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Why is Grain Growth Not Curvature Flow?

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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

k-commutativity and measurement reduction for expectation values

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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

LANDSCAPE ESTIMATES OF THE INTEGRATED DENSITY OF STATES FOR JACOBI OPERATORS ON GRAPHS

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arXiv 2024年

作者： Shou, Laura Wang, Wei Zhang, Shiwen Condensed Matter Theory Center Joint Quantum Institute Department of Physics University of Maryland College ParkMD20742 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 Mathematics and Statistics University of Massachusetts Lowell Southwick Hall 11 University Ave. LowellMA01854 United States

We show the integrated density of states for a variety of Jacobi operators on graphs, such as the Anderson model and random hopping models on graphs with Gaussian heat kernel bounds, can be estimated from above and below in terms of the localization landscape counting function. Specific examples of these graphs include stacked and decorated lattices, graphs corresponding to band matrices, and aperiodic tiling graphs. The upper bound part of the landscape law also applies to the fractal Sierpinski gasket graph. As a consequence of the landscape law, we obtain landscape-based proofs of the Lifshitz tails in several models including random band matrix models, certain bond percolation Hamiltonians on Zd, and Jacobi operators on certain stacks of graphs. We also present intriguing numerical simulations exploring the behavior of the landscape counting function across various models. Copyright © 2024, The Authors. All rights reserved.

关键词： Graphic methods

Spectral Galerkin Method for Solving Elastic Wave Scattering Problems with Multiple Open Arcs

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SSRN

SSRN 2022年

作者： Jerez-Hanckes, Carlos Pinto, José Yin, Tao Faculty of Engineering and Sciences Universidad Adolfo Ibáñez Diagonal Las Torres 2700 Peñalolén Santiago Chile Institute of Computational Mathematics and Scientific Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

We study the elastic time-harmonic wave scattering problems on unbounded domains with boundaries composed of finite collections of disjoints finite open arcs (or cracks) in two dimensions. Specifically, we present a fast spectral Galerkin method for solving the associated weakly- and hyper-singular boundary integral equations (BIEs) arising from Dirichlet and Neumann boundary conditions, respectively. Discretization bases of the resulting BIEs employ weighted Chebyshev polynomials that capture the solutions’ edge behavior. We show that these bases guarantee exponential convergence in the polynomial degree when assuming analyticity of sources and arcs geometries. Numerical examples demonstrate the accuracy and robustness of the proposed method with respect to number of arcs and wavenumber. © 2022, The Authors. All rights reserved.

关键词： Boundary integral equations

On the hyper-singular boundary integral equation methods for dynamic poroelasticity: three dimensional case

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arXiv 2022年

作者： Zhang, Lu Xu, Liwei Yin, Tao School of Mathematical Sciences University of Electronic Science and Technology of China Sichuan Chengdu611731 China LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

In our previous work [SIAM J. Sci. Comput. 43(3) (2021) B784-B810], an accurate hyper-singular boundary integral equation method for dynamic poroelasticity in two dimensions has been developed. This work is devoted to studying the more complex and difficult three-dimensional problems with Neumann boundary condition and both the direct and indirect methods are adopted to construct combined boundary integral equations. The strongly-singular and hyper-singular integral operators are reformulated into compositions of weakly-singular integral operators and tangential-derivative operators, which allow us to prove the jump relations associated with the poroelastic layer potentials and boundary integral operators in a simple manner. Relying on both the investigated spectral properties of the strongly-singular operators, which indicate that the corresponding eigenvalues accumulate at three points whose values are only dependent on two Lamé constants, and the spectral properties of the Calderón relations of the poroelasticity, we propose low-GMRES-iteration regularized integral equations. Numerical examples are presented to demonstrate the accuracy and efficiency of the proposed methodology by means of a Chebyshev-based rectangular-polar solver. Copyright © 2022, The Authors. All rights reserved.

关键词： Boundary integral equations

Sensing With Communication Signals: From Information Theory to Signal Processing

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arXiv 2025年

作者： Liu, Fan Liu, Ya-Feng Cui, Yuanhao Masouros, Christos Xu, Jie Han, Tony Xiao Buzzi, Stefano Eldar, Yonina C. Jin, Shi National Mobile Communications Research Laboratory School of Information Science and Engineering Southeast University Nanjing210096 China 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 Department of Communication Engineering Beijing University of Posts and Telecommunications Beijing100876 China Department of Electronic and Electrical Engineering University College London LondonWC1E 7JE United Kingdom Guangdong518172 China Huawei Technologies Co. Ltd China Department of Electrical and Information Engineering University of Cassino and Southern Lazio CassinoI-03043 Italy Department of Electronics Information and Bioengineering Politecnico di Milano MilanoI-20133 Italy ParmaI-43124 Italy Faculty of Mathematics and Computer Science Weizmann Institute of Science Rehovot Israel

