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At least 487 records · Page 27

Variationally consistent Maxwell stress in flexoelectric structures under finite deformation and immersed in free space

Maxwell stress refers to the mechanical stress exerted on a dielectric material due to the presence of electric fields. It plays a significant role in the interaction between a dielectric material and the surrounding free space under finite deformation. Previous research on finite deformation of flexoelectricity mainly adopted a modified form of Maxwell stress, potentially not able to correctly capture some physical phenomena, such as the compression of a dielectric droplet in an electric field. In this work, we propose a consistent and complete variational principle for flexoelectricity, in which the Maxwell stress emerges naturally from the derivation, without introducing additional assumptions. An Isogeometric analysis-based numerical framework is developed accordingly and verified by both linear and nonlinear benchmark cases compared with experimental results. The present framework successfully captures and quantifies the behaviors of conductive liquids and soft dielectric solids subjected to an external electric field. Finally, a novel scenario is investigated in which a flexoelectric beam immersed in free space is analyzed, showing the interesting distribution of Maxwell stress-induced tractions at opposing boundaries. The test demonstrates that a higher dielectric constant can effectively enhance the material's stiffness in response to the external electric loading.

36 MATERIALS SCIENCE↗

Partitioned exponential methods for coupled multiphysics systems

Multiphysics problems involving two or more coupled physical phenomena are ubiquitous in science and engineering. This work develops a new partitioned exponential approach for the time integration of multiphysics problems. After a possible semi-discretization in space, the class of problems under consideration is modeled by a system of ordinary differential equations where the right-hand side is a summation of two component functions, each corresponding to a given set of physical processes. The partitioned-exponential methods proposed herein evolve each component of the system via an exponential integrator, and information between partitions is exchanged via coupling terms. Here, the traditional approach to constructing exponential methods, based on the variation-of-constants formula, is not directly applicable to partitioned systems. Rather, our approach to developing new partitioned-exponential families is based on a general-structure additive formulation of the schemes. Two method formulations are considered, one based on a linear-nonlinear splitting of the right hand component functions, and another based on approximate Jacobians. The paper develops classical (non-stiff) order conditions theory for partitioned exponential schemes based on particular families of T-trees and B-series theory. Several practical methods of third order are constructed that extend the Rosenbrock-type and EPIRK families of exponential integrators. Several implementation optimizations specific to the application of these methods to reaction-diffusion systems are also discussed. Numerical experiments reveal that the new partitioned-exponential methods can perform better than traditional unpartitioned exponential methods on some problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Tracer particle transport dynamics in the diffusive sandpile cellular automaton

The confinement properties of the diffusive running sandpile are characterized by tracking the motion of a population of marked grains of sand. It is found that, as the relative strength of the avalanching to the diffusive transport channel is varied, a point is reached at which the particle global confinement time and the probability density functions of the jump-sizes and waiting-times of the tracked grains experience a sudden change, thus revealing a dynamical transition, that is consistent with previous studies (Newman DE et al., Phys Rev Lett 2002;88(20):204304). Across this transition, the sandpile moves from a regime characterized by self-similarity and memory, where avalanches of all possible sizes dominate transport across the system, to another regime where transport is taken over by near system-size, quasi-periodic avalanches. Values for the fractional transport exponents that quantify effective transport across the sandpile prior to the transition are also obtained.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

HTR solver: An open-source exascale-oriented task-based multi-GPU high-order code for hypersonic aerothermodynamics

In this study, the open-source Hypersonics Task-based Research (HTR) solver for hypersonic aerothermodynamics is described. The physical formulation of the code includes thermochemical effects induced by high temperatures (vibrational excitation and chemical dissociation). The HTR solver uses high-order TENO-based spatial discretization on structured grids and efficient time integrators for stiff systems, is highly scalable in GPU-based supercomputers as a result of its implementation in the Regent/Legion stack, and is designed for direct numerical simulations of canonical hypersonic flows at high Reynolds numbers. Additionally, the performance of the HTR solver is tested with benchmark cases including inviscid vortex advection, low- and high-speed laminar boundary layers, inviscid one-dimensional compressible flows in shock tubes, supersonic turbulent channel flows, and hypersonic transitional boundary layers of both calorically perfect gases and dissociating air.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Solving the Grad–Shafranov equation using spectral elements for tokamak equilibrium with toroidal rotation

