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Thermodynamics up to the melting point in a TaVCrW high entropy alloy: Systematic ab initio study aided by machine learning potentials

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Physical Review B 2022年第21期105卷 214302-214302页

作者： Ying Zhou Prashanth Srinivasan Fritz Körmann Blazej Grabowski Roger Smith Pooja Goddard Andrew Ian Duff School of Science Loughborough University LE11 3TU United Kingdom Institute of Materials Science University of Stuttgart Pfaffenwaldring 55 D-70569 Stuttgart Germany Materials Science and Engineering Delft University of Technology 2628 CD Delft The Netherlands Department for Computational Materials Design Max-Planck-Institut für Eisenforschung GmbH 40237 Düsseldorf Germany Scientific Computing Department STFC Daresbury Laboratory Warrington WA4 4AD United Kingdom

Multi-principal-component alloys have attracted great interest as a novel paradigm in alloy design, with often unique properties and a vast compositional space auspicious for materials discovery. High entropy alloys (HEAs) belong to this class and are being investigated for prospective nuclear applications with reported superior mechanical properties including high-temperature strength and stability compared to conventional alloys. computational materials design has the potential to play a key role in screening such alloys, yet for high-temperature properties, challenges remain in finding an appropriate balance between accuracy and computational cost. Here we develop an approach based on density-functional theory (DFT) and thermodynamic integration aided by machine learning based interatomic potential models to address this challenge. We systematically evaluate and compare the efficiency of computing the full free energy surface and thermodynamic properties up to the melting point at different stages of the thermodynamic integration scheme. Our new approach provides a ×4 speed-up with respect to comparable free energy approaches at the level of DFT, with errors on high-temperature free energy predictions less than 1 meV/atom. Calculations are performed on an equiatomic HEA, TaVCrW—a low-activation composition and therefore of potential interest for next generation fission and fusion reactors.

关键词： Thermodynamics Disordered alloys Ab initio molecular dynamics Density functional theory

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Time-Division Energy Beamforming for Multiuser Wireless Power Transfer with Non-Linear Energy Harvesting

arXiv

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arXiv 2020年

作者： Ma, Ganggang Xu, Jie Liu, Ya-Feng Vedady Moghadam, Mohammad R. Shenzhen China Shenzhen China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China TransferFi Pte Ltd Singapore

Energy beamforming has emerged as a promising technique for enhancing the energy transfer efficiency of wireless power transfer (WPT). However, the performance of conventional energy beamforming may seriously degrade due to the nonlinear radio frequency (RF) to direct current (DC) conversion at energy receivers (ERs). To tackle this issue, this letter proposes a new time-division energy beamforming, in which different energy beamforming matrices (of high ranks in general) are time shared to exploit the "convex-concave" shape of the RF-DC power relation at ERs. By considering a particular time duration for WPT, we maximize the minimum harvested DC energy among all ERs, by jointly optimizing the energy beamforming matrices and the corresponding time allocation. In order to solve the non-convex min-DC-energy maximization problem, we propose an efficient solution by using the techniques of alternating optimization and successive convex approximation (SCA). Numerical results show that the proposed time-division energy beamforming design indeed outperforms the conventional multi-beam and time-division-multiple-access (TDMA)-based energy transmissions. Copyright © 2020, The Authors. All rights reserved.

关键词： Energy harvesting

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WAVEx: Stabilized Finite Elements for Spectral Wind Wave Models Using FEniCSx

arXiv

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arXiv 2023年

作者： Loveland, Mark Valseth, Eirik Meixner, Jessica Dawson, Clint Oden Institute for Computational Engineering and Sciences University of Texas at Austin 201 E. 24th St. AustinTX78712 United States The Department of Data Science The Norwegian University of Life Science Drøbakveien 31 Ås1433 Norway Department of Scientific Computing and Numerical Analysis Simula Research Laboratory Kristian Augusts gate 23 Oslo0164 Norway NWS NCEP EMC 830 University Research Court College ParkMD20740 United States

