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First-principles determination of the phonon-point defect scattering and thermal transport due to fission products in ThO2

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Physical Review Materials 2024年第2期8卷 025401-025401页

作者： Linu Malakkal Ankita Katre Shuxiang Zhou Chao Jiang David H. Hurley Chris A. Marianetti Marat Khafizov Computational Mechanics and Materials Department Idaho National Laboratory Idaho Falls Idaho 83415 USA Department of Scientific Computing Modeling and Simulation SP Pune University Pune 411007 India Idaho National Laboratory Idaho Falls Idaho 83415 USA Department of Applied Physics and Applied Mathematics Columbia University 500 West 120th Street New York New York 10027 USA Department of Mechanical and Aerospace Engineering The Ohio State University 201 West 19th Avenue Columbus Ohio 43210 USA

This work presents the first-principles calculations of the lattice thermal conductivity degradation due to point defects in thorium dioxide using an iterative solution of the Peierls-Boltzmann transport equation. We have used the nonperturbative Green's function methodology to compute the phonon-point defect scattering rates that consider the local distortion around the point defect, including the mass difference changes, interatomic force constants, and structural relaxation near the point defects. The point defects considered in this work include the vacancy of thorium (VTh) and oxygen (VO), substitutions of helium (HeTh), krypton (KrTh), zirconium (ZrTh), iodine (ITh), and xenon (XeTh) in the thorium site, and the three different configurations of the Schottky defects. The results of the phonon-defect scattering rate reveal that among all the considered intrinsic defects, the thorium vacancy and helium substitution in the thorium site scatter the phonon most due to the substantial changes in the force constant and structural distortions. The scattering of phonons due to the substitutional defects unveils that the zirconium atom scatters phonons the least, followed by xenon, iodine, krypton, and helium. This is contrary to the intuition that the scattering strength follows HeTh>KrTh>ZrTh>ITh>XeTh based on the mass difference. This striking difference in the zirconium phonon scattering is due to the local chemical environment changes. Zirconium is an electropositive element with valency similar to thorium and, therefore, can bond with the oxygen atoms, thus creating less force constant variance compared to iodine, an electronegative element, and the noble gases helium, xenon, and krypton. These results can serve as a benchmark for analytical models and help the engineering-scale modeling effort for nuclear design.

关键词： Carrier dynamics Energy materials Heat transfer Irradiation effects Lattice dynamics Nuclear power Phonons Thermal conductivity Thermal properties

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TAYLOR-HOOD LIKE FINITE ELEMENTS FOR NEARLY INCOMPRESSIBLE STRAIN GRADIENT ELASTICITY PROBLEMS

arXiv

引用

arXiv 2021年

作者： Liao, Yulei Ming, Pingbing Xu, Yun LSEC Institute of Computational Mathematics and Scientific/Engineering Computing AMSS Chinese Academy of Sciences No. 55 East Road Zhong-Guan-Cun Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing100088 China

We propose a family of mixed finite elements that are robust for the nearly incompressible strain gradient model, which is a fourth-order singular perturbed elliptic system. The element is similar to [C. Taylor and P. Hood, Comput. & Fluids, 1(1973), 73-100] in the Stokes flow. Using a uniform discrete B-B inequality for the mixed finite element pairs, we show the optimal rate of convergence that is robust in the incompressible limit. By a new regularity result that is uniform in both the materials parameter and the incompressibility, we prove the method converges with 1/2 order to the solution with strong boundary layer effects. Moreover, we estimate the convergence rate of the numerical solution to the unperturbed second-order elliptic system. Numerical results for both smooth solutions and the solutions with sharp layers confirm the theoretical *** Codes 65N15, 65N30 (Primary), 74K20 (Secondary) Copyright © 2021, The Authors. All rights reserved.