The Grad–Shafranov equation is solved using spectral elements for tokamak equilibrium with toroidal rotation. The Grad–Shafranov solver builds upon and extends the NIMEQ code (Howell and Sovinec, 2014) previously developed for static tokamak equilibria. Both geometric and algebraic convergence are achieved as the polynomial degree of the spectral-element basis increases. A new analytical solution to the Grad–Shafranov equation is obtained for Solov’ev equilibrium in presence of rigid toroidal rotation, in addition to a previously obtained analytical solution for a different set of equilibrium and rotation profiles. The numerical solutions from the extended NIMEQ are benchmarked with the analytical solutions, with good agreements. Besides, the extended NIMEQ code is benchmarked with the FLOW code (Guazzotto et al., 2004). The modification of pressure profile induced by toroidal flow is investigated. The relative change of pressure profile is found significant around the edge.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Pilgrim : A thermal rate constant calculator and a chemical kinetics simulator

Pilgrim is a program written in Python and designed to use direct dynamics in the calculation of thermal rate constants of chemical reactions by the variational transition state theory (VTST), based on electronic structure calculations for the potential energy surface. Pilgrim can also simulate reaction mechanisms using kinetic Monte Carlo (KMC). For reaction processes with many elementary steps, the rate constant of each of these steps can be calculated by means of conventional transition state theory (TST) or by using VTST. In the current version, Pilgrim can evaluate thermal rates using the canonical version of reaction-path VTST, which requires the calculation of the minimum energy path (MEP) associated with each elementary step or transition structure. Multi-dimensional quantum effects can be incorporated through the small-curvature tunneling (SCT) approximation. These methodologies are available both for reactions involving a single structure of the reactants and the transition state and also for reactions involving flexible molecules with multiple conformations of the reactant and/or of the transition state. For systems with many conformers, the program can evaluate each of the elementary reaction rate constants by multipath canonical VTST or multi-structural VTST. Moreover, the reactant can be unimolecular or bimolecular. Torsional anharmonicity can be incorporated through either the MSTor or the Q2DTor programs. Dual-level calculations are also available in Pilgrim: automatic high-level single-point energies can be used to correct the energy of reactants, transition states, products, and MEP points using the interpolated single-point energies (ISPE) algorithm. When the rate constants of all the chemical processes of interest are known, by means of their calculation using Pilgrim or alternatively through analytical fits to the rate constants as functions of temperature, it is possible to simulate a multistep mechanism under specified laboratory conditions using KMC. Finally, this algorithm allows performing a kinetic simulation to monitor the evolution of each chemical species with time and obtain the product yields.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

SOMAFOAM: An OpenFOAM based solver for continuum simulations of low-temperature plasmas

Here, we report the development of SOMAFOAM, a finite volume framework for performing continuum simulations of low-temperature plasmas. The primary goal of this work is to discuss the features of SOMAFOAM along with representative results provided as examples for a range of operating conditions and geometries. This includes plasma and plasma–dielectric systems operating in direct current, radio frequency, and microwave regimes from pressures as low as 100 mTorr to atmospheric pressure. The code has several useful features including the ability to run massively parallel simulations using arbitrary geometries, structured/unstructured meshes, choice of models such as drift–diffusion/full-momentum at runtime, and species-dependent timesteps to name a few. The verification/validation studies presented include comparison with previously published continuum simulations (low-pressure direct current and radio frequency plasma), with experiments (Gaseous Electronics Conference Reference Cell and microwave microplasma ignited in a split ring resonator), and previously published kinetic simulations (low-pressure radio frequency plasma). Other examples provided include a direct current atmospheric pressure microplasma bounded by dielectric sidewalls and a helium–nitrogen plasma ignited using a needle electrode facing a dielectric. The performance of the code is also discussed with serial and distributed memory parallel runs demonstrated up to 512 cores. The design and implementation of the code in a modular object-oriented framework allows for easy extension and seamless coupling with other codes and can be expected to play an important role in both academia and industry.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A multi-center quadrature scheme for the molecular continuum

