synthetic data simulated based on the analytical theory and then fine-tuned using experimental data.
The Unified Model (UM) code supports simulation of weather, climate and earth system processes. It is primarily developed by the UK Met Office, but in recent years a wider community of users and developers have grown around the code.
The dynamic properties of fluid, including density, surface tension, diffusivity and viscosity, are temperature-dependent and can significantly influence the flow dynamics of mesoscopic non-isothermal systems. To capture the correct temperature-dependence of a fluid, a many-body dissipative particle dynamics model wit...
A detailed analysis of the remainder obtained by truncating the Euler series up to the $n$th-order term is presented. In particular, by using an approach recently proposed by Weniger, asymptotic expansions of the remainder, both in inverse powers and in inverse rising factorials of $n$, are obtained.
Using extensive numerical simulations, we study the fluidisation process of dense amorphous materials subjected to an external shear stress, using a three-dimensional colloidal glass model. In order to disentangle possible boundary effects from finite size effects in the process of fluidisation, we implement a novel g...
We study the magnetic field effects on the diluted spin-ice materials using the replica-exchange Monte Carlo simulation. We observe five plateaus in the magnetization curve of the diluted nearest-neighbor spin-ice model on the pyrochlore lattice when a magnetic field is applied in the [111] direction.
As one of the most popular interface-capturing methods, the level-set method is inherently non-conservative, and its evolution usually leads to unphysical mass gain/loss. In this paper, a novel conservative level set method is developed for incompressible multiphase flows simulations.
The quantum anomalous Hall (QAH) effect is a novel topological spintronic phenomenon arising from inherent magnetization and spin-orbit coupling. Various theoretical and experimental efforts have been devoted in search of robust intrinsic QAH insulators.
We numerically study two-component capillary bridges formed when a liquid droplet is placed in between two liquid infused surfaces (LIS). In contrast to commonly studied one-component capillary bridges on non-infused solid surfaces, two-component liquid bridges can exhibit a range of different morphologies where the l...
Monte Carlo simulation code has been developed and tested for studying the passage of charged particle beams and radiation through the crystalline matter at energies from tens of MeV up to hundreds of GeV. The developed Monte Carlo code simulates electron, positron and photon shower in single crystals and amorphous me...
Several sources of total cross sections for e$^+$e$^-$ pair production by photon interaction with matter, used by major Monte Carlo codes for particle transport, are quantitatively evaluated with respect to experimental measurements collected from the literature. They include data libraries deriving from theoretical c...
Machine-learned interatomic potentials (MLIPs) are typically trained on datasets that encompass a restricted subset of possible input structures, which presents a potential challenge for their generalization to a broader range of systems outside the training set. Nevertheless, MLIPs have demonstrated impressive accura...
The Kolmogorov-Arnold Network (KAN) has emerged as a promising neural network architecture for small-scale AI+Science applications. However, it suffers from inflexibility in modeling ridge functions, which is widely used in representing the relationships in physical systems.
In this work we describe a $\delta f$ particle simulation method where the bulk density is periodically remapped on a coarse spline grid using a Forward-Backward Lagrangian (FBL) approach. This method is designed to handle plasma regimes where the densities strongly deviate from their initial state and may evolve into...
We present a new approach to calculate excited states with the full configuration interaction quantum Monte Carlo (FCIQMC) method. The approach uses a Gram-Schmidt procedure, instantaneously applied to the stochastically evolving distributions of walkers, to orthogonalize higher energy states against lower energy ones...
In this paper, we present a new version of the $i$QIST software package, which is capable of solving various quantum impurity models by using the hybridization expansion (or strong coupling expansion) continuous-time quantum Monte Carlo algorithm. In the revised version, the software architecture is completely redesig...
We investigated the mechanism of Na/Ta(110) and Ta/Na(110) interfaces using a combination of bond band barrier (BBB) and zone selective electron spectroscopy (ZES) correlation. We found that 7/9 ML and 8/9 ML Ta metal on a Na(110) surface form one dimensional (1D) chain and two dimensional (2D) ring structures, respec...

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