关键词： Elasticity

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Quantum Circuits for the Heat Equation with Physical Boundary Conditions Via Schrödingerisation

SSRN

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SSRN 2024年

作者： Jin, Shi Liu, Nana Yu, Yue School of Mathematical Sciences Institute of Natural Sciences MOE-LSC Shanghai Jiao Tong University Shanghai200240 China University of Michigan Shanghai Jiao Tong University Joint Institute Shanghai200240 China School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education National Center for Applied Mathematics in Hunan Xiangtan University Hunan Xiangtan411105 China

This paper explores the explicit design of quantum circuits for quantum simulation of partial differential equations (PDEs) with physical boundary conditions. These equations and/or their discretized forms usually do not evolve via unitary dynamics, thus are not suitable for quantum simulation. Boundary conditions (either time-dependent or independent) make the problem more difficult. To tackle this challenge, the Schrödingerisation method can be employed, which converts linear partial and ordinary differential equations with non-unitary dynamics into systems of Schrödinger-type equations, via the so-called warped phase transformation that maps the equation into one higher dimension. Despite advancements in Schrödingerisation techniques, the explicit implementation of quantum circuits for solving general PDEs, especially with physical boundary conditions, remains underdeveloped. We present two methods for handling the inhomogeneous terms arising from time-dependent physical boundary conditions. One approach utilizes Duhamel's principle to express the solution in integral form and employs linear combination of unitaries (LCU) for coherent state preparation. Another method applies an augmentation to transform the inhomogeneous problem into a homogeneous one. We then apply the quantum simulation technique from [CJL23] to transform the resulting non-autonomous system to an autonomous system in one higher dimension. We provide detailed implementations of these two methods and conduct a comprehensive complexity analysis in terms of queries to the time evolution input oracle. © 2024, The Authors. All rights reserved.

关键词： Boundary conditions

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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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Why is Grain Growth Not Curvature Flow?

arXiv

引用

arXiv 2024年

作者： Qiu, Caihao Srolovitz, David J. Rohrer, Gregory S. Han, Jian Salvalaglio, Marco Department of Materials Science and Engineering City University of Hong Kong Hong Kong Department of Mechanical Engineering The University of Hong Kong Pokfulam Road Hong Kong The University of Hong Kong Shenzhen China Department of Materials Science and Engineering Carnegie Mellon University PittsburghPA United States Institute of Scientific Computing TU Dresden Dresden01062 Germany Dresden Center for Computational Materials Science TU Dresden Dresden01062 Germany

Grain growth describes the increase in the mean grain size with time during the annealing of a polycrystal;it is widely accepted that this is driven by capillarity (surface tension). Although classically modeled and interpreted as mean curvature flow, a growing body of evidence has demonstrated that this is overly simplistic and inconsistent with experimental observations. Despite many proposals for the source of this failure, it remains a subject of ongoing debate. By considering the fundamental microscopic mechanism of grain boundary (GB) migration, we demonstrate that internal stress (shear coupling) associated with GB motion is the primary factor causing deviations in grain growth from mean curvature flow. This is achieved through the application of a two-dimensional bicrystallography-respecting continuum model for GB migration to grain growth, implemented in a diffuse-interface approach. These results are validated by comparison with atomistic simulations and the scatter in the curvature-velocity relationship is shown to be in excellent agreement with experimental results for grain growth in 3D polycrystals (not possible based on other proposed explanations). This work also demonstrates how to account for the mechanical effects that are integral to grain growth in crystalline solids. Copyright © 2024, The Authors. All rights reserved.