We report a common way to evaluate electronic integrals for polyatomic molecules is to use Becke’s partitioning scheme (Becke and Chem, 1988) in conjunction with overlapping grids centered at each atomic site. The Becke scheme was designed for integrands that fall off rapidly at large distances, such as those approximating bound electronic states. When applied to states in the electronic continuum, however, Becke scheme exhibits slow convergence and it is highly redundant. Here, we present a modified version of Becke scheme that is applicable to functions of the electronic continuum, such as those involved in molecular photoionization and electron–molecule scattering, and which ensures convergence and efficiency comparable to those realized in the calculation of bound states. In this modified scheme, the atomic weights already present in Becke’s partition are smoothly switched off within a range of few bond lengths from their respective nuclei, and complemented by an asymptotically unitary weight. The atomic integrals are evaluated on small spherical grids, centered on each atom, with size commensurate to the support of the corresponding atomic weight. The residual integral of the interstitial and long-range region is evaluated with a central master grid. The accuracy of the method is demonstrated by evaluating integrals involving integrands containing Gaussian Type Orbitals and Yukawa potentials, on the atomic sites, as well as spherical Bessel functions centered on the master grid. These functions are representative of those encountered in realistic electron-scattering and photoionization calculations in polyatomic molecules.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

MechElastic: A Python library for analysis of mechanical and elastic properties of bulk and 2D materials

We report the MechElastic Python package evaluates the mechanical and elastic properties of bulk and 2D materials using the elastic coefficient matrix ( C ij ) obtained from any ab-initio density-functional theory (DFT) code. The current version of this package reads the output of VASP, ABINIT, and Quantum Espresso codes (but it can be easily generalized to any other DFT code) and performs the appropriate post-processing of elastic constants as per the requirement of the user. This program can also detect the input structure's crystal symmetry and test the mechanical stability of all crystal classes using the Born-Huang criteria. Various useful material-specific properties such as elastic moduli, longitudinal and transverse elastic wave velocities, Debye temperature, elastic anisotropy, 2D layer modulus, hardness, Pugh's ratio, Cauchy's pressure, Kleinman's parameter, and Lame's coefficients, can be estimated using this program. Another existing feature of this program is to employ the ELATE package (2016) [29] and plot the spatial variation of several elastic properties such as Poisson's ratio, linear compressibility, shear modulus, and Young's modulus in three dimensions. Further, the MechElastic package can plot the equation of state (EOS) curves for energy and pressure for a variety of EOS models such as Murnaghan, Birch, Birch-Murnaghan, and Vinet, by reading the inputted energy/pressure versus volume data obtained via numerical calculations or experiments. This package is particularly useful for the high-throughput analysis of elastic and mechanical properties of materials.

2D materials↗

Anisotropic fluid dynamical simulations of heavy-ion collisions

We present VAH, a (3+1)–dimensional simulation that evolves the far-from-equilibrium quark-gluon plasma produced in ultrarelativistic heavy-ion collisions with anisotropic fluid dynamics. We solve the hydrodynamic equations on an Eulerian grid using the Kurganov–Tadmor algorithm in combination with a new adaptive Runge–Kutta method. Our numerical scheme allows us to start the simulation soon after the nuclear collision, largely avoiding the need to integrate it with a separate pre-equilibrium dynamics module. We test the code's performance by simulating on the Eulerian grid conformal and non-conformal Bjorken flow as well as conformal Gubser flow, whose (0+1)–dimensional solutions are precisely known. Finally, we compare non-conformal anisotropic hydrodynamics to second-order viscous hydrodynamics in central Pb+Pb collisions and find that the former's longitudinal flow profile responds more consistently to the fluid's gradients along the spacetime rapidity direction.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

