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Quantum phase transition from mixed atom-molecule phase to pure molecule phase: Characteristic scaling laws and Berry-curvature signature

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Physical Review A 2011年第2期84卷 023605-023605页

作者： Sheng-Chang Li Li-Bin Fu Science and Technology Computation Physics Laboratory Institute of Applied Physics and Computational Mathematics Beijing 100088 China Graduate School China Academy of Engineering Physics Beijing 100088 China Center for Applied Physics and Technology Peking University Beijing 100084 China

We investigate the quantum phase transition in an ultracold atom-molecule conversion system. It is found that the system undergoes a phase transition from a mixed atom-molecule phase to a pure molecule phase when the energy bias exceeds a critical value. By constructing a coherent state as variational state, we get a good approximation of the quantum ground state of the system. Using this variational state, we deduce the critical point analytically. We then discuss the scaling laws characterizing the transition and obtain the corresponding critical exponents. Furthermore, the Berry curvature signature of the transition is studied. In particular, we find that the derivatives of the Berry curvature with respect to total particle number intersect at the critical point. The underlying mechanism of this finding is discussed as well.

关键词： ATOMS PHASE transformations (Physics) SCALING laws (Nuclear physics) QUANTUM theory PARTICLES (Nuclear physics) QUANTUM Hall effect

Diffusion spreadability as a probe of the microstructure of complex media across length scales

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arXiv 2021年

作者： Torquato, Salvatore Department of Chemistry Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Understanding time-dependent diffusion processes in multiphase media is of great importance in physics, chemistry, materials science, petroleum engineering and biology. Consider the time-dependent problem of mass transfer of a solute between two phases and assume that the solute is initially distributed in one phase (phase 2) and absent from the other (phase 1). We desire the fraction of total solute present in phase 1 as a function of time, S(t), which we call the spreadability, since it is a measure of the spreadability of diffusion information as a function of time. We derive exact direct-space formulas for S(t) in any Euclidean space dimension d in terms of the autocovariance function as well as corresponding Fourier representations of S(t) in terms of the spectral density, which are especially useful when scattering information is available experimentally or theoretically. These are singular results because they are rare examples of mass transport problems where exact solutions are possible. We derive closed-form general formulas for the short- and long-time behaviors of the spreadability in terms of crucial small- and large-scale microstructural information, respectively. The long-time behavior of S(t) enables one to distinguish the entire spectrum of microstructures that span from hyperuniform to nonhyperuniform media. For hyperuniform media, disordered or not, we show that the "excess" spreadability, S(∞) − S(t), decays to its long-time behavior exponentially faster than that of any nonhyperuniform two-phase medium, the "slowest" being antihyperuniform media. The stealthy hyperuniform class is characterized by an excess spreadability with the fastest decay rate among all translationally invariant microstructures. We obtain exact results for S(t) for a variety of specific ordered and disordered model microstructures across dimensions that span from hyperuniform to antihyperuniform media. Moreover, we establish a remarkable connection between the spreadability

关键词： Microstructure

DeePCG: Constructing coarse-grained models via deep neural networks

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arXiv 2018年

作者： Weinan, E. Zhang, Linfeng Han, Jiequn Wang, Han Car, Roberto Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Institute of Applied Physics and Computational Mathematics Fenghao East Road 2 Beijing100094 China Caep Software Center for High Performance Numerical Simulation Huayuan Road 6 Beijing100088 China Program in Applied and Computational Mathematics Princeton Institute for Science and Technology of Materials Princeton University PrincetonNJ08544 United States Department of Mathematics and Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Beijing Institute of Big Data Research Beijing100871 China

We introduce a general framework for constructing coarse-grained potential models without ad hoc approximations such as limiting the potential to two- A nd/or three-body contributions. The scheme, called Deep Coarse-Grained Potential (abbreviated DeePCG), exploits a carefully crafted neural network to construct a many-body coarse-grained potential. The network is trained with full atomistic data in a way that preserves the natural symmetries of the system. The resulting model is very accurate and can be used to sample the configurations of the coarse-grained variables in a much faster way than with the original atomistic model. As an application we consider liquid water and use the oxygen coordinates as the coarse-grained variables, starting from a full atomistic simulation of this system at the ab initio molecular dynamics level. We find that the two-body, three-body, and higher-order oxygen correlation functions produced by the coarse-grained and full atomistic models agree very well with each other, illustrating the effectiveness of the DeePCG model on a rather challenging task. Copyright © 2018, The Authors. All rights reserved.

