Hasil untuk "physics.comp-ph"

Huan Zhang, Robert J. Webber, Michael Lindsey et al.

Neural network parametrizations have increasingly been used to represent the ground and excited states in variational Monte Carlo (VMC) with promising results. However, traditional VMC methods only optimize the wave function in regions of peak probability. The wave function is uncontrolled in the tails of the probability distribution, which can limit the accuracy of the trained wavefunction approximation. To improve the approximation accuracy in the probability tails, this paper interprets VMC as a gradient flow in the space of wave functions, followed by a projection step. From this perspective, arbitrary probability distributions can be used in the projection step, allowing the user to prioritize accuracy in different regions of state space. Motivated by this theoretical perspective, the paper tests a new weighted VMC method on the antiferromagnetic Heisenberg model for a periodic spin chain. Compared to traditional VMC, weighted VMC reduces the error in the ground state energy by a factor of 2 and it reduces the errors in the local energies away from the mode by large factors of $10^2$--$10^4$.

Rüdiger Kürsten

The package performs molecular-dynamics-like agent-based simulations for models of aligning self-propelled particles in two dimensions such as e.g. the seminal Vicsek model or variants of it. In one class of the covered models, the microscopic dynamics is determined by certain time discrete interaction rules. Thus, it is no Hamiltonian dynamics and quantities such as energy are not defined. In the other class of considered models (that are generally believed to behave qualitatively the same) Brownian dynamics is considered. However, also there, the forces are not derived from a Hamiltonian. Furthermore, in most cases, the forces depend on the state of all particles and can not be decomposed into a sum of forces that only depend on the states of pairs of particles. Due to the above specified features of the microscopic dynamics of such models, they are not implemented in major molecular dynamics simulation frameworks to the best of the authors knowledge. Models that are covered by this package have been studied with agent-based simulations by dozens of papers. However, no simulation framework of such models seems to be openly available. The program is provided as a Python package. The simulation code is written in C. In the current version, parallelization is not implemented.

Zdzislaw Burda, Malgorzata J. Krawczyk, Krzysztof Kulakowski

We discuss a cellular automaton simulating the process of reaching Heider balance in a fully connected network. The dynamics of the automaton is defined by a deterministic, synchronous and global update rule. The dynamics has a very rich spectrum of attractors including fixed points and limit cycles, the length and number of which change with the size of the system. In this paper we concentrate on a class of limit cycles that preserve energy spectrum of the consecutive states. We call such limit cycles perfect. Consecutive states in a perfect cycle are separated from each other by the same Hamming distance. Also the Hamming distance between any two states separated by $k$ steps in a perfect cycle is the same for all such pairs of states. The states of a perfect cycle form a very symmetric trajectory in the configuration space. We argue that the symmetry of the trajectories is rooted in the permutation symmetry of vertices of the network and a local symmetry of a certain energy function measuring the level of balance/frustration of triads.

S. Pilati, E. M. Inack, P. Pieri

The projective quantum Monte Carlo (PQMC) algorithms are among the most powerful computational techniques to simulate the ground state properties of quantum many-body systems. However, they are efficient only if a sufficiently accurate trial wave function is used to guide the simulation. In the standard approach, this guiding wave function is obtained in a separate simulation that performs a variational minimization. Here we show how to perform PQMC simulations guided by an adaptive wave function based on a restricted Boltzmann machine. This adaptive wave function is optimized along the PQMC simulation via unsupervised machine learning, avoiding the need of a separate variational optimization. As a byproduct, this technique provides an accurate ansatz for the ground state wave function, which is obtained by minimizing the Kullback-Leibler divergence with respect to the PQMC samples, rather than by minimizing the energy expectation value as in standard variational optimizations. The high accuracy of this self-learning PQMC technique is demonstrated for a paradigmatic sign-problem-free model, namely, the ferromagnetic quantum Ising chain, showing very precise agreement with the predictions of the Jordan-Wigner theory and of loop quantum Monte Carlo simulations performed in the low-temperature limit.

Hristo N. Djidjev, Georg Hahn, Susan M. Mniszewski et al.

The simulation of the physical movement of multi-body systems at an atomistic level, with forces calculated from a quantum mechanical description of the electrons, motivates a graph partitioning problem studied in this article. Several advanced algorithms relying on evaluations of matrix polynomials have been published in the literature for such simulations. We aim to use a special type of graph partitioning in order to efficiently parallelize these computations. For this, we create a graph representing the zero-nonzero structure of a thresholded density matrix, and partition that graph into several components. Each separate submatrix (corresponding to each subgraph) is then substituted into the matrix polynomial, and the result for the full matrix polynomial is reassembled at the end from the individual polynomials. This paper starts by introducing a rigorous definition as well as a mathematical justification of this partitioning problem. We assess the performance of several methods to compute graph partitions with respect to both the quality of the partitioning and their runtime.