TUMME: Tsinghua University Minnesota Master Equation program

We report that TUMME is a program for assembling and solving master equations for gas-phase chemical kinetics based on chemically significant eigenmodes. TUMME has interfaces to the Gaussian, Polyrate, and/or MSTor output files that allow the master equation code to obtain the microcanonical flux coefficients needed for the coefficient matrix of the master equation. The flux coefficients for reactions with barriers can be calculated by multi-structural variational transition state theory with small-curvature tunneling (MS-VTST/SCT) or by simpler approximations to this such as conventional transition state theory without tunneling (also called RRKM theory). The flux coefficients for barrierless reactions are provided by a hard-sphere model. TUMME is written in double precision with Python 3; quadruple and octuple precision are also available for some subtasks in C++. The Python code can run in serial or parallel (MP or MPI), and the C++ code can run on a single processor or on multiple processors with OpenMP.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

TensorBNN: Bayesian inference for neural networks using TensorFlow

We report that TensorBNN is a new package based on TensorFlow that implements Bayesian inference for modern neural network models. The posterior density of neural network model parameters is represented as a point cloud sampled using Hamiltonian Monte Carlo. The TensorBNN package leverages TensorFlow's architecture and its ability to use modern graphics processing units in both the training and prediction stages.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Quasi-Helmholtz decomposition, Gauss' laws and charge conservation for finite element particle-in-cell

Development of particle-in-cell (PIC) methods using finite element based methods (FEMs) have been a topic of renewed interest; this has largely been driven by (a) the ability of finite element methods to better model geometry, (b) better understanding of function spaces that are necessary to represent all Maxwell quantities, and (c) more recently, the fundamental rubrics that should be obeyed in space and time so as to satisfy Gauss' laws and the equation of continuity. In that vein, methods have been developed recently that satisfy these equations and are agnostic to time stepping methods. While this development is indeed a significant advance, it should be noted that implicit FEM transient solvers support an underlying null space that corresponds to a gradient of a scalar potential ∇Φ(r) (or t∇Φ(r) in the case of wave equation solvers). While explicit schemes do not suffer from this drawback, they are only conditionally stable with time step sizes that are mesh dependent and very small. Furthermore, the null space produces spurious charge that can corrupt the desired physics of a PIC simulation. The way to overcome this bottleneck, and indeed, satisfy all four Maxwell's equation is to use a quasi-Helmholtz formulation on a tessellation. In the re-formulation presented, we strictly satisfy the equation of continuity and Gauss' laws for both the electric and magnetic flux densities. Results illustrating the efficacy of this scheme will be demonstrated by analyzing non-neutral beams with space-charge and the adiabatic expansion of a neutral plasma with realistic parameters (Debye length and real mass ratios).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

GenASiS Basics: Object-oriented utilitarian functionality for large-scale physics simulations (Version 4)

GenASiS Basics provides modern Fortran classes furnishing extensible object-oriented utilitarian functionality for large-scale physics simulations on distributed memory supercomputers. This functionality includes physical units and constants; display to the screen or standard output device; message passing; I/O to disk; and runtime parameter management and usage statistics. Herein, this revision—Version 4 of Basics—includes a name change and additions to functionality, including the facilitation of direct communication between GPUs.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Accelerating multicanonical sampling with irreversibility

Flat-histogram Monte Carlo simulations are well-established, robust methods to perform random walks in a physical observable or parameter space, making them suitable for finding ground states or studying phase transitions in complex systems in statistical physics. However, their efficiency can be limited by the time to attain the desired flat distribution, which is generally unknown prior to the simulations. In particular, they might suffer from slowing down towards the end of a simulation due to the diffusive nature of random walks. In this work we apply irreversibility to the multicanonical Monte Carlo method via the lifting approach to alleviate this behavior. We achieve a 2–4 times speedup in ground-state search for a two-dimensional (2D) Ising model, and up to an order of magnitude of speedup for finding the ground-state energy in an Edwards–Anderson spin glass, compared to traditional multicanonical sampling. In conclusion, the round-trip times between ground states show a narrower distribution and are significantly shorter compared to the reversible counterpart, suggesting that a lower convergence time with a smaller time variance is feasible.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Model for the electrical conductivity in dense plasma mixtures

A new density functional theory, average atom based model for the electrical conductivity of dense plasmas with a mixture of ion species, containing no adjustable parameters, is presented herein. The model takes the temperature, mass density and relative abundances of the species as input. It takes into account partial ionization, ionic structure, and core-valence orthogonality, and uses quantum mechanical calculations of cross sections. Comparison to an existing high fidelity but computationally expensive method reveals good agreement. The new model is computationally efficient and can reach high temperatures. A new mixing rule is also presented that gives reasonably accurate conductivities for high temperature plasma mixtures.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Catalytic consequences of hydrogen addition events and solvent-adsorbate interactions during guaiacol-H 2 reactions at the H 2 O-Ru(0 0 0 1) interface

Catalytic reactions of biomass-derived phenolics and H 2 occur on transition metal surfaces via competitive C–O cleavage and ring saturation pathways, with both requiring multiple hydrogen addition events before forming their respective rate limiting transition states. These events are markedly affected by solvent chemical identity, with polar protic solvents ionizing hydrogen adatoms (H*) to interfacial protons (H + ) and opening up new catalytic routes. Here, we establish the reaction coordinate space for guaiacol-H 2 reactions on Ru(0 0 0 1) using density functional theory and describe the atomic-scale effect of a polar protic solvent, H 2 O. Coupled H + and H* attack leads to quasi-equilibrated enol and keto intermediates as the precursors for C–O cleavage and ring saturation, respectively. For C–O cleavage, H 2 O solvent enables a lower energy pathway via concomitant transfer of the hydroxyl H + to the methoxy oxygen during C–OCH 3 cleavage, forming a charge separated [Ru(s)–(C 6 H 5 O – )…(H + )…OCH 3 ] transition state and reducing the barrier by up to 0.8 eV as compared to unassisted C–OCH 3 cleavage. For ring saturation, H* attack onto an unsaturated meta carbon is rate limiting with no direct solvent participation, suggesting that protic polar solvents selectively promote the C–O cleavage pathway. Taken together, we show that activating guaiacol for either C–O bond cleavage or ring saturation product formation depends on the reactive hydrogen identity (H* or H + ), enol/keto isomerization equilibrium, and accessibility of the proton assisted Car–OCH 3 cleavage transition state. Here, all such factors are tunable via changes to the solvent or metal identity.

09 BIOMASS FUELS↗

DPM: A deep learning PDE augmentation method with application to large-eddy simulation

A framework is introduced that leverages known physics to reduce overfitting in machine learning for scientific applications. The partial differential equation (PDE) that expresses the physics is augmented with a neural network that uses available data to learn a description of the corresponding unknown or unrepresented physics. Training within this combined system corrects for missing, unknown, or erroneously represented physics, including discretization errors associated with the PDE's numerical solution. For optimization of the network within the PDE, an adjoint PDE is solved to provide high-dimensional gradients, and a stochastic adjoint method (SAM) further accelerates training. Additionally, the approach is demonstrated for large-eddy simulation (LES) of turbulence. High-fidelity direct numerical simulations (DNS) of decaying isotropic turbulence provide the training data used to learn sub-filter-scale closures for the filtered Navier–Stokes equations. Out-of-sample comparisons show that the deep learning PDE method outperforms widely-used models, even for filter sizes so large that they become qualitatively incorrect. It also significantly outperforms the same neural network when a priori trained based on simple data mismatch, not accounting for the full PDE. Measures of discretization errors, which are well-known to be consequential in LES, point to the importance of the unified training formulation's design, which without modification corrects for them. For comparable accuracy, simulation runtime is significantly reduced. A relaxation of the typical discrete enforcement of the divergence-free constraint in the solver is also successful, instead allowing the DPM to approximately enforce incompressibility physics. Since the training loss function is not restricted to correspond directly to the closure to be learned, training can incorporate diverse data, including experimental data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