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At least 775 records · Page 43

Application-specific machine-learned interatomic potentials: exploring the trade-off between DFT convergence, MLIP expressivity, and computational cost

Machine-learned interatomic potentials (MLIPs) are revolutionizing computational materials science and chemistry by offering an efficient alternative to ab initio molecular dynamics (MD) simulations. However, fitting high-quality MLIPs remains a challenging, time-consuming, and computationally intensive task where numerous trade-offs have to be considered, e.g., How much and what kind of atomic configurations should be included in the training set? Which level of ab initio convergence should be used to generate the training set? Which loss function should be used for fitting the MLIP? Which machine learning architecture should be used to train the MLIP? The answers to these questions significantly impact both the computational cost of MLIP training and the accuracy and computational cost of subsequent MLIP MD simulations. In this study, we use a configurationally diverse beryllium dataset and quadratic spectral neighbor analysis potential. We demonstrate that joint optimization of energy versus force weights, training set selection strategies, and convergence settings of the ab initio reference simulations, as well as model complexity can lead to a significant reduction in the overall computational cost associated with training and evaluating MLIPs. This opens the door to computationally efficient generation of high-quality MLIPs for a range of applications which demand different accuracy versus training and evaluation cost trade-offs.

36 MATERIALS SCIENCE↗

Evaluation of effective-stress-function algorithm for nuclear fuel simulation

In a pressurized water reactor (PWR), the mechanical integrity of nuclear fuel is the most critical issue as it is an important barrier for fission products released into the environment. The integrity of zirconium cladding that surrounds uranium oxide can be threatened during off-normal operation owing to a pellet-cladding mechanical interaction (PCMI). To analyze the fuel and cladding behavior during off-operation, the fuel performance code should calculate an inelastic analysis in two - or three-dimensional calculations. In this paper, the effective stress function (ESF) algorithm based on a two-dimensional FE module has been implemented to simulate the inelastic behavior of the cladding with stability and accuracy. The ESF algorithm solves the governing equations of the inelastic constitutive behavior by calculating the zero of the appropriate effective-stress-function. To verify the accuracy of the ESF algorithm for an inelastic analysis, a code-to-code benchmark was performed using the commercial FE code, ANSYS 13.0. To demonstrate the stability and convergence of the implemented algorithm, the number of iterations in the ESF algorithm was compared with that in a sequential algorithm in the case of an inelastic problem. Consequently, the evaluation results demonstrate that the implemented ESF algorithm improves the efficiency of the computation without a loss of accuracy for an inelastic analysis. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Design, analysis and preliminary numerical results for the nonconforming VEM for parabolic problems

The virtual element method (VEM) is a numerical methodology for solving partial differential equations on unstructured polytopal meshes. In this work, we extend the nonconforming high-order formulation suitable to time-dependent diffusion problems with possibly nonlinear forcing terms. Coupling high-order virtual element formulations in space with time-marching schemes based on Backward Differention Formulas (BDFs) makes a fully discrete method with optimal order of convergence in the Method of Lines framework. We investigate and assess the performance of the method through theoretical analysis and a set of numerical experiments.

97 MATHEMATICS AND COMPUTING↗

Convergence acceleration of the Proteus computer code with multigrid methods

Presented here is the first part of a study to implement convergence acceleration techniques based on the multigrid concept in the Proteus computer code. A review is given of previous studies on the implementation of multigrid methods in computer codes for compressible flow analysis. Also presented is a detailed stability analysis of upwind and central-difference based numerical schemes for solving the Euler and Navier-Stokes equations. Results are given of a convergence study of the Proteus code on computational grids of different sizes. The results presented here form the foundation for the implementation of multigrid methods in the Proteus code.

Demuren, A. O.↗

Spectral element methods for the incompressible Navier-Stokes equations

Spectral element methods are high-order weighted-residual techniques for partial differential equations that combine the geometric flexibility of finite element techniques with the rapid convergence rate of spectral schemes. The theoretical foundations and numerical implementation of spectral element methods for the incompressible Navier-Stokes equations are presented, considering the construction and analysis of optimal-order spectral element discretizations for elliptic and saddle (Stokes) problems, as well as the efficient solution of the resulting discrete equations by rapidly convergent tensor-product-based iterative procedures. Several examples of spectral element simulation of moderate Reynolds number unsteady flow in complex geometry are presented.

Maday, Yvon↗

Conceptual Design Method Developed for Advanced Propulsion Nozzles

As part of a contract with the NASA Lewis Research Center, a simple, accurate method of predicting the performance characteristics of a nozzle design has been developed for use in conceptual design studies. The Nozzle Performance Analysis Code (NPAC) can predict the on- and off-design performance of axisymmetric or two-dimensional convergent and convergent-divergent nozzle geometries. NPAC accounts for the effects of overexpansion or underexpansion, flow divergence, wall friction, heat transfer, and small mass addition or loss across surfaces when the nozzle gross thrust and gross thrust coefficient are being computed. NPAC can be used to predict the performance of a given nozzle design or to develop a preliminary nozzle system design for subsequent analysis. The input required by NPAC consists of a simple geometry definition of the nozzle surfaces, the location of key nozzle stations (entrance, throat, exit), and the nozzle entrance flow properties. NPAC performs three analysis "passes" on the nozzle geometry. First, an isentropic control volume analysis is performed to determine the gross thrust and gross thrust coefficient of the nozzle. During the second analysis pass, the skin friction and heat transfer losses are computed. The third analysis pass couples the effects of wall shear and heat transfer with the initial internal nozzle flow solutions to produce a system of equations that is solved at steps along the nozzle geometry. Small mass additions or losses, such as those resulting from leakage or bleed flow, can be included in the model at specified geometric sections. A final correction is made to account for divergence losses that are incurred if the nozzle exit flow is not purely axial.

Nadell, Shari-Beth↗

Information transfer satellite concept study. Volume 4: computer manual

The Satellite Telecommunications Analysis and Modeling Program (STAMP) provides the user with a flexible and comprehensive tool for the analysis of ITS system requirements. While obtaining minimum cost design points, the program enables the user to perform studies over a wide range of user requirements and parametric demands. The program utilizes a total system approach wherein the ground uplink and downlink, the spacecraft, and the launch vehicle are simultaneously synthesized. A steepest descent algorithm is employed to determine the minimum total system cost design subject to the fixed user requirements and imposed constraints. In the process of converging to the solution, the pertinent subsystem tradeoffs are resolved. This report documents STAMP through a technical analysis and a description of the principal techniques employed in the program.

Bergin, P.↗

Numerical Method for Fractional Advection-Diffusion Equation with Heredity

We propose a method of construction of difference schemes for fractional partial differential equations with delay in time. For the fractional equation with two-sided diffusion, fractional transfer in time, and a functional aftereffect, we construct an implicit difference scheme. We use the shifted Grünwald–Letnikov formulas for the approximation of fractional derivatives with respect to spatial variables and the L1-algorithm for the approximation of fractional derivatives in time. Also we use piecewise constant interpolation and extrapolation by extending the discrete prehistory of the model in time. The algorithm is a fractional analog of a purely implicit method; on each time step, it is reduced to the solution of linear algebraic systems. We prove the stability of the method and find its order of convergence.

97 MATHEMATICS AND COMPUTING↗

A relaxed two-step splitting iteration method for computing PageRank

In this paper, we extend the two-step matrix splitting iteration approach by introducing a new relaxation parameter. The main idea is based on the inner–outer iteration for solving the PageRank problems proposed by Gleich et al. (J Sci Comput 32(1): 349–371, 2010) and Bai (Numer Algebra Cont Optim 2(4): 855–862, 2012) and the two-step splitting iteration presented by Gu et al. (Appl Math Comput 271: 337–343, 2015). The theoretical analysis results show that the proposed method is efficient. Numerical experiments demonstrate that the convergence performances of the method are better than the existing methods.

97 MATHEMATICS AND COMPUTING↗

Regularizing the linearly extrapolated BDF2 scheme for incompressible flows with time relaxation

This paper presents a highly-efficient finite element scheme for the time relaxation model (TRM). The efficiency is achieved through the second-order BDF2 time-stepping scheme with linear extrapolation (BDF2LE). The accuracy of the scheme is also greatly enhanced through the use of the divergence-free Scott-Vogeulis finite elements, and van Cittert approximate deconvolution. A complete finite element analysis is provided, which includes rigorous proofs for the stability, well-possessedness, and convergence of both velocity and pressure solutions. Furthermore, we also demonstrate that the inclusion of the linear time relaxation term preserves the long-time stability of the unregularized BDF2LE scheme. Finally, numerical experiments are presented that demonstrate the added stability and accuracy that time relaxation can provide.