Jason Zalev, Michael C. Kolios

Simulation involves predicting responses of a physical system. In this article, we simulate opto-acoustic signals generated in a three-dimensional volume due to absorption of an optical pulse. A separable computational model is developed that permits an order-of-magnitude improvement in computational efficiency over a non-separable model. The simulated signals represent acoustic waves, measured by a probe with a linear transducer array, in a rotated and translated coordinate frame. Light is delivered by an optical source that moves with the probe's frame. A spatio-temporal impulse response for rectangular element transducer geometry is derived using a Green's function solution to the acoustic wave equation. The approach permits fast and accurate simulation for a probe with arbitrary trajectory. For a 3D volume of $n^3$ voxels, computation is accelerated by a factor of $n$. This may potentially have application for opto-acoustic imaging, where clinicians visualize structural and functional features of biological tissue for assessment of cancer and other diseases.

Laurence Nevay, Jochem Snuverink, Andrey Abramov et al.

Beam Delivery Simulation (BDSIM) is a program that simulates the passage of particles in a particle accelerator. It uses a suite of standard high energy physics codes (Geant4, ROOT and CLHEP) to create a computational model of a particle accelerator that combines accurate accelerator tracking routines with all of the physics processes of particles in Geant4. This unique combination permits radiation and detector background simulations in accelerators where both accurate tracking of all particles is required over long range or over many revolutions of a circular machine, as well as interaction with the material of the accelerator.

T. Binder, S. Copplestone, A. Mirza et al.

In the context of the validation of PICLas, a kinetic particle suite for the simulation of rarefied, non-equilibrium plasma flows, the biased hypersonic nitrogen flow around a blunted cone was simulated with the Direct Simulation Monte Carlo method. The setup is characterized by a complex flow with strong local gradients and thermal non-equilibrium resulting in a highly inhomogeneous computational load. Especially, the load distribution is of interest, because it allows to exploit the utilized computational resources efficiently. Different load distribution algorithms are investigated and compared within a strong scaling. This investigation of the parallel performance of PICLas is accompanied by simulation results in terms of the velocity magnitude, translational temperature and heat flux, which is compared to experimental measurements.

Francesco Nattino, Matthew Truscott, Nicola Marzari et al.

Continuum electrolyte models represent a practical tool to account for the presence of the diffuse layer at electrochemical interfaces. However, despite the increasing popularity of these in the field of materials science it remains unclear which features are necessary in order to accurately describe interface-related observables such as the differential capacitance (DC) of metal electrode surfaces. We present here a critical comparison of continuum diffuse-layer models that can be coupled to an atomistic first-principles description of the charged metal surface in order to account for the electrolyte screening at electrified interfaces. By comparing computed DC values for the prototypical Ag(100) surface in an aqueous solution to experimental data we validate the accuracy of the models considered. Results suggest that a size-modified Poisson-Boltzmann description of the electrolyte solution is sufficient to qualitatively reproduce the main experimental trends. Our findings also highlight the large effect that the dielectric cavity parameterization has on the computed DC values.

Mohammadreza Niknam Hamidabad, Rouhollah Haji Abdolvahab

We employ a three-dimensional molecular dynamics to simulate translocation of a polymer through a nanopore driven by an external force. The translocation is investigated for different three pore diameter and two different external forces. In order to see the polymer and pore interaction effects on translocation time, we studied 9 different interaction energies. Moreover, to better understand the simulation results we investigate polymer center of mass, shape factor and the monomer distribution through the translocation. Our results unveil that while increasing the polymer-pore interaction energy slows down the translocation, expanding the pore diameter, makes the translocation faster. The shape analysis of the results reveals that the polymer shape is very sensitive to the interaction energy. In high interactions, the monomers come close to the pore from both sides. As a result, the translocation becomes fast at first and slows down at last.

Brian K. Spears

Machine learning is finding increasingly broad application in the physical sciences. This most often involves building a model relationship between a dependent, measurable output and an associated set of controllable, but complicated, independent inputs. We present a tutorial on current techniques in machine learning -- a jumping-off point for interested researchers to advance their work. We focus on deep neural networks with an emphasis on demystifying deep learning. We begin with background ideas in machine learning and some example applications from current research in plasma physics. We discuss supervised learning techniques for modeling complicated functions, beginning with familiar regression schemes, then advancing to more sophisticated deep learning methods. We also address unsupervised learning and techniques for reducing the dimensionality of input spaces. Along the way, we describe methods for practitioners to help ensure that their models generalize from their training data to as-yet-unseen test data. We describe classes of tasks -- predicting scalars, handling images, fitting time-series -- and prepare the reader to choose an appropriate technique. We finally point out some limitations to modern machine learning and speculate on some ways that practitioners from the physical sciences may be particularly suited to help.

H. Leivestad, I. Muniz

Manuel Jung, Tobias F. Illenseer, Wolfgang J. Duschl

The importance of contact discontinuities in 2D isothermal flows has rarely been discussed, since most Riemann solvers are derived for 1D Euler equations. We present a new contact resolving approximate Riemann solver for the isothermal Euler equations and show its performance for several one- and two-dimensional test problems. The new solver extends the well-known HLL solver, while retaining its computational simplicity. The significant gain in resolution of vortices is displayed by a simulation of the Kármán vortex street. We discuss the loss of Galilean invariance and its implications for the resolution of contact discontinuities, which is experienced by all modern numerical schemes for hydrodynamics in non-moving grids.

A. Covington, R. Bates, R. Durst

René Hammer, Walter Pötz, Anton Arnold

A finite difference scheme is presented for the Dirac equation in (1+1)D. It can handle space- and time-dependent mass and potential terms and utilizes exact discrete transparent boundary conditions (DTBCs). Based on a space- and time-staggered leap-frog scheme it avoids fermion doubling and preserves the dispersion relation of the continuum problem for mass zero (Weyl equation) exactly. Considering boundary regions, each with a constant mass and potential term, the associated DTBCs are derived by first applying this finite difference scheme and then using the Z-transform in the discrete time variable. The resulting constant coefficient difference equation in space can be solved exactly on each of the two semi-infinite exterior domains. Admitting only solutions in $l_2$ which vanish at infinity is equivalent to imposing outgoing boundary conditions. An inverse Z-transformation leads to exact DTBCs in form of a convolution in discrete time which suppress spurious reflections at the boundaries and enforce stability of the whole space-time scheme. An exactly preserved functional for the norm of the Dirac spinor on the staggered grid is presented. Simulations of Gaussian wave packets, leaving the computational domain without reflection, demonstrate the quality of the DTBCs numerically, as well as the importance of a faithful representation of the energy-momentum dispersion relation on a grid.

P. C. Caldwell

J. Thornton

Nail A. Gumerov, Ramani Duraiswami

Vortex element methods are often used to efficiently simulate incompressible flows using Lagrangian techniques. Use of the FMM (Fast Multipole Method) allows considerable speed up of both velocity evaluation and vorticity evolution terms in these methods. Both equations require field evaluation of constrained (divergence free) vector valued quantities (velocity, vorticity) and cross terms from these. These are usually evaluated by performing several FMM accelerated sums of scalar harmonic functions. We present a formulation of the vortex methods based on the Lamb-Helmholtz decomposition of the velocity in terms of two scalar potentials. In its original form, this decomposition is not invariant with respect to translation, violating a key requirement for the FMM. One of the key contributions of this paper is a theory for translation for this representation. The translation theory is developed by introducing "conversion" operators, which enable the representation to be restored in an arbitrary reference frame. Using this form, extremely efficient vortex element computations can be made, which need evaluation of just two scalar harmonic FMM sums for evaluating the velocity and vorticity evolution terms. Details of the decomposition, translation and conversion formulae, and sample numerical results are presented.

Benjamin Seibold, Martin Frank

We present a simple method to solve spherical harmonics moment systems, such as the the time-dependent $P_N$ and $SP_N$ equations, of radiative transfer. The method, which works for arbitrary moment order $N$, makes use of the specific coupling between the moments in the $P_N$ equations. This coupling naturally induces staggered grids in space and time, which in turn give rise to a canonical, second-order accurate finite difference scheme. While the scheme does not possess TVD or realizability limiters, its simplicity allows for a very efficient implementation in Matlab. We present several test cases, some of which demonstrate that the code solves problems with ten million degrees of freedom in space, angle, and time within a few seconds. The code for the numerical scheme, called StaRMAP (Staggered grid Radiation Moment Approximation), along with files for all presented test cases, can be downloaded so that all results can be reproduced by the reader.

Robin Oliver, Daniel J. Read, Oliver G. Harlen et al.

We describe a novel coarse-grained simulation method for modelling the dynamics of globular macromolecules, such as proteins. The macromolecule is treated as a continuum that is subject to thermal fluctuations. The model includes a non-linear treatment of elasticity and viscosity with thermal noise that is solved using finite element analysis. We have validated the method by demonstrating that the model provides average kinetic and potential energies that are in agreement with the classical equipartition theorem. In addition, we have performed Fourier analysis on the simulation trajectories obtained for a series of linear beams to confirm that the correct average energies are present in the first two Fourier bending modes. We have then used the new modelling method to simulate the thermal fluctuations of a representative protein over 500ns timescales. Using reasonable parameters for the material properties, we have demonstrated that the overall deformation of the biomolecule is consistent with the results obtained for proteins in general from atomistic molecular dynamics simulations.