The prediction of the wind wave spectrum of the ocean using numerical models are an important tool for researchers, engineers, and communities living in coastal areas. The governing equation of the wind wave models, the Wave Action Balance Equation, presents unique challenges for implementing reliable numerical models because it is highly advective, highly nonlinear and high dimensional. Historically, most operational models have utilized finite difference methods, others have used finite volume methods but relatively few attempts at using finite element methods. In this work, we seek to fill this gap by investigating several different finite element discretizations of the Wave Action Balance Equation. The methods, which include streamline upwind Petrov-Galerkin (SUPG), least squares, and discontinuous Galerkin, are implemented and convergence properties are examined for some simplified 2-D test cases. Then, a new spectral wind wave model, WAVEx, is formulated and implemented for the full problem setting. WAVEx uses continuous finite elements along with SUPG stabilization in geographic/spectral space that allows for fully unstructured triangular meshes in both geographic and spectral space. For propagation in time, a second order fully implicit finite difference method is used. When source terms are active, a second order operator splitting scheme is used to linearize the problem. In the splitting scheme, propagation is solved using the implicit method and the nonlinear source terms are treated explicitly. Several test cases, including analytic tests and laboratory experiments, are demonstrated and results are compared to analytic solutions, observations, as well as output from another model that is used operationally. © 2023, CC BY.

关键词： Python

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Physics-informed neural networks to learn cardiac fiber orientation from multiple electroanatomical maps

arXiv

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arXiv 2022年

作者： Herrera, Carlos Ruiz Grandits, Thomas Plank, Gernot Perdikaris, Paris Costabal, Francisco Sahli Pezzuto, Simone Department of Mechanical and Metallurgical Engineering School of Engineering Pontificia Universidad Católica de Chile Santiago Chile Institute of Mathematics and Scientific Computing University of Graz Graz Austria Department of Mechanical Engineering and Applied Mechanics University of Pennsylvania Philadelphia United States Institute for Biological and Medical Engineering Schools of Engineering Medicine and Biological Sciences Pontificia Universidad Católica de Chile Santiago Chile Center for Computational Medicine in Cardiology Euler Institute Università della Svizzera italiana via Buffi 13 Lugano6900 Switzerland Gottfried Schatz Research Center Division of Biophysics Medical University of Graz Graz Austria

We propose FiberNet, a method to estimate in-vivo the cardiac fiber architecture of the human atria from multiple catheter recordings of the electrical activation. Cardiac fibers play a central role in the electromechanical function of the heart, yet they are difficult to determine in-vivo, and hence rarely truly patient-specific in existing cardiac models. FiberNet learns the fiber arrangement by solving an inverse problem with physics-informed neural networks. The inverse problem amounts to identifying the conduction velocity tensor of a cardiac propagation model from a set of sparse activation maps. The use of multiple maps enables the simultaneous identification of all the components of the conduction velocity tensor, including the local fiber angle. We extensively test FiberNet on synthetic 2-D and 3-D examples, diffusion tensor fibers, and a patient-specific case. We show that 3 maps are sufficient to accurately capture the fibers, also in the presence of noise. With fewer maps, the role of regularization becomes prominent. Moreover, we show that the fitted model can robustly reproduce unseen activation maps. We envision that FiberNet will help the creation of patient-specific models for personalized medicine. The full code is available at http://***/fsahli/FiberNet. © 2022, CC BY-NC-ND.

关键词： Inverse problems

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mathematical analysis and numerical approximations of density functional theory models for metallic systems

arXiv

引用

arXiv 2022年

作者： Dai, Xiaoying De Gironcoli, Stefano Yang, Bin Zhou, Aihui LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China CNR-IOM DEMOCRITOS Simulation Centre Via Bononea 265 Trieste34146 Italy NCMIS Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

In this paper, we investigate the energy minimization model of the ensemble Kohn-Sham density functional theory for metallic systems, in which a pseudo-eigenvalue matrix and a general smearing approach are involved. We study the invariance and the existence of the minimizer of the energy functional. We propose an adaptive double step size strategy and the corresponding preconditioned conjugate gradient methods for solving the energy minimization model. Under some mild but reasonable assumptions, we prove the global convergence of our algorithms. Numerical experiments show that our algorithms are efficient, especially for large scale metallic systems. In particular, our algorithms produce convergent numerical approximations for some metallic systems, for which the traditional self-consistent field iterations fail to converge. Copyright © 2022, The Authors. All rights reserved.

关键词： Conjugate gradient method

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Parameter Estimation with Maximal Updated Densities

arXiv

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arXiv 2022年

作者： Pilosov, Michael del-Castillo-Negrete, Carlos Yen, Tian Yu Butler, Troy Dawson, Clint Mind the Math LLC DenverCO80203 United States Oden Institute for Computational Engineering and Sciences University of Texas at Austin AustinTX78712 United States Sandia National Laboratories Center for Computing Research AlbuquerqueNM87175 United States Department of Mathematical and Statistical Sciences University of Colorado Denver DenverCO80202 United States

A recently developed measure-theoretic framework solves a stochastic inverse problem (SIP) for models where uncertainties in model output data are predominantly due to aleatoric (i.e., irreducible) uncertainties in model inputs (i.e., parameters). The subsequent inferential target is a distribution on parameters. Another type of inverse problem is to quantify uncertainties in estimates of "true" parameter values under the assumption that such uncertainties should be reduced as more data are incorporated into the problem, i.e., the uncertainty is considered epistemic. A major contribution of this work is the formulation and solution of such a parameter identification problem (PIP) within the measure-theoretic framework developed for the SIP. The approach is novel in that it utilizes a solution to a stochastic forward problem (SFP) to update an initial density only in the parameter directions informed by the model output data. In other words, this method performs "selective regularization" only in the parameter directions not informed by data. The solution is defined by a maximal updated density (MUD) point where the updated density defines the measure-theoretic solution to the PIP. Another significant contribution of this work is the full theory of existence and uniqueness of MUD points for linear maps with Gaussian distributions. Data-constructed Quantity of Interest (QoI) maps are also presented and analyzed for solving the PIP within this measure-theoretic framework as a means of reducing uncertainties in the MUD estimate. We conclude with a demonstration of the general applicability of the method on two problems involving either spatial or temporal data for estimating uncertain model parameters. The first problem utilizes spatial data from a stationary partial differential equation to produce a MUD estimate of an uncertain boundary condition. The second problem utilizes temporal data obtained from the state-of-the-art ADvanced CIRCulation (ADCIRC) model to obtain

关键词： Inverse problems

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POLYLLA: Polygonal meshing algorithm based on terminal-edge regions

arXiv

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arXiv 2022年

作者： Salinas, Sergio Hitschfeld-Kahler, Nancy Ortiz-Bernardin, Alejandro Si, Hang Department of Computer Sciences Universidad de Chile Av. Beauchef 851 RM Santiago8370456 Chile Computational and Applied Mechanics Laboratory Department of Mechanical Engineering Universidad de Chile Av. Beauchef 851 RM Santiago8370456 Chile Numerical Mathematics and Scientific Computing Weierstrass Institute for Applied Analysis and Stochastics Mohrenstr. 39 Berlin Berlin10117 Germany

This paper presents an algorithm to generate a new kind of polygonal mesh obtained from triangulations. Each polygon is built from a terminal-edge region surrounded by edges that are not the longest-edge of any of the two triangles that share them. The algorithm is termed Polylla and is divided into three phases. The first phase consists of labeling each edge of the input triangulation according to its size;the second phase builds polygons (simple or not) from terminal-edges regions using the label system;and the third phase transforms each non simple polygon into simple ones. The final mesh contains polygons with convex and non convex shape. Since Voronoi based meshes are currently the most used polygonal meshes, we compare some geometric properties of our meshes against constrained Voronoi meshes. Several experiments were run to compare the shape and size of polygons, the number of final mesh points and polygons. For the same input, Polylla meshes contain less polygons than Voronoi meshes, and the algorithm is simpler and faster than the algorithm to generate constrained Voronoi meshes. Finally, we have validated Polylla meshes by solving the Laplace equation on an L-shaped domain using the Virtual Element Method (VEM). We show that the numerical performance of the VEM using Polylla meshes and Voronoi meshes is similar. Copyright © 2022, The Authors. All rights reserved.

关键词： Mesh generation

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LANDSCAPE APPROXIMATION OF THE GROUND STATE EIGENVALUE FOR GRAPHS AND RANDOM HOPPING MODELS

arXiv

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arXiv 2022年

作者： Shou, Laura Wang, Wei Zhang, Shiwen School of Mathematics University of Minnesota 206 Church St SE MinneapolisMN55455 United States LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China Department of Mathematical Sciences University of Massachusetts Lowell South-wick Hall 11 University Ave. LowellMA01854 United States

We consider the localization landscape function u and ground state eigenvalue λ for operators on graphs. We first show that the maximum of the landscape function is comparable to the reciprocal of the ground state eigenvalue if the operator satisfies certain semigroup kernel upper bounds. This implies general upper and lower bounds on the landscape product λu∞ for several models, including the Anderson model and random hopping (bond-disordered) models, on graphs that are roughly isometric to d, as well as on some fractal-like graphs such as the Sierpinski gasket graph. Next, we specialize to a random hopping model on , and show that as the size of the chain grows, the landscape product λu∞ approaches π2/8 for Bernoulli off-diagonal disorder, and has the same upper bound of π2/8 for Uniform([0,1]) off-diagonal disorder. We also numerically study the random hopping model when the band width (hopping distance) is greater than one, and provide strong numerical evidence that a similar approximation holds for low-lying energies in the spectrum. © 2022, CC BY-NC-ND.

关键词： Ground state

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Stability implies robust convergence of a class of preconditioned parallel-in-time iterative algorithms

arXiv

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arXiv 2021年

作者： Wu, Shu-Lin Zhou, Tao Zhou, Zhi School of Mathematics and Statistics Northeast Normal University Changchun130024 China LSEC Institute of Computational Mathematics and Scientific/Engineering Computing AMSS Chinese Academy of Sciences Beijing100190 China Department of Applied Mathematics Hong Kong Polytechnic University Kowloon Hong Kong

Solving evolutionary equations in a parallel-in-time manner is an attractive topic and many algorithms are proposed in recent two decades. The algorithm based on the block α-circulant preconditioning technique has shown promising advantages, especially for wave propagation problems. By fast Fourier transform for factorizing the involved circulant matrices, the preconditioned iteration can be computed efficiently via the so-called diagonalization technique, which yields a direct parallel implementation across all time levels. In recent years, considerable efforts have been devoted to exploring the convergence of the preconditioned iteration by studying the spectral radius of the iteration matrix, and this leads to many case-by-case studies depending on the used time-integrator. In this paper, we propose a unified convergence analysis for the algorithm applied to u0 + Au = f, where σ(A) ⊂ C+ with σ(A) being the spectrum of A ∈ Cm×m. For any one-step method (such as the Runge-Kutta methods) with stability function R(z), we prove that the decay rate of the global error is bounded by α/(1 - α), provided the method is stable, i.e., maxλ∈σ(A) |R(∆tλ)| ≤ 1. For any linear multistep method, such a bound becomes cα/(1 - cα), where c ≥ 1 is a constant specified by the multistep method itself. Our proof only relies on the stability of the time-integrator and the estimate is independent of the step size ∆t and the spectrum σ(A). © 2021, CC0.

关键词： Stability

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Cramér-rao bound optimization for joint radar-communication design

arXiv

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arXiv 2021年

作者： Liu, Fan Liu, Ya-Feng Li, Ang Masouros, Christos Eldar, Yonina C. The Department of Electrical and Electronic Engineering Southern University of Science and Technology Shenzhen518055 China The State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematicsand Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China The School of Information and Communications Engineering Faculty of Electronic and Information Engineering Xi’an Jiaotong University Xi’anShaanxi710049 China The Department of Electronic and Electrical Engineering University College London LondonWC1E 7JE United Kingdom The Faculty of Mathematics and Computer Science Weizmann Institute of Science Rehovot Israel

In this paper, we propose multi-input multi-output (MIMO) beamforming designs towards joint radar sensing and multi-user communications. We employ the Cramér-Rao bound (CRB) as a performance metric of target estimation, under both point and extended target scenarios. We then propose minimizing the CRB of radar sensing while guaranteeing a pre-defined level of signal-to-interference-plus-noise ratio (SINR) for each communication user. For the single-user scenario, we derive a closed form for the optimal solution for both cases of point and extended targets. For the multi-user scenario, we show that both problems can be relaxed into semidefinite programming by using the semidefinite relaxation approach, and prove that the global optimum can always be obtained. Finally, we demonstrate numerically that the globally optimal solutions are reachable via the proposed methods, which provide significant gains in target estimation performance over state-of-the-art benchmarks. Copyright © 2021, The Authors. All rights reserved.

关键词： Signal to noise ratio

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