Physics - Computational Physics Publications (50)


Physics - Computational Physics Publications

This paper is a survey on exponential integrators to solve cubic-quintic complex Ginzburg-Landau equations and related stiff problems. In particular, we are interested in accurate computation near the explosive soliton solutions where two different time scales exist. We explore time adaptive variations of three types of exponential integrators: integrating factor (IF) methods, exponential Runge-Kutta (ERK) methods and split-step (SS) methods, and their embedded versions for computation and comparison. Read More

In this work, we study the crystalline nuclei growth in glassy systems focusing primarily on the early stages of the process, at which the size of a growing nucleus is still comparable with the critical size. On the basis of molecular dynamics simulation results for two crystallizing glassy systems, we evaluate the growth laws of the crystalline nuclei and the parameters of the growth kinetics at the temperatures corresponding to deep supercoolings; herein, the statistical treatment of the simulation results is done within the mean-first-passage-time method. It is found for the considered systems at different temperatures that the crystal growth laws rescaled onto the waiting times of the critically-sized nucleus follow the unified dependence, that can simplify significantly theoretical description of the post-nucleation growth of crystalline nuclei. Read More

Variational approaches for the calculation of vibrational wave functions and energies are a natural route to obtain highly accurate results with controllable errors. However, the unfavorable scaling and the resulting high computational cost of standard variational approaches limit their application to small molecules with only few vibrational modes. Here, we demonstrate how the density matrix renormalization group (DMRG) can be exploited to optimize vibrational wave functions (vDMRG) expressed as matrix product states. Read More

Do quantum correlations play a role in high temperature dynamics of many-body systems? A common expectation is that thermal fluctuations lead to fast decoherence and make dynamics classical. In this paper, we provide a striking example of a single particle created in a featureless, infinite temperature spin bath which not only exhibits non-classical dynamics but also induces strong long-lived correlations between the surrounding spins. We study the non-equilibrium dynamics of a hole created in a fermionic or bosonic Mott insulator in the atomic limit, which corresponds to a degenerate spin system. Read More

In electroencephalography (EEG) source imaging, the inverse source estimates are depth biased in such a way that their maxima are often close to the sensors. This depth bias can be quantified by inspecting the statistics (mean and co-variance) of these estimates. In this paper, we find weighting factors within a Bayesian framework for the used L1/L2 sparsity prior that the resulting maximum a posterior (MAP) estimates do not favor any particular source location. Read More

Knowing the correct skull conductivity is crucial for the accuracy of EEG source imaging, but unfortunately, its true value, which is inter- and intra-individually varying, is difficult to determine. In this paper, we propose a statistical method based on the Bayesian approximation error approach to compensate for source imaging errors related to erroneous skull conductivity. We demonstrate the potential of the approach by simulating EEG data of focal source activity and using the dipole scan algorithm and a sparsity promoting prior to reconstruct the underlying sources. Read More

A simple robust genuinely multidimensional convective pressure split (CPS) , contact preserving, shock stable Riemann solver (GM-K-CUSP-X) for Euler equations of gas dynamics is developed. The convective and pressure components of the Euler system are separated following the Toro-Vazquez type PDE flux splitting [Toro et al, 2012]. Upwind discretization of these components are achieved using the framework of Mandal et al [Mandal et al, 2015]. Read More

We propose an algorithm for calculating matrix elements of the non-linear Boltzmann equation collision integral in isotropic case. These matrix elements are used as starting ones in the recurrence procedure for calculating the matrix elements of the collision integral, which is non-isotropic with respect to velocities, as described in our previous paper. In addition, isotropic matrix elements are of independent interest for the calculation of isotropic relaxation in a number of problems of physical-chemical kinetics. Read More

Development of high strength carbon fibers (CFs) requires an understanding of the relationship between the processing conditions, microstructure and resulting properties. We developed a molecular model that combines kinetic Monte Carlo (KMC) and molecular dynamics (MD) techniques to predict the microstructure evolution during the carbonization process of carbon fiber manufacturing. The model accurately predicts the cross-sectional microstructure of carbon fibers, predicting features such as graphitic sheets and hairpin structures that have been observed experimentally. Read More

Energy dissipation in sheared dry and wet granulates is explored experimentally and computationally as a function of confining pressure $P_{\rm cf}$. For vanishing confining pressure, $P_{\rm cf} \rightarrow 0$, the energy dissipation fades in the case of dry granulates. In the case of wet granulates, a finite energy dissipation for $P_{\rm cf} \rightarrow 0$ is observed and explained quantitatively by a combination of two effects related to capillary forces: frictional resistance of the granulate in presence of an internal cohesion by virtue of attractive capillary forces and energy dissipation due to the rupture and reformation of liquid bridges. Read More

The approaches taken to describe and develop spatial discretisations of the domains required for geophysical simulation models are commonly ad hoc, model or application specific and under-documented. This is particularly acute for simulation models that are flexible in their use of multi-scale, anisotropic, fully unstructured meshes where a relatively large number of heterogeneous parameters are required to constrain their full description. As a consequence, it can be difficult to reproduce simulations, ensure a provenance in model data handling and initialisation, and a challenge to conduct model intercomparisons rigorously. Read More

Geophysical model domains typically contain irregular, complex fractal-like boundaries and physical processes that act over a wide range of scales. Constructing geographically constrained boundary-conforming spatial discretizations of these domains with flexible use of anisotropically, fully unstructured meshes is a challenge. The problem contains a wide range of scales and a relatively large, heterogeneous constraint parameter space. Read More

The present work reports the formation and the characterization of antipleptic and symplectic metachronal waves in 3D cilia arrays immersed in a two-fluid environment, with a viscosity ratio of 20. A coupled lattice-Boltzmann-Immersed-Boundary solver is used. The periciliary layer is confined between the epithelial surface and the mucus. Read More

Graphene, one of the strongest materials ever discovered, triggered the exploration of many 2D materials in the last decade. However, the successful synthesis of a stable nanomaterial requires a rudimentary understanding of the relationship between its structure and strength. In the present study, we investigate the mechanical properties of 8 different carbon-based 2D nanomaterials by performing extensive density functional theory calculations. Read More

The power of polymorphism in carbon is vividly manifested by the numerous applications of carbon-based nano-materials. Ranging from environmental issues to biomedical applications, it has the potential to address many of today's dire problems. However, an understanding of the mechanism of transformation between carbon allotropes at a microscopic level is crucial for its development into highly desirable materials. Read More

Quantum Tunneling is ubiquitous across different fields, from quantum chemical reactions, and magnetic materials to quantum simulators and quantum computers. While simulating the real-time quantum dynamics of tunneling is infeasible for high-dimensional systems, quantum tunneling also shows up in quantum Monte Carlo (QMC) simulations that scale polynomially with system size. Here we extend a recent results obtained for quantum spin models {[{Phys. Read More

A set of fully numerical algorithms for evaluating the four-dimensional singular integrals arising from Galerkin surface integral equation methods over conforming quadrilateral meshes is presented. This work is an extension of DIRECTFN, which was recently developed for the case of triangular patches, utilizing in a same fashion a series of coordinate transformations together with appropriate integration re-orderings. The resulting formulas consist of sufficiently smooth kernels and exhibit several favorable characteristics when compared with the vast majority of the methods currently available. Read More

A new scheme for an OAM communications system which exploits the radial component p of Laguerre Gauss modes in addition to the azimuthal component l generally used is presented. We derive a new encoding algorithm which makes use of the spatial distribution of intensity to create an alphabet dictionary for communication. We investigate the probability of error in decoding, for several detector options. Read More

Recent studies showed that the in-plane and inter-plane thermal conductivities of two-dimensional (2D) MoS2 are low, posing a significant challenge in heat management in MoS2-based electronic devices. To address this challenge, we design the interfaces between MoS2 and graphene by fully utilizing graphene, a 2D material with an ultra-high thermal conduction. We first perform ab initio atomistic simulations to understand the bonding nature and structure stability of the interfaces. Read More

