Simulation Of Large Systems Research Articles

A Multifidelity Aero-Thermal Design Approach for Secondary Air Systems

Abstract The paper presents a multidisciplinary approach for aero-thermal and heat transfer analysis for internal flows. The versatility and potential benefit offered by the approach are described through the application to a realistic low pressure turbine assembly. The computational method is based on a run time code-coupling architecture that allows mixed models and simulations to be integrated together for the prediction of the subsystem aero-thermal performance. In this specific application, the model is consisting of two rotor blades, the embedded vanes, the interstage cavity, and the solid parts. The geometry represents a real engine situation. The key element of the approach is the use of a fully modular coupling strategy that aims to combine (1) flexibility for design needs, (2) variable level of modeling for better accuracy, and (3) in memory code coupling for preserving computational efficiency in large system and subsystem simulations. For this particular example, Reynolds averaged Navier–Stokes (RANS) equations are solved for the fluid regions and thermal coupling is enforced with the metal (conjugate heat transfer, CHT). Fluid–fluid interfaces use mixing planes between the rotating parts while overlapping regions are exploited to link the cavity flow to the main annulus flow as well as in the cavity itself for mapping of the metal parts and leakages. Metal temperatures predicted by the simulation are compared to those retrieved from a thermal model of the engine, and the results are discussed with reference to the underlying flow physics.

Efficient exponential time integration for simulating nonlinear coupled oscillators

In this paper, we propose an advanced time integration technique associated with explicit exponential Rosenbrock-based methods for the simulation of large stiff systems of nonlinear coupled oscillators. In particular, a novel reformulation of these systems is introduced and a general family of efficient exponential Rosenbrock schemes for simulating the reformulated system is derived. Moreover, we show the required regularity conditions and prove the convergence of these schemes for the system of coupled oscillators. We present an efficient implementation of this new approach and discuss several applications in scientific and visual computing. The accuracy and efficiency of our approach are demonstrated through a broad spectrum of numerical examples, including a nonlinear Fermi–Pasta–Ulam–Tsingou model, elastic and nonelastic deformations as well as collision scenarios focusing on relevant aspects such as stability and energy conservation, large numerical stiffness, high fidelity, and visual accuracy.

A general implementation of time-dependent vibrational coupled-cluster theory.

The first general excitation level implementation of the time-dependent vibrational coupled cluster (TDVCC) method introduced in a recent publication [J. Chem. Phys. 151, 154116 (2019)] is presented. The general framework developed for time-independent vibrational coupled cluster (VCC) calculations has been extended to the time-dependent context. This results in an efficient implementation of TDVCC with general coupling levels in the cluster operator and Hamiltonian. Thus, the convergence of the TDVCC[k] hierarchy toward the complete-space limit can be studied for any sum-of-product Hamiltonian. Furthermore, a scheme for including selected higher-order excitations for a subset of modes is introduced and studied numerically. Three different definitions of the TDVCC autocorrelation function (ACF) are introduced and analyzed in both theory and numerical experiments. Example calculations are presented for an array of systems including imidazole, formyl fluoride, formaldehyde, and a reduced-dimensionality bithiophene model. The results show that the TDVCC[k] hierarchy converges systematically toward the full-TDVCC limit and that the implementation allows accurate quantum-dynamics simulations of large systems to be performed. Specifically, the intramolecular vibrational-energy redistribution of the 21-dimensional imidazole molecule is studied in terms of the decay of the ACF. Furthermore, the importance of product separability in the definition of the ACF is highlighted when studying non-interacting subsystems.

Simulated tempering with irreversible Gibbs sampling techniques.

We present here two novel algorithms for simulated tempering simulations, which break the detailed balance condition (DBC) but satisfy the skewed detailed balance to ensure invariance of the target distribution. The irreversible methods we present here are based on Gibbs sampling and concern breaking DBC at the update scheme of the temperature swaps. We utilize three systems as a test bed for our methods: a Markov chain Monte Carlo simulation on a simple system described by a one-dimensional double well potential, the Ising model, and molecular dynamics simulations on alanine pentapeptide (ALA5). The relaxation times of inverse temperature, magnetic susceptibility, and energy density for the Ising model indicate clear gains in sampling efficiency over conventional Gibbs sampling techniques with DBC and also over the conventionally used simulated tempering with the Metropolis-Hastings (MH) scheme. Simulations on ALA5 with a large number of temperatures indicate distinct gains in mixing times for inverse temperature and consequently the energy of the system compared to conventional MH. With no additional computational overhead, our methods were found to be more efficient alternatives to the conventionally used simulated tempering methods with DBC. Our algorithms should be particularly advantageous in simulations of large systems with many temperature ladders, as our algorithms showed a more favorable constant scaling in Ising spin systems as compared with both reversible and irreversible MH algorithms. In future applications, our irreversible methods can also be easily tailored to utilize a given dynamical variable other than temperature to flatten rugged free energy landscapes.