The Integrated Sensing and Communications (ISAC) paradigm is anticipated to be a cornerstone of the upcoming 6G networks. In order to optimize the use of wireless resources, 6G ISAC systems need to harness the communication data payload signals, which are inherently random, for both sensing and communication (S&C) purposes. This tutorial paper provides a comprehensive technical overview of the fundamental theory and signal processing methodologies for ISAC transmission with random communication signals. We begin by introducing the deterministic-random tradeoff (DRT) between S&C from an information-theoretic perspective, emphasizing the need for specialized signal processing techniques tailored to random ISAC signals. Building on this foundation, we review the core signal models and processing pipelines for communication-centric ISAC systems, and analyze the average squared auto-correlation function (ACF) of random ISAC signals, which serves as a fundamental performance metric for multi-target ranging tasks. Drawing insights from these theoretical results, we outline the design principles for the three key components of communication-centric ISAC systems: modulation schemes, constellation design, and pulse shaping filters. The goal is to either enhance sensing performance without compromising communication efficiency or to establish a scalable tradeoff between the two. We then extend our analysis from a single-antenna ISAC system to its multi-antenna counterpart, discussing recent advancements in multiinput multi-output (MIMO) precoding techniques specifically designed for random ISAC signals. We conclude by highlighting several open challenges and future research directions in the field of sensing with communication signals. Copyright © 2025, The Authors. All rights reserved.

关键词： Signal modulation

Covariance-Based Activity Detection in Cooperative Multi-Cell Massive MIMO: Scaling Law and Efficient Algorithms

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arXiv 2023年

作者： Wang, Ziyue Liu, Ya-Feng Wang, Zhaorui Yu, Wei The 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 The School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China Guangdong Provincial Key Laboratory of Future Networks of Intelligence The Chinese University of Hong Kong Shenzhen518172 China The Edward S. Rogers Sr. Department of Electrical and Computer Engineering University of Toronto TorontoONM5S 3G4 Canada

This paper focuses on the covariance-based activity detection problem in a multi-cell massive multiple-input multiple-output (MIMO) system. In this system, active devices transmit their signature sequences to multiple base stations (BSs), and the BSs cooperatively detect the active devices based on the received signals. While the scaling law for the covariance-based activity detection in the single-cell scenario has been extensively analyzed in the literature, this paper aims to analyze the scaling law for the covariance-based activity detection in the multi-cell massive MIMO system. Specifically, this paper demonstrates a quadratic scaling law in the multi-cell system, under the assumption that the path-loss exponent of the fading channel γ > 2. This finding shows that, in the multi-cell massive MIMO system, the maximum number of active devices that can be correctly detected in each cell increases quadratically with the length of the signature sequence and decreases logarithmically with the number of cells (as the number of antennas tends to infinity). Moreover, in addition to analyzing the scaling law for the signature sequences randomly and uniformly distributed on a sphere, the paper also establishes the scaling law for signature sequences based on a finite alphabet, which are easier to generate and store. Finally, this paper proposes two efficient accelerated coordinate descent (CD) algorithms with a convergence guarantee for solving the device activity detection problem. The first algorithm reduces the complexity of CD by using an inexact coordinate update strategy. The second algorithm avoids unnecessary computations of CD by using an active set selection strategy. Simulation results show that the proposed algorithms exhibit excellent performance in terms of computational efficiency and detection error probability. Copyright © 2023, The Authors. All rights reserved.

关键词： Fading channels

Monte Carlo PINNs: deep learning approach for forward and inverse problems involving high dimensional fractional partial differential equations

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arXiv 2022年

作者： Guo, Ling Wu, Hao Yu, Xiaochen Zhou, Tao Department of Mathematics Shanghai Normal University Shanghai China School of Mathematical sciences Tongji University Shanghai China Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

We introduce a sampling based machine learning approach, Monte Carlo physics informed neural networks (MC-PINNs), for solving forward and inverse fractional partial differential equations (FPDEs). As a generalization of physics informed neural networks (PINNs), our method relies on deep neural network surrogates in addition to a stochastic approximation strategy for computing the fractional derivatives of the DNN outputs. A key ingredient in our MC-PINNs is to construct an unbiased estimation of the physical soft constraints in the loss function. Our directly sampling approach can yield less overall computational cost compared to fPINNs proposed in [1] and thus provide an opportunity for solving high dimensional fractional PDEs. We validate the performance of MC-PINNs method via several examples that include high dimensional integral fractional Laplacian equations, parametric identification of time-space fractional PDEs, and fractional diffusion equation with random inputs. The results show that MC-PINNs is flexible and promising to tackle high-dimensional FPDEs. © 2022, CC BY.

关键词： Deep neural networks

Novel structure-preserving schemes for stochastic Klein–Gordon–Schrödinger equations with additive noise

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arXiv 2023年

作者： Hong, Jialin Hou, Baohui Sun, Liying Zhang, Xiaojing 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 Department of Mathematics Shanghai University Shanghai200444 China Capital Normal University Beijing100048 China

Stochastic Klein–Gordon–Schrödinger (KGS) equations are important mathematical models and describe the interaction between scalar nucleons and neutral scalar mesons in the stochastic environment. In this paper, we propose novel structure-preserving schemes to numerically solve stochastic KGS equations with additive noise, which preserve averaged charge evolution law, averaged energy evolution law, symplecticity, and multi-symplecticity. By applying central difference, sine pseudo-spectral method, or finite element method in space and modifying finite difference in time, we present some charge and energy preserved fully-discrete scheme for the original system. In addition, combining the symplectic Runge-Kutta method in time and finite difference in space, we propose a class of multi-symplectic discretizations preserving the geometric structure of the stochastic KGS equation. Finally, numerical experiments confirm theoretical findings. © 2023, CC BY.

关键词： Runge Kutta methods