We present an open-source software package WannierTools, a tool for investigation of novel topological materials. This code works in the tight-binding framework, which can be generated by another software package Wannier90 . It can help to classify the topological phase of a given materials by calculating the Wilson loop, and can get the surface state spectrum which is detected by angle resolved photoemission (ARPES) and in scanning tunneling microscopy (STM) experiments . Read More

In this paper we combine concepts from Riemannian Optimization and the theory of Sobolev gradients to derive a new conjugate gradient method for direct minimization of the Gross-Pitaevskii energy functional with rotation. The conservation of the number of particles in the system constraints the minimizers to lie on a Riemannian manifold corresponding to the unit $L^2$ norm. The idea developed here is to transform the original constrained optimization problem to an unconstrained problem on this (spherical) Riemannian manifold, so that faster minimization algorithms can be applied. Read More

We present a numerical spectral method to solve systems of differential equations on an infinite interval $y\in (-\infty, \infty)$ in presence of linear differential operators of the form $Q(y) \left(\partial/\partial_y\right)^b$ (where $Q(y)$ is a rational fraction and $b$ a positive integer). Even when these operators are not parity-preserving, we demonstrate how a mixed expansion in interleaved Chebyshev rational functions $TB_n(y)$ and $SB_n(y)$ preserves the sparsity of their discretization. This paves the way for fast $O(N\ln N)$ and spectrally accurate mixed implicit-explicit time-marching of sets of linear and nonlinear equations in unbounded geometries. Read More

The cardiovascular system is composed of the heart, blood and blood vessels. Regarding the heart, cardiac conditions are determined by the electrocardiogram, that is a noninvasive medical procedure. In this work, we propose autoregressive process in a mathematical model based on coupled differential equations in order to model electrocardiogram signals. Read More

In the standard SPH method, the interaction between two particles might be not pairwise when the support domain varies, which can result in a reduction of accuracy. To deal with this problem, a modified SPH approach is presented in this paper. First of all, a Lagrangian kernel is introduced to eliminate spurious distortions of the domain of material stability, and the gradient is corrected by a linear transformation so that linear completeness is satisfied. Read More

It is generally accepted that all models are wrong -- the difficulty is determining which are useful. Here, a useful model is considered as one that is capable of combining data and expert knowledge, through an inversion or calibration process, to adequately characterize the uncertainty in predictions of interest. This paper derives conditions that specify which simplified models are useful and how they should be calibrated. Read More

We present how to implement the special relativity in computer games. The resultant relativistic world exactly shows the time dilation and Lorentz contraction, not only for the player but also for all the non-player characters, who obey the correct relativistic equation of motion according to their own accelerations. The causality is explicitly maintained in our formulation by use of the covariant velocities, proper times, worldlines, and light cones. Read More

We investigate the transition to a Landau-Levich-Derjaguin film in forced dewetting using a quadtree adaptive solution to the Navier-Stokes equations with surface tension. A discretization of the capillary forces near the receding contact line is used that yields an equilibrium for a specified contact angle $\theta_\Delta$ called the numerical contact angle. Despite the well-known contact line singularity, dynamic simulations can proceed without any explicit additional numerical procedure, yielding an implicitly dynamic contact angle model. Read More

Ab initio quantum chemistry calculations for systems with large active spaces are notoriously difficult and cannot be successfully tackled by standard methods. In this letter, we generalize a Green's function QM/QM embedding method called self-energy embedding theory (SEET) that has the potential to be successfully employed to treat large active spaces. In generalized SEET, active orbitals are grouped into intersecting groups of few orbitals allowing us to perform multiple parallel calculations yielding results comparable to the full active space treatment. Read More

Drag laws for particles in fluids are often expressed in terms of the undisturbed fluid velocity, defined as the fluid velocity a particle sees before the disturbance develops in the fluid. In two-way coupled point-particle simulations the information from the undisturbed state is not available and must be approximated using the disturbed velocity field. Horwitz and Mani (2016) recently developed a procedure to estimate the undisturbed velocity for particles moving at low Reynolds number and obeying the Stokes drag law. Read More