关键词： Polycrystals

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Smoothness and continuity of cost functionals for ECG mismatch computation

arXiv

引用

arXiv 2022年

作者： Grandits, Thomas Pezzuto, Simone Plank, Gernot Institute of Mathematics and Scientific Computing University of Graz Graz Austria Gottfried Schatz Research Center Division of Biophysics Medical University of Graz Graz Austria Center for Computational Medicine in Cardiology Euler Institute Università della Svizzera italiana Lugano Switzerland BioTechMed-Graz Graz Austria

The field of cardiac electrophysiology tries to abstract, describe and finally model the electrical characteristics of a heartbeat. With recent advances in cardiac electrophysiology, models have become more powerful and descriptive as ever. However, to advance to the field of inverse electrophysiological modeling, i.e. creating models from electrical measurements such as the ECG, the less investigated field of smoothness of the simulated ECGs w.r.t. model parameters need to be further explored. The present paper discusses smoothness in terms of the whole pipeline which describes how from physiological parameters, we arrive at the simulated ECG. Employing such a pipeline, we create a test-bench of a simplified idealized left ventricle model and demonstrate the most important factors for efficient inverse modeling through smooth cost functionals. Such knowledge will be important for designing and creating inverse models in future optimization and machine learning methods. Copyright © 2022, The Authors. All rights reserved.

关键词： Electrocardiograms

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Towards Efficient Large-Scale Network Slicing: An LP Dynamic Rounding-and-Refinement Approach

arXiv

引用

arXiv 2021年

作者： Chen, Wei-Kun Liu, Ya-Feng Liu, Fan Dai, Yu-Hong Luo, Zhi-Quan School of Mathematics and Statistics Beijing Key Laboratory on MCAACI Beijing Institute of Technology Beijing100081 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 Beijing100190 China Department of Electrical and Electronic Engineering Southern University of Science and Technology Shenzhen518055 China Shenzhen Research Institute of Big Data The Chinese University of Hong Kong Shenzhen518172 China

In this paper, we propose an efficient algorithm for the network slicing problem which attempts to map multiple customized virtual network requests (also called services) to a common shared network infrastructure and allocate network resources to meet diverse service requirements. The problem has been formulated as a mixed integer linear programming (MILP) formulation in the literature. We first propose a novel linear programming (LP) relaxation of the MILP formulation. We show that compared with a natural LP relaxation of the MILP formulation, the novel LP relaxation is much more compact in terms of smaller numbers of variables and constraints, and much stronger in terms of providing a better LP bound, which makes it particularly suitable to be embedded in an LP relaxation based algorithm. Then we design an efficient two-stage LP dynamic rounding-and-refinement algorithm based on this novel LP relaxation. In the first stage, the proposed algorithm uses an LP dynamic rounding procedure to place the virtual network functions of all services into cloud nodes while taking traffic routing of all services into consideration;in the second stage, the proposed algorithm uses an iterative LP refinement procedure to obtain a solution for traffic routing of all services with their end-to-end delay constraints being satisfied. Compared with the existing algorithms which either have an exponential complexity or return a low-quality solution, our proposed algorithm achieves a better trade-off between the solution quality and the computational complexity. In particular, the worst-case complexity of our proposed algorithm is polynomial, which makes it suitable for solving large-scale problems. Numerical results demonstrate the effectiveness and efficiency of our proposed algorithm. Copyright © 2021, The Authors. All rights reserved.

关键词： Iterative methods

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Quantum Circuits for the heat equation with physical boundary conditions via Schrödingerisation

arXiv

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arXiv 2024年

This paper explores the explicit design of quantum circuits for quantum simulation of partial differential equations (PDEs) with physical boundary conditions. These equations and/or their discretized forms usually do not evolve via unitary dynamics, thus are not suitable for quantum simulation. Boundary conditions (either time-dependent or independent) make the problem more difficult. To tackle this challenge, the Schrödingerisation method can be employed, which converts linear partial and ordinary differential equations with non-unitary dynamics into systems of Schrödinger-type equations, via the so-called warped phase transformation that maps the equation into one higher dimension. Despite advancements in Schrödingerisation techniques, the explicit implementation of quantum circuits for solving general PDEs, especially with physical boundary conditions, remains underdeveloped. We present two methods for handling the inhomogeneous terms arising from time-dependent physical boundary conditions. One approach utilizes Duhamel’s principle to express the solution in integral form and employs linear combination of unitaries (LCU) for coherent state preparation. Another method applies an augmentation to transform the inhomogeneous problem into a homogeneous one. We then apply the quantum simulation technique from [CJL23] to transform the resulting non-autonomous system to an autonomous system in one higher dimension. We provide detailed implementations of these two methods and conduct a comprehensive complexity analysis in terms of queries to the time evolution input oracle. © 2024, CC BY-NC-ND.