97 MATHEMATICS AND COMPUTING↗

Adsorption mechanisms of cesium at calcium-silicate-hydrate surfaces using molecular dynamics simulations

We report understanding the mechanisms of interactions and immobilization of radionuclides in cement systems at the molecular level is key to developing safe and novel solutions for the long-term storage of nuclear wastes. The molecular level adsorption mechanisms of cesium (Cs + ) ions onto tobermorite 9 Å, tobermorite 14 Å, and jennite – three crystalline structural analogues for calcium-silicate-hydrates, the main components in cement-based materials, were investigated using molecular dynamics (MD) simulations. Convergence monitoring of the simulations, using the root mean square displacement with average correlation analysis, indicated that MD trajectories of 10–15 ns were needed given the size of the selected computational cell to properly capture the dynamic process of adsorption. Cs + ions adsorbed as inner-sphere complexes at the tobermorite surfaces, while they showed lower affinity for jennite. The charge and structure of the surface layer strongly influenced the adsorption mechanisms of Cs + ions. Strong association with the hexagonal cavities of the silica sites were seen at the tetrahedral SiO 4 surface of the tobermorite structures. Cs + ion adsorption was attributed to co-ion adsorption at the octahedral CaO 6 surface of tobermorite 9 Å, cation exchange at that of tobermorite 14 Å, and electrostatic interaction with the surface hydroxyl groups for jennite. Distribution coefficients of Cs + ions onto cement pastes derived from molecular dynamics by taking the surface structure and dynamics of Cs + ions directly into account showed a range of overlap with experimental results.

42 ENGINEERING↗

Electron inelastic mean free path in water

Liquid phase transmission electron microscopy (LPTEM) is rapidly developing as a powerful tool for probing processes in liquid environments with close to atomic resolution. Knowledge of the water thickness is needed for reliable interpretation and modelling of analytical studies in LPTEM, and is particularly essential when using thin liquid layers, required for achieving the highest spatial resolutions. Furthermore, the log-ratio method in electron energy-loss spectroscopy (EELS) is often applied in TEM to quantify the sample thickness, which is measured relative to the inelastic mean free path ( λ IMFP ). However, λ IMFP itself is dependent on sample material, the electron energy, and the convergence and divergence angles of the microscope electronoptics. Here, we present a detailed quantitative analysis of the λ IMFP of water as functions of the EELS collection angle ( β ) at 120 keV and 300 keV in a novel nanochannel liquid cell. We observe good agreement with earlier studies conducted on ice, but find that the most widely used theoretical models significantly underestimate λ IMFP of water. We determine an adjusted average energy-loss term E m, water , and characteristic scattering angle θ E, water that improve the accuracy. The results provide a comprehensive knowledge of the λ IMFP of water (or ice) for reliable interpretation and quantification of observations in LPTEM and cryo-TEM studies.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Quasi-equilibrium electron density along a magnetic field line

A methodology is developed to determine the density of high-energy electrons along a magnetic field line for a low-{beta} plasma. This method avoids the expense and statistical noise of traditional particle tracking techniques commonly used for high-energy electrons in bombardment plasma generators. By preserving the magnetic mirror and assuming a mixing timescale, typically the elastic collision frequency with neutrals, a quasi-equilibrium electron distribution can be calculated. Following the transient decay, the analysis shows that both the normalized density and the reduction fraction due to collision converge to a single quasi-equilibrium solution.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Spin-free formulation of the multireference driven similarity renormalization group: A benchmark study of first-row diatomic molecules and spin-crossover energetics

We report a spin-free formulation of the multireference (MR) driven similarity renormalization group (DSRG) based on the ensemble normal ordering of Mukherjee and Kutzelnigg (1997). This ensemble averages over all microstates of a given total spin quantum number, and therefore, it is invariant with respect to SU(2) transformations. As such, all equations may be reformulated in terms of spin-free quantities and they closely resemble those of spin-adapted closed-shell coupled cluster (CC) theory. The current implementation is used to assess the accuracy of various truncated MR-DSRG methods (perturbation theory up to third order and iterative methods with single and double excitations) in computing the constants of 33 first-row diatomic molecules. The accuracy trends for these first-row diatomics are consistent with our previous benchmark on a small subset of closed-shell diatomic molecules. We then present the first MR-DSRG application on transition-metal complexes by computing the spin splittings of the [Fe(H 2 O) 6 ] 2+ and [Fe(NH 3 ) 6 ] 2+ molecules. A focal point analysis (FPA) shows that third-order perturbative corrections are essential to achieve reasonably converged energetics. The FPA based on the linearized MR-DSRG theory with one- and two-body operators and up to a quintuple- ζ basis set predicts the spin splittings of [Fe(H 2 O) 6 ] 2+ and [Fe(NH 3 ) 6 ] 2+ to be –35.7 and –17.1 kcal mol –1 , respectively, showing good agreement with the results of local CC theory with singles, doubles, and perturbative triples.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Efficient perturbation-tracking method for directly probing the spectral phonon properties from molecular dynamics simulations