关键词： Deep neural networks

UAV-Aided Data Acquisition Using Gaining-Sharing Knowledge Optimization Algorithm

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Computers, Materials & Continua 2022年第9期72卷 5999-6013页

作者： Rania M Tawfik Hazem A.A.Nomer M.Saeed Darweesh Ali Wagdy Mohamed Hassan Mostafa Wireless Intelligent Networks Center(WINC) School of Engineering and Applied SciencesNile UniversityGiza12677Egypt School of Information Technology and Computer Science(ITCS) Nile UniversityGiza12677Egypt Operations Research Department Faculty of Graduate Studies for Statistical ResearchCairo UniversityGiza12613Egypt Department of Mathematics and Actuarial Science School of Science and EngineeringThe American University in CairoEgypt Electronics and Communications Engineering Department Cairo UniversityEgypt University of Science and Technology Nanotechnology and Nanoelectronics ProgramZewal City of Science and TechnologyOctober Gardens6th of OctoberGiza12578Egypt

Unmanned Aerial Vehicles(UAVs)provide a reliable and energyefficient solution for data collection from the Narrowband Internet of Things(NB-IoT)***,the UAV’s deployment optimization,including locations of the UAV’s stop points,is a necessity to minimize the energy consumption of the UAV and the NB-IoT devices and also to conduct the data collection *** this regard,this paper proposes GainingSharing Knowledge(GSK)algorithm for optimizing the UAV’s *** GSK,the number of UAV’s stop points in the three-dimensional space is encapsulated into a single individual with a fixed length representing an entire *** superiority of using GSK in the tackled problem is verified by simulation in seven *** provides significant results in all seven scenarios compared with other four optimization algorithms used before with the same ***,the NB-IoT is proposed as the wireless communication technology between the UAV and IoT devices.

关键词： NB-IoT UAV GSK stop points optimization

Introducing Grid WAR: Rethinking WAR for Starting Pitchers

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arXiv 2022年

作者： Brill, Ryan S. Wyner, Abraham J. Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania United States Dept. of Statistics and Data Science The Wharton School University of Pennsylvania United States

The baseball statistic "Wins Above Replacement" (WAR) has emerged as one of the most popular evaluation metrics. But it is not readily observed and tabulated;WAR is an estimate of a parameter in a vaguely defined model with all its attendant assumptions. Industry-standard models of WAR for starting pitchers from FanGraphs and Baseball Reference all assume that season-long averages are sufficient statistics for a pitcher’s performance. This provides an invalid mathematical foundation for many reasons, especially because WAR should not be linear with respect to any counting statistic. To repair this defect, as well as many others, we devise a new measure, Grid WAR, which accurately estimates a starting pitcher’s WAR on a per-game basis. The convexity of Grid WAR diminishes the impact of "blow-up" games and up-weights exceptional games, raising the valuation of pitchers like Sandy Koufax, Whitey Ford, and Catfish Hunter who exhibit fundamental game-by-game variance. Although Grid WAR is designed to accurately measure historical performance, it has predictive value insofar as a pitcher’s Grid WAR is better than Fangraphs’ FIP WAR at predicting future performance. Finally, at https://*** we host a Shiny app which displays the Grid WAR results of each MLB game since 1952, including career, season, and game level results, which updates automatically every morning. Copyright © 2022, The Authors. All rights reserved.

关键词： Baseball

The Loser’s Curse and the Critical Role of the Utility Function

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arXiv 2024年

A longstanding question in the judgment and decision making literature is whether experts, even in high-stakes environments, exhibit the same cognitive biases observed in controlled experiments with inexperienced participants. In their seminal work, Massey and Thaler (2013) provide a notable example of bias and irrationality in expert decision making: general managers’ behavior in the National Football League draft pick trade market. They argue that general managers systematically overvalue top draft picