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

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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Phase-field-based lattice Boltzmann method for the transport of insoluble surfactant in two-phase flows

arXiv

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arXiv 2024年

作者： Zhan, Chengjie Liang, Hong Chai, Zhenhua Shi, Baochang School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Institute of Interdisciplinary Research for Mathematics and Applied Science Huazhong University of Science and Technology Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China Department of Physics Hangzhou Dianzi University Hangzhou310018 China

In this work, we present a general second-order phase-field model for the transport of insoluble surfactant in incompressible two-phase flows. In this model, the second-order local Allen-Cahn equation is applied for interface capturing, a general form of the simple scalar transport equation [S. S. Jain, J. Comput. Phys. 515, 113277 (2024)] is adopted for interface-confined surfactant, and the consistent and conservative Navier-Stokes equations with the Marangoni force is used for fluid flows. To solve this model, we further developed a mesoscopic lattice Boltzmann (LB) method, in which the LB model for surfactant transport equation is proposed under the general LB framework for the convection-diffusion type equation, and it can correctly recover the governing equation for surfactant transport. The accuracy of the present LB method is tested by several benchmark problems, and the numerical results show it has a good performance for the transport of the insoluble surfactant in two-phase flows. © 2024, CC BY-NC-ND.

关键词： Navier Stokes equations

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Score-Based Physics-Informed Neural Networks for High-Dimensional Fokker-Planck Equations

arXiv

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arXiv 2024年

作者： Hu, Zheyuan Zhang, Zhongqiang Em Karniadakis, George Kawaguchi, Kenji Department of Computer Science National University of Singapore Singapore119077 Singapore Department of Mathematical Sciences Worcester Polytechnic Institute WorcesterMA01609 United States Division of Applied Mathematics Brown University USA ProvidenceRI02912 United States Advanced Computing Mathematics and Data Division Pacific Northwest National Laboratory RichlandWA United States

The Fokker-Planck (FP) equation is a foundational partial differential equation (PDE) in stochastic processes involving Brownian motions. However, the curse of dimensionality (CoD) poses a formidable challenge when dealing with high-dimensional FP equations. Although Monte Carlo simulation and (vanilla) Physics-Informed Neural Networks (PINNs) have shown the potential to tackle CoD, both methods exhibit significant numerical errors in high dimensions when dealing with the probability density function (PDF) associated with Brownian motion. The point-wise PDF values tend to decrease exponentially as dimensionality increases, surpassing the precision of numerical simulations and resulting in substantial errors. Moreover, due to its massive sampling, Monte Carlo fails to offer fast sampling. modeling the logarithm likelihood (LL) via vanilla PINNs transforms the FP equation into a notoriously difficult Hamilton-Jacobi-Bellman (HJB) equation, which is impractical for PINN learning, whose error grows rapidly with dimension. To this end, we propose a novel approach utilizing a score-based solver to fit the score function in stochastic differential equations (SDEs). The score function, defined as the gradient of the LL, plays a fundamental role in inferring LL and PDF and enables fast SDE sampling, offering an effective means to overcome the CoD. Three fitting methods, Score Matching (SM), Sliced Score Matching (SSM), and Score-PINN, are introduced, each contributing unique advantages in computational complexity, accuracy, and generality. The proposed score-based SDE solver operates in two stages: first, employing score matching or Score-PINN to acquire the score function;and second, solving the LL via an ordinary differential equation (ODE) using the obtained score function. Comparative evaluations across these methods showcase varying trade-offs. The proposed methodology is evaluated across diverse SDEs, including anisotropic Ornstein-Uhlenbeck processes, geometric Browni

关键词： Fokker Planck equation

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Stability and Error Analysis of the Linear, Decoupled Imex Schemes for Sixth-Order Cahn-Hilliard-Type Equations

SSRN

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SSRN 2024年

作者： Zheng, Nan Shen, Jie Department of Applied Mathematics The Hong Kong Polytechnic University Hung Hom Kowloon Hong Kong School of Mathematical Sciences Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific Computing Xiamen University Fujian Xiamen361005 China School of Mathematical Science Eastern Institute of Technology Ningbo China

In this paper, we develop efficient implicit-explicit (IMEX) schemes for solving sixth-order Cahn-Hilliard-type equations based on the generalized scalar auxiliary variable (GSAV) approach. These novel schemes provide several remarkable advantages: (i) they are linear and only require solving one elliptic equation with constant coefficients at each time step;(ii) they are unconditionally energy stable and yield a uniform bound for the numerical solution. We also establish rigorous error estimates of up to fifth-order for these schemes, and present various numerical experiments to validate the stability and accuracy of the proposed schemes. © 2024, The Authors. All rights reserved.

关键词： Error analysis

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HOMOGENIZATION OF THE DISTRIBUTION-DEPENDENT STOCHASTIC ABSTRACT FLUID MODELS

arXiv

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arXiv 2023年

作者： Chen, Junlong Qiu, Zhaoyang Tang, Yanbin School of Sciences Great Bay University Great Bay Institute for Advanced Study Dongguan523000 China School of Mathematics University of Science and Technology of China Anhui Hefei230026 China School of Applied Mathematics Nanjing University of Finance and Economics Nanjing210046 China School of Mathematics and Statistics Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Hubei Wuhan430074 China

In this paper, we study the homogenization of the distribution-dependent stochastic abstract fluid models by combining the two−scale convergence and martingale representative approach. A general framework of the homogenization research is established for stochastic abstract fluid models which are the type of nonlinear partial differential equations including the (distribution-dependent) stochastic Navier-Stokes equations, stochastic magneto-hydrodynamic equations, stochastic Boussinesq equations, stochastic micropolar equations, stochastic Allen-Cahn equations. Copyright © 2023, The Authors. All rights reserved.

关键词： Navier Stokes equations

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State-space models are accurate and efficient neural operators for dynamical systems

arXiv

引用

arXiv 2024年

作者： Hu, Zheyuan Daryakenari, Nazanin Ahmadi Shen, Qianli Kawaguchi, Kenji Em Karniadakis, George Department of Computer Science National University of Singapore Singapore119077 Singapore Center for Biomedical Engineering School of Engineering Brown University ProvidenceRI02912 United States Division of Applied Mathematics Brown University ProvidenceRI02912 United States Advanced Computing Mathematics and Data Division Pacific Northwest National Laboratory RichlandWA United States

Physics-informed machine learning (PIML) has emerged as a promising alternative to classical methods for predicting dynamical systems, offering faster and more generalizable solutions. However, existing models, including recurrent neural networks (RNNs), transformers, and neural operators, face challenges such as long-time integration, long-range dependencies, chaotic dynamics, and extrapolation, to name a few. To this end, this paper introduces state-space models implemented in Mamba for accurate and efficient dynamical system operator learning. Mamba addresses the limitations of existing architectures by dynamically capturing long-range dependencies and enhancing computational efficiency through reparameterization techniques. To extensively test Mamba and compare against another 11 baselines, we introduce several strict extrapolation testbeds that go beyond the standard interpolation benchmarks. We demonstrate Mamba’s superior performance in both interpolation and challenging extrapolation tasks. Mamba consistently ranks among the top models while maintaining the lowest computational cost and exceptional extrapolation capabilities. Moreover, we demonstrate the good performance of Mamba for a real-world application in quantitative systems pharmacology for assessing the efficacy of drugs in tumor growth under limited data scenarios. Taken together, our findings highlight Mamba’s potential as a powerful tool for advancing scientific machine learning in dynamical systems modeling. (The code will be available at https://***/zheyuanhu01/State_ Space_Model_Neural_Operator upon acceptance.) © 2024, CC BY.

关键词： Recurrent neural networks

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Tackling the Curse of Dimensionality in Fractional and Tempered Fractional Pdes with Physics-Informed Neural Networks

SSRN

引用

SSRN 2024年

作者： Hu, Zheyuan Kawaguchi, Kenji Zhang, Zhongqiang Karniadakis, George Em National University of Singapore 21 Lower Kent Ridge Road 119077 Singapore Department of Mathematical Sciences Worcester Polytechnic Institute WorcesterMA01609 United States Division of Applied Mathematics Brown University 182 George Street ProvidenceRI02912 United States Advanced Computing Mathematics and Data Division Pacific Northwest National Laboratory RichlandWA United States

Fractional and tempered fractional partial differential equations (PDEs) are effective models of long-range interactions, anomalous diffusion, and non-local effects. Traditional numerical methods for these problems are mesh-based, thus struggling with the curse of dimensionality (CoD). Physics-informed neural networks (PINNs) offer a promising solution due to their universal approximation, generalization ability, and mesh-free training. In principle, Monte Carlo fractional PINN (MC-fPINN) estimates fractional derivatives using Monte Carlo methods and thus could lift CoD. However, this may cause significant variance and errors, hence affecting convergence;in addition, MC-fPINN is sensitive to hyperparameters. In general, numerical methods and specifically PINNs for tempered fractional PDEs are under-developed. Herein, we extend MC-fPINN to tempered fractional PDEs to address these issues, resulting in the Monte Carlo tempered fractional PINN (MC-tfPINN). To reduce possible high variance and errors from Monte Carlo sampling, we replace the one-dimensional (1D) Monte Carlo with 1D Gaussian quadrature, applicable to both MC-fPINN and MC-tfPINN. We validate our methods on various forward and inverse problems of fractional and tempered fractional PDEs, scaling up to 100,000 dimensions. Our improved MC-fPINN/MC-tfPINN using quadrature consistently outperforms the original versions in accuracy and convergence speed in very high dimensions. © 2024, The Authors. All rights reserved.

关键词： Numerical methods

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An alternated inertial general splitting method with linearization for the split feasibility problem

引用

Optimization 2023年第10期72卷 2585-2607页

作者： Qiao-Li Dong Lulu Liu Xiaolong Qin Jen-Chih Yao a Tianjin Key Laboratory for Advanced Signal Processing and College of Science Civil Aviation University of China Tianjin People's Republic of China b Department of Mathematics Hangzhou Normal University Hangzhou People's Republic of China c Research Center for Interneural Computing China Medical University Hospital China Medical University Taichung Taiwand Department of Applied Mathematics National Sun Yat-sen University Kaohsiung Taiwan

In this paper, we propose an alternated inertial general splitting method with linearization for a split feasibility problem. Four rules of inertial parameters and relaxation parameters are discussed, where the adaptive inertial parameters are firstly investigated. The convergence of the proposed method is established under standard conditions. The numerical examples are presented to test four choices of the parameters and illustrate the advantage of our methods. An application in signal processing is presented to illustrate the recovery of the proposed algorithm for the sparse signal.

关键词： Split feasibility problem alternated inertial general splitting method with linearization general splitting methods with linearization alternated inertial CQ algorithm 47H05 47J20 47J25 65K15 90C25

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Distributed Pinning Set Stabilization of Large-Scale Boolean Networks

arXiv

引用

arXiv 2022年

作者： Zhu, Shiyong Lu, Jianquan Sun, Liangjie Cao, Jinde The Department of Systems Science School of Mathematics Southeast University Nanjing210096 China The Advanced Modeling and Applied Computing Laboratory Department of Mathematics The University of Hong Kong Hong Kong The School of Mathematics Frontiers Science Center for Mobile Information Communication and Security Southeast University Nanjing210096 China The Purple Mountain Laboratories Nanjing211111 China The Yonsei Frontier Lab Yonsei University Seoul03722 Korea Republic of

In this article, we design the distributed pinning controllers to globally stabilize a Boolean network (BN), specially a sparsely connected large-scale one, towards a preassigned subset of state space through the node-to-node message exchange. Given an appointed state set, system nodes are partitioned into two disjoint parts, which respectively gather the nodes whose states are fixed or arbitrary with respect to the given state set. With such node division, three parts of pinned nodes are selected and the state feedback controllers are accordingly designed such that the resulting BN satisfies three conditions: the states of the other nodes cannot affect the nodal dynamics of fixed-state nodes, the subgraph of network structure induced by the fixed-state nodes is acyclic, and the steady state of the subnetwork induced by the fixed-state nodes lies in the state set given beforehand. If the BN after control is acyclic, the stabilizing time is revealed to be no more than the length of the longest path in the current network structure plus one. This enables us to further design the pinning controllers with the constraint of stabilizing time. Noting that the overall procedure runs in an exponentially increasing time with respect to the largest number of functional variables in the dynamics of pinned nodes, the sparsely-connected large-scale BNs can be well addressed in a reasonable amount of time. Finally, we demonstrate the applications of our theoretical results in a T-LGL survival signal network with 29 nodes and T-cell receptor signaling network with 90 nodes. Copyright © 2022, The Authors. All rights reserved.

关键词： Controllers

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A Column-Wise Update Algorithm for Sparse Stochastic Matrix Factorization

arXiv

引用

arXiv 2021年

作者： Xiao, Guiyun Bai, Zheng-Jian Ching, Wai-Ki School of Mathematical Sciences Xiamen University Xiamen361005 China School of Mathematical Sciences Fujian Provincial Key Laboratory on Mathematical Modeling & High Performance Scientific Computing Xiamen University Xiamen361005 China Advanced Modeling and Applied Computing Laboratory Department of Mathematics The University of Hong Kong Pokfulam Road Hong Kong

Nonnegative matrix factorization arises widely in machine learning and data analysis. In this paper, for a given factorization of rank r, we consider the sparse stochastic matrix factorization (SSMF) of decomposing a prescribed m-by-n stochastic matrix V into a product of an m-by-r stochastic matrix W and an r-by-n stochastic matrix H, where both W and H are required to be sparse. With the prescribed sparsity level, we reformulate the SSMF as an unconstrained nonconvex-nonsmooth minimization problem and introduce a column-wise update algorithm for solving the minimization problem. We show that our algorithm converges globally. The main advantage of our algorithm is that the generated sequence converges to a special critical point of the cost function, which is nearly a global minimizer over each column vector of the W-factor and is a global minimizer over the H-factor as a whole if there is no sparsity requirement on H. Numerical experiments on both synthetic and real data sets are given to demonstrate the effectiveness of our proposed *** Codes 65K05, 90C06, 90C26 Copyright © 2021, The Authors. All rights reserved.

关键词： Gradient methods

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