Improving molecular dynamics calculation of diffusivity in liquids with theoretical models

An effect of the collective motions on the variance of diffusivity in liquids is considered. It is shown theoretically and with simulation that collective fluctuations increase statistical uncertainty of diffusivity in liquids. On this basis we develop approach that combines molecular dynamics and theoretical models to calculate diffusion coefficient in liquids. We decompose diffusivity into a low scale molecular part and a large scale hydrodynamic part. The low scale term is calculated with the molecular dynamics. It is performed using a small simulation box with less than 100 particles. Local molecular motions appear in such simulations while collective hydrodynamical fluctuations are absent. The large scale hydrodynamics is included with a theoretical model. Thus, molecular dynamics term includes only molecular processes such as rearrangements of molecules, and hydrodynamical term includes collective processes. This approach provides lower statistical uncertainty compared with simulations of large systems. The improvement in statistical accuracy is shown theoretically and confirmed with simulations. It is connected to the relation between diffusivity due to local molecular processes and diffusivity due to hydrodynamics. To illustrate the application of this approach, we compute the self-diffusion coefficient in Lennard-Jones liquid and liquid water, diffusivity of divalent ions in aqueous solutions.

Neural-network assisted study of nitrogen atom dynamics on amorphous solid water – I. adsorption and desorption

ABSTRACT Dynamics of adsorption and desorption of (4S)-N on amorphous solid water are analysed using molecular dynamic simulations. The underlying potential energy surface was provided by machine-learned interatomic potentials. Binding energies confirm the latest available theoretical and experimental results. The nitrogen sticking coefficient is close to unity at dust temperatures of 10 K but decreases at higher temperatures. We estimate a desorption time-scale of 1 μs at 28 K. The estimated time-scale allows chemical processes mediated by diffusion to happen before desorption, even at higher temperatures. We found that the energy dissipation process after a sticking event happens on the picosecond time-scale at dust temperatures of 10 K, even for high energies of the incoming adsorbate. Our approach allows the simulation of large systems for reasonable time-scales at an affordable computational cost and ab initio accuracy. Moreover, it is generally applicable for the study of adsorption dynamics of interstellar radicals on dust surfaces.

Statistical mechanics of polarizable force fields based on classical Drude oscillators with dynamical propagation by the dual-thermostat extended Lagrangian.

Polarizable force fields based on classical Drude oscillators offer a practical and computationally efficient avenue to carry out molecular dynamics (MD) simulations of large biomolecular systems. To treat the polarizable electronic degrees of freedom, the Drude model introduces a virtual charged particle that is attached to its parent nucleus via a harmonic spring. Traditionally, the need to relax the electronic degrees of freedom for each fixed set of nuclear coordinates is achieved by performing an iterative self-consistent field (SCF) calculation to satisfy a selected tolerance. This is a computationally demanding procedure that can increase the computational cost of MD simulations by nearly one order of magnitude. To avoid the costly SCF procedure, a small mass is assigned to the Drude particles, which are then propagated as dynamic variables during the simulations via a dual-thermostat extended Lagrangian algorithm. To help clarify the significance of the dual-thermostat extended Lagrangian propagation in the context of the polarizable force field based on classical Drude oscillators, the statistical mechanics of a dual-temperature canonical ensemble is formulated. The conditions for dynamically maintaining the dual-temperature properties in the case of the classical Drude oscillator are analyzed using the generalized Langevin equation.

A chirality-dependent peridynamic model for the fracture analysis of graphene sheets

Based on the bond-based peridynamic (BPD) method, a chirality-dependent peridynamic (CDPD) model is proposed for the fracture analysis of single layer graphene sheets (SLGS). The peridynamic (PD) parameters in the CDPD model are derived by analyzing the stress-strain relations of SLGS at atomic scale, and thus the CDPD model can provide a multiscale insight into the fracture analysis of SLGS with considering the effect of chirality. In order to increase the efficiency of CDPD simulations of large atomic-scale systems, a special coarse-grain (CG) technique is employed by considering the chiral structure of SLGS in the CDPD simulations. The effect of grid type, grid orientation and grid spacing on the numerical convergence is investigated. The proposed CDPD model is validated by comparing with the available molecular dynamics (MD) results, and the comparisons demonstrate the importance of considering the atomistic structure of SLGS when PD theory is applied in the fracture analysis because the chirality dominates the propagating directions of cracks. The crack propagations in SLGS with various chiralities are studied using the CDPD model. The numerical results indicate that the fracture of SLGS is significantly dependent on the chirality. Especially, examples of large-sized SLGS (750 nm × 750 nm) with about 20 million atoms in the corresponding fully atomistic systems demonstrate the applicability and effectiveness of the proposed CDPD model in the simulation of microscale structures of SLGS without loss of chiral features. To study such large systems is almost impractical for the fully atomistic simulation. This study also provides a significant insight for extending the PD model to the studies on chirality-related materials at microscale.

Large-scale magnetic resonance simulations: A tutorial.

Computational modeling is becoming an essential tool in magnetic resonance to design and optimize experiments, test the performance of theoretical models, and interpret experimental data. Recent theoretical research and software development made possible simulations of large spin systems, for example, proteins with thousands of spins, in reasonable time. In the last few years, the Fokker-Planck formalism also re-emerged due to its ability to handle spatial dynamics. The purpose of this tutorial is to describe advantages and disadvantages of the most common formalisms, the latest developments and strategies to improve the computational efficiency, and to guide users in the setting up of a simulation using the Spinach software.

A QM/MD Coupling Method to Model the Ion-Induced Polarization of Graphene.

We report a new Quantum Mechanical/Molecular Dynamics (QM/MD) simulation loop to model the coupling between the electron and atom dynamics in solid/liquid interfacial systems. The method can describe simultaneously both the quantum mechanical surface polarizability emerging from the proximity to the electrolyte and the electrolyte structure and dynamics. In the current setup, Density Functional Tight Binding calculations for the electronic structure calculations of the surface are coupled with classical molecular dynamics to simulate the electrolyte solution. The reduced computational cost of the QM part makes the coupling with a classical simulation engine computationally feasible and allows simulation of large systems for hundreds of nanoseconds. We tested the method by simulating both a noncharged graphene flake and a noncharged and charged infinite graphene sheet immersed in an NaCl electrolyte solution. We found that, when no bias is applied, ions preferentially remained in solution, and only cations are mildly attracted to the surface of the graphene. This preferential adsorption of cations vs anions seems to persist also when the surface is moderately charged and rules out any substantial ions/surface charge transfer.

Chebyshev polynomial method to Landauer–Büttiker formula of quantum transport in nanostructures

The Landauer–Büttiker formula describes the electronic quantum transport in nanostructures and molecules. It will be numerically demanding for simulations of complex or large size systems due to, for example, matrix inversion calculations. Recently, the Chebyshev polynomial method has attracted intense interest in numerical simulations of quantum systems due to the high efficiency in parallelization because the only matrix operation it involves is just the product of sparse matrices and vectors. Much progress has been made on the Chebyshev polynomial representations of physical quantities for isolated or bulk quantum structures. Here, we present the Chebyshev polynomial method to the typical electronic scattering problem, the Landauer–Büttiker formula for the conductance of quantum transport in nanostructures. We first describe the full algorithm based on the standard bath kernel polynomial method (KPM). Then, we present two simple but efficient improvements. One of them has time consumption remarkably less than that of the direct matrix calculation without KPM. Some typical examples are also presented to illustrate the numerical effectiveness.

Large-scale simulation of biomembranes incorporating realistic kinetics into coarse-grained models

Biomembranes are two-dimensional assemblies of phospholipids that are only a few nanometres thick, but form micrometre-sized structures vital to cellular function. Explicit molecular modelling of biologically relevant membrane systems is computationally expensive due to the large number of solvent particles and slow membrane kinetics. Coarse-grained solvent-free membrane models offer efficient sampling but sacrifice realistic kinetics, thereby limiting the ability to predict pathways and mechanisms of membrane processes. Here, we present a framework for integrating coarse-grained membrane models with continuum-based hydrodynamics. This framework facilitates efficient simulation of large biomembrane systems with large timesteps, while achieving realistic equilibrium and non-equilibrium kinetics. It helps to bridge between the nanometer/nanosecond spatiotemporal resolutions of coarse-grained models and biologically relevant time- and lengthscales. As a demonstration, we investigate fluctuations of red blood cells, with varying cytoplasmic viscosities, in 150-milliseconds-long trajectories, and compare kinetic properties against single-cell experimental observations.

Numeric analysis of reversibility of classic movement equations and constructive criteria of estimating quality of molecular dynamic simulations

The fundamental criteria of the quality of molecular dynamics (MD) simulation represent a pivotal challenge, especially in the case of MD simulations of large systems (in particular, proteins).This work presents a simple theoretical analysis of time reversibility in classical mechanics that has allowed us to formulate a number of constructive criteria for evaluating the quality of the trajectories, generated in MD simulations. The results of testing the criteria on the structures of eight small proteins are presented. The criteria can be useful for solving different MD problems, such as: choosing the most appropriate thermostats for a MD system under study, the methods for sampling conformations, etc. Communicated by Ramaswamy H. Sarma

A Surface Site Interaction Point Method for Dissipative Particle Dynamics Parametrization: Application to Alkyl Ethoxylate Surfactant Self-Assembly

Dissipative particle dynamics (DPD) is a coarse-grained approach to the simulation of large supramolecular systems, but one limitation has been that the parameters required to describe the noncovalent interactions between beads are not readily accessible. A first-principles computational method has been developed so that bead interaction parameters can be calculated directly from ab initio gas-phase molecular electrostatic potential surfaces of the molecular fragments that represent the beads. A footprinting algorithm converts the molecular electrostatic potential surfaces into a discrete set of surface site interaction points (SSIPs), and these SSIPs are used in the SSIMPLE (surface site interaction model for the properties of liquids at equilibrium) algorithm to calculate the free energies of transfer of one bead into a solution of any other bead. The bead transfer free energies are then converted into the required DPD interaction parameters for all pairwise combinations of different beads. The reliability of the parameters was demonstrated using DPD simulations of a range of alkyl ethoxylate surfactants. The simulations reproduce the experimentally determined values of the critical micelle concentration and mean aggregation number well for all 22 surfactants studied.

Reaction-diffusion equations on complex networks and Turing patterns, via p-adic analysis

Nakao and Mikhailov proposed using continuous models (mean-field models) to study reaction-diffusion systems on networks and the corresponding Turing patterns. This work aims to show that p-adic analysis is the natural tool to carry out this program. This is possible due to the fact that the discrete Laplacian attached to a network turns out to be a particular case of a p-adic Laplacian. By embedding the graph attached to the system into the field of p-adic numbers, we construct a continuous p-adic version of a reaction-diffusion system on a network. The existence and uniqueness of the Cauchy problems for these systems are established. We show that Turing criteria for the p-adic continuous reaction-diffusion system remain essentially the same as in the classical case. However, the properties of the emergent patterns are very different. The classical Turing patterns consisting of alternating domains do not occur in the p-adic continuous case. Instead of this, several domains (clusters) occur. Multistability, that is, coexistence of a number of different patterns with the same parameter values occurs. Clustering and multistability have been observed in the computer simulations of large reaction-diffusion systems on networks. Such behavior can be naturally explained in the p-adic continuous model, in a rigorous mathematical way, but not in the original discrete model.

DFTB+, a software package for efficient approximate density functional theory based atomistic simulations.

DFTB+ is a versatile community developed open source software package offering fast and efficient methods for carrying out atomistic quantum mechanical simulations. By implementing various methods approximating density functional theory (DFT), such as the density functional based tight binding (DFTB) and the extended tight binding method, it enables simulations of large systems and long timescales with reasonable accuracy while being considerably faster for typical simulations than the respective ab initio methods. Based on the DFTB framework, it additionally offers approximated versions of various DFT extensions including hybrid functionals, time dependent formalism for treating excited systems, electron transport using non-equilibrium Green's functions, and many more. DFTB+ can be used as a user-friendly standalone application in addition to being embedded into other software packages as a library or acting as a calculation-server accessed by socket communication. We give an overview of the recently developed capabilities of the DFTB+ code, demonstrating with a few use case examples, discuss the strengths and weaknesses of the various features, and also discuss on-going developments and possible future perspectives.

Active particles methods and challenges in behavioral systems

This paper first provides an introduction to the mathematical approach to the modeling, qualitative analysis, and simulation of large systems of living entities, specifically self-propelled particles. Subsequently, a presentation of the papers published in this special issue follows. Finally, a critical analysis of the overall contents of the issue is proposed, thus leading to define some challenging research perspectives.

DP-GEN: A concurrent learning platform for the generation of reliable deep learning based potential energy models

In recent years, promising deep learning based interatomic potential energy surface (PES) models have been proposed that can potentially allow us to perform molecular dynamics simulations for large scale systems with quantum accuracy. However, making these models truly reliable and practically useful is still a very non-trivial task. A key component in this task is the generation of datasets used in model training. In this paper, we introduce the Deep Potential GENerator (DP-GEN), an open-source software platform that implements the recently proposed ”on-the-fly” learning procedure (Zhang et al. 2019) and is capable of generating uniformly accurate deep learning based PES models in a way that minimizes human intervention and the computational cost for data generation and model training. DP-GEN automatically and iteratively performs three steps: exploration, labeling, and training. It supports various popular packages for these three steps: LAMMPS for exploration, Quantum Espresso, VASP, CP2K, etc. for labeling, and DeePMD-kit for training. It also allows automatic job submission and result collection on different types of machines, such as high performance clusters and cloud machines, and is adaptive to different job management tools, including Slurm, PBS, and LSF. As a concrete example, we illustrate the details of the process for generating a general-purpose PES model for Cu using DP-GEN. Program summaryProgram Title: DP-GENProgram Files doi:http://dx.doi.org/10.17632/sxybkgc5xc.1Licensing provisions: LGPLProgramming language: PythonNature of problem: Generating reliable deep learning based potential energy models with minimal human intervention and computational cost.Solution method: The concurrent learning scheme is implemented. Supports for sampling configuration space with LAMMPS, generating ab initio data with Quantum Espresso, VASP, CP2K and training potential models with DeePMD-kit are provided. Supports for different machines including workstations, high performance clusters and cloud machines are provided. Supports for job management tools including Slurm, PBS, LSF are provided.

Accelerated molecular dynamics simulation of large systems with parallel collective variable-driven hyperdynamics

The limitation in time and length scale is a major issue of molecular dynamics (MD) simulation. Although several methods have been developed to extend the MD time scale, their performance usually deteriorates with increasing system size. Therefore, an acceleration method which is applicable to large systems is required to bridge the gap between the MD simulations and target phenomena. In this study, an accelerated MD method for large system is developed based on the collective variable-driven hyperdynamics (CVHD) method [K.M. Bal and E.C. Neyts, 2015]. The key idea is to run CVHD in parallel with rate control and accelerate multiple possible events simultaneously. Using this novel method, carbon diffusion in bcc-iron bicrystal with grain boundary is examined as an application for practical materials. Carbon atoms reaching at the grain boundary are trapped whereas carbon atoms in the bulk region diffuse randomly, and both dynamic regimes can be simultaneously accelerated with the parallel CVHD technique.

Catalytic materials and chemistry development using a synergistic combination of machine learning and ab initio methods

First principles-based molecular modelling plays a crucial role in the development of novel catalytic materials and in the investigation of catalytic chemical reactions. However, the computational cost and/or the accuracy of these models remains a bottleneck in carrying out these simulations for complex or large scale systems, as in the case of catalysis. Over the past two decades, machine learning (ML) has made an impact in the field of computational catalysis. Modern-day researchers have started using machine learning-based data-driven techniques to overcome the limitations of these molecular simulations. In this review, we summarize the recent progress in the utilization of ML algorithms to assist molecular simulations, followed by its applications in the field of catalysis. Furthermore, we provide our perspective on promising avenues for research in the future regarding the incorporation of ML in molecular simulations in catalysis.