The Wannier localization problem in quantum physics is mathematically analogous to finding a localized representation of a subspace corresponding to a nonlinear eigenvalue problem. While Wannier localization is well understood for insulating materials with isolated eigenvalues, less is known for metallic systems with entangled eigenvalues. Currently, the most widely used method for treating systems with entangled eigenvalues is to first obtain a reduced subspace (often referred to as disentanglement) and then to solve the Wannier localization problem by treating the reduced subspace as an isolated system. Read More

We provide the necessary framework for carrying out stochastic positive-P and gauge-P simulations of bosonic systems with long range interactions. In these approaches, the quantum evolution is sampled by trajectories in phase space, allowing calculation of correlations without truncation of the Hilbert space or other approximations to the quantum state. The main drawback is that the simulation time is limited by noise arising from interactions. Read More

A new highly efficient method is developed for computation of traveling periodic waves (Stokes waves) on the free surface of deep water. A convergence of numerical approximation is determined by the complex singularites above the free surface for the analytical continuation of the travelling wave into the complex plane. An auxiliary conformal mapping is introduced which moves singularities away from the free surface thus dramatically speeding up numerical convergence by adapting the numerical grid for resolving singularities while being consistent with the fluid dynamics. Read More

Machine learning has proven to be a valuable tool to approximate functions in high-dimensional spaces. Unfortunately, analysis of these models to extract the relevant physics is never as easy as applying machine learning to a large dataset in the first place. Here we present a description of atomic systems that generates machine learning representations with a direct path to physical interpretation. Read More

We developed a combined atomistic-continuum hierarchical multiscale approach to explore the effective thermal conductivity of graphene laminates. To this aim, we first performed molecular dynamics simulations in order to study the heat conduction at atomistic level. Using the non-equilibrium molecular dynamics method, we evaluated the length dependent thermal conductivity of graphene as well as the thermal contact conductance between two individual graphene sheets. Read More

All-carbon heterostructures have been produced recently via focused ion beam patterning of single layer graphene. Amorphized graphene is similar to a graphene sheet in which some hexagons are replaced by a combination of pentagonal, heptagonal and octagonal rings. The present investigation provides a general view regarding phonon and load transfer along amorphous graphene. Read More

Silicene, germanene and stanene likely to graphene are atomic thick material with interesting properties. We employed first-principles density functional theory (DFT) calculations to investigate and compare the interaction of Na or Li ions on these films. We first identified the most stable binding sites and their corresponding binding energies for a single Na or Li adatom on the considered membranes. Read More

Recent experimental advances for the fabrication of various borophene sheets introduced new structures with a wide prospect of applications. Borophene is the boron atoms analogue of graphene. Borophene exhibits various structural polymorphs all of which are metallic. Read More

In this paper, we present a dual-horizon peridynamics formulation which allows for simulations with dual-horizon with minimal spurious wave reflection. We prove the general dual property for dual-horizon peridynamics, based on which the balance of momentum and angular momentum in PD are naturally satisfied. We also analyze the crack pattern of random point distribution and the multiple materials issue in peridynamics. Read More

We examine the applicability of diffusive lattice Boltzmann methods to simulate the fluid transport through barrier coatings, finding excellent agreement between simulations and analytical predictions for standard parameter choices. To examine more interesting non-Fickian behavior and multiple layers of different coatings, it becomes necessary to explore a wider range of parameters. However, such a range of parameters exposes deficiencies in such an implementation. Read More

The electric field integral equation is a well known workhorse for obtaining fields scattered by a perfect electric conducting (PEC) object. As a result, the nuances and challenges of solving this equation have been examined for a while. Two recent papers motivate the effort presented in this paper. Read More

A novel and scalable geometric multi-level algorithm is presented for the numerical solution of elliptic partial differential equations, specially designed to run with high occupancy of streaming processors inside Graphics Processing Units(GPUs). The algorithm consists of iterative, superposed operations on a single grid, and it is composed of two simple full-grid routines: a restriction and a coarsened interpolation-relaxation. The restriction is used to collect sources using recursive coarsened averages, and the interpolation-relaxation simultaneously applies coarsened finite-difference operators and interpolations. Read More