Existing methods for directly extracting the spectral phonon properties from molecular dynamics (MD) simulations, like the normal mode analysis (NMA) and spectral energy density analysis, all require a very long simulation time to produce reliable results with good convergence. So far, these methods are mainly applied in studies using small systems and with empirical potentials, as the heavy computational load has greatly hindered their further applications. Here we propose a perturbation-tracking (PT) method for directly probing the mode-wise phonon anharmonic frequencies and lifetimes. We show that results obtained from our method are in excellent agreement with those from the conventional NMA approach, using Si as the model material system. Comparing with the NMA approach, the PT method offers a greater accuracy and significant improvement of efficiency. It takes an average of two orders of magnitude and up to three orders of magnitude less simulation time to obtain the same lifetime result of a phonon mode with intermediate to high accuracy. Meanwhile, our method preserves all the dynamics of probed phonon mode from a particular state, which means it is capable of studying the transient thermal transport processes in a nonequilibrium system. Besides the exceptional efficiency, our method also comes with freedom to choose to probe only those modes of interest. This makes it ideal for use with large systems and in computationally demanding applications, such as ab initio MD simulations. Moreover, the PT method we propose here is very straightforward and easy to implement.

74 ATOMIC AND MOLECULAR PHYSICS↗

Adaptive Path-Following Control for Ground Vehicles Using a Switching Non-Quadratic Lyapunov Function

The application of adaptive control techniques in the development of control systems for intelligent vehicles, especially for ground vehicle path-following controllers, has gained popularity due to their ability to handle large-scale parametric uncertainties. However, the use of a standard quadratic Lyapunov function in existing adaptive control-based path-following controllers can lead to poor transient performance, such as slow convergence and/or large overshoot. To address this limitation, this study proposes the use of a switching non-quadratic Lyapunov function to design a model reference adaptive path-following controller that aims to provide superior transient performance. The stability and signal convergence of the closed-loop system are demonstrated through a Lyapunov-like analysis. Through dSPACE ASM simulation, the effectiveness of the proposed controller is illustrated, which confirms improved tracking performance over a baseline solution.

Zhou, Xingyu↗

A Refinement-by-Superposition -Method for (curl)- and (div)-Conforming Discretizations

Here, we present refinement-by-superposition (RBS) hp-refinement infrastructure for computational electromagnetics (CEMs), which permits exponential rates of convergence. In contrast to dominant approaches to hp-refinement for continuous Galerkin methods, which rely on explicit constraint equations, the multilevel strategy presented drastically reduces the implementation complexity. Through the RBS methodology, enforcement of continuity occurs by construction, enabling arbitrary levels of refinement with ease, and without the practical (but not theoretical) limitations of constrained-node refinement. We outline the construction of the RBS hp-method for refinement with H (curl)- and H (div)-conforming finite cells. Numerical simulations for the 2-D finite element method (FEM) solution of the Maxwell eigenvalue problem demonstrate the effectiveness of RBS hp-refinement. As an additional goal of this work, we aim to promote the use of mixed-order (low- and high-order) elements in practical CEM applications.

42 ENGINEERING↗

The Modulation of Gulf Stream Influence on the Troposphere by the Eddy-Driven Jet

This study suggests that the Gulf Stream influence on the wintertime North Atlantic troposphere is most pronounced when the eddy-driven jet (EDJ) is farthest south and better collocated with the Gulf Stream. Using the reanalysis dataset NCEP-CFSR for December–February 1979–2009, the daily EDJ latitude is separated into three regimes (northern, central, and southern). It is found that the average trajectory of atmospheric fronts covaries with EDJ latitude. In the southern EDJ regime (~19% of the time), the frequency of near-surface atmospheric fronts that pass across the Gulf Stream is maximized. Analysis suggests that this leads to significant strengthening in near-surface atmospheric frontal convergence resulting from strong air–sea sensible heat flux gradients (due to strong temperature gradients in the atmosphere and ocean). In recent studies, it was shown that the pronounced band of time-mean near-surface wind convergence across the Gulf Stream is set by atmospheric fronts. Here, it is shown that an even smaller subset of atmospheric fronts—those associated with a southern EDJ—primarily sets the time mean, due to enhanced Gulf Stream air–sea interaction. Furthermore, statistically significant anomalies in vertical velocity extending well above the boundary layer are identified in association with changes in EDJ latitude. These anomalies are particularly strong for a southern EDJ and are spatially consistent with increases in near-surface atmospheric frontal convergence over the Gulf Stream. These results imply that much of the Gulf Stream influence on the time-mean atmosphere is modulated on synoptic time scales, and enhanced when the EDJ is farthest south.

54 ENVIRONMENTAL SCIENCES↗