关键词： Ordinary differential equations

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Large contributions from optical phonons to thermal transport in hexagonal carbon-boron-nitrogen monolayers

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Physical Review B 2023年第23期108卷 235420-235420页

作者： Xue-Kun Chen (陈学坤) Yue Zhang (张越) Qing-Qing Luo (罗青清) Xue Chen (陈雪) Pin-Zhen Jia (贾聘真) Wu-Xing Zhou (周五星) School of Mathematics and Physics and Hunan Key Laboratory of Mathematical Modeling and Scientific Computing University of South China Hengyang 421001 China Department of Mathematics and Physics Hunan Institute of Technology Hengyang 421002 China School of Materials Science and Engineering and Hunan Provincial Key Laboratory of Advanced Materials for New Energy Storage and Conversion Hunan University of Science and Technology Xiangtan 411201 People's Republic of China

As representative semiconducting hexagonal carbon-boron-nitride lattices, C6BN and C2BN are experimentally realized two-dimensional (2D) plane materials and have recently become the focus of research. Herein, combining first-principles calculations with the Boltzmann transport equation, we performed a comprehensive study on the phonon interaction and thermal conductivity in C6BN and C2BN monolayers. It is found that the thermal conductivities of C6BN and C2BN monolayers at room temperature are reduced by 79% and 73%, respectively, due to four-phonon scattering, compared with the results including three-phonon scattering only. We can attribute this phenomenon to giant four-phonon scattering exclusive for the heat-carrying out-of-plane acoustic (ZA) phonons, because the reflection symmetry allows four-ZA processes much higher than three-ZA processes, and the quasiparallel behavior between the ZA and low-lying out-of-plane optical (ZO) branches contribute to a broad phase space for four-phonon scattering as well. Moreover, C6BN monolayer exhibits unusual behavior that optical phonons contribute about ∼60% to the overall thermal conductivity under the four-phonon picture, which differs from the traditional case that acoustic phonons dominate thermal conductivity. Unexpectedly, two low-lying ZO modes have as high as 38% contributions to the thermal transport at 300 K under the four-phonon picture, causing 60% contribution of optical phonon modes, apparently larger than that of the three-phonon case (15%) and many other 2D materials, also indicating the four-phonon scattering has a more significant effect on acoustic phonons than on optical phonons. This finding not only highlights insight into the nature of phonon transport, but also provides a promising strategy for manipulation of heat transport based on optical phonon modes.

关键词： Phonons Thermal conductivity Boron nitride Graphene First-principles calculations Lattice-Boltzmann methods

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k-commutativity and measurement reduction for expectation values

arXiv

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arXiv 2023年

作者： DalFavero, Ben Sarkar, Rahul Camps, Daan Sawaya, Nicolas LaRose, Ryan Center for Quantum Computing Science and Engineering Michigan State University East LansingMI48823 United States Institute for Computational & Mathematical Engineering Stanford University United States National Energy Research Scientific Computing Center Lawrence Berkeley National Laboratory BerkeleyCA United States HPI Biosciences OaklandCA94608 United States Azulene Labs Inc. San FranciscoCA94115 United States

We introduce a notion of commutativity between operators on a tensor product space, nominally Pauli strings on qubits, that interpolates between qubit-wise commutativity and (full) commutativity. We apply this notion, which we call k-commutativity, to measuring expectation values of observables in quantum circuits and show a reduction in the number measurements at the cost of increased circuit depth. Last, we discuss the asymptotic measurement complexity of k-commutativity for several families of n-qubit Hamiltonians, showing examples with O(1), O(√n), and O(n) scaling. © 2023, CC BY.

关键词： Qubits

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