The sensitivity of molecular dynamics on changes in the potential energy function plays an important role in understanding the dynamics and function of complex molecules.We present a method to obtain path ensemble averages of a perturbed dynamics from a set of paths generated by a reference dynamics. It is based on the concept of path probability measure and the Girsanov theorem, a result from stochastic analysis to estimate a change of measure of a path ensemble. Read More

We present a method for using solid state detectors with directional sensitivity to dark matter interactions to detect low-mass Weakly Interacting Massive Particles (WIMPs) originating from galactic sources. In spite of a large body of literature for high-mass WIMP detectors with directional sensitivity, there is no available technique to cover WIMPs in the mass range <1 GeV. We argue that single-electron resolution semiconductor detectors allow for directional sensitivity once properly calibrated. Read More

The experimental realization of increasingly complex synthetic quantum systems calls for the development of general theoretical methods, to validate and fully exploit quantum resources. Quantum-state tomography (QST) aims at reconstructing the full quantum state from simple measurements, and therefore provides a key tool to obtain reliable analytics. Brute-force approaches to QST, however, demand resources growing exponentially with the number of constituents, making it unfeasible except for small systems. Read More

We investigate finite-size effects on diffusion in confined fluids using molecular dynamics simulations and hydrodynamic calculations. Specifically, we consider a Lennard-Jones fluid in slit pores without slip at the interface and show that the use of periodic boundary conditions in the directions along the surfaces results in dramatic finite-size effects, in addition to that of the physically relevant confining length. As in the simulation of bulk fluids, these effects arise from spurious hydrodynamic interactions between periodic images and from the constraint of total momentum conservation. Read More

We develop a generalization of the density functional theory + Hubbard $U$ (DFT+$U$) method to the excited-state regime, in the form of Hubbard $U$ corrected linear-response time-dependent DFT or 'TDDFT+$U$'. Combined with calculated linear-response Hubbard $U$ parameters, this represents a computationally light, first-principles method for the simulation of tightly-bound excitons on transition-metal ions and more generally. In detailed calculations on closed-shell nickel coordination complexes, we find that the exchange-like Hubbard $U$ correction to the TDDFT interaction kernel acts to substantially mitigate the excitation energy increase with $U$ in the underlying Kohn-Sham eigenvalues. Read More

We present a simple electromechanical finite difference model to study the response of a piezoelectric polyvinylidenflourid (PVDF) transducer to optoacoustic (OA) pressure waves in the acoustic nearfield prior to thermal relaxation of the OA source volume. The assumption of nearfield conditions, i.e. Read More

The $N$-particle wavefunction has too many dimensions for a direct time propagation of a many-body system according to the time-dependent Schr\"odinger equation (TDSE). On the other hand, time-dependent density functional theory (TDDFT) tells us that the single-particle density is, in principle, sufficient. However, a practicable equation of motion (EOM) for the accurate time evolution of the single-particle density is unknown. Read More

We present a systematic derivation of relativistic lattice kinetic equations for finite-mass particles, reaching close to the zero-mass ultra-relativistic regime treated in the previous literature. Starting from an expansion of the Maxwell-Juettner distribution on orthogonal polynomials, we perform a Gauss-type quadrature procedure and discretize the relativistic Boltzmann equation on space-filling Cartesian lattices. The model is validated through numerical comparison with standard benchmark tests and solvers in relativistic fluid dynamics such as Boltzmann approach multiparton scattering (BAMPS) and previous relativistic lattice Boltzmann models. Read More

The inverse problem of density functional theory (DFT) is often solved in an effort to benchmark and design approximate exchange-correlation potentials. The forward and inverse problems of DFT rely on the same equations but the numerical methods for solving each problem are substantially different. We examine both problems in this tutorial with a special emphasis on the algorithms and error analysis needed for solving the inverse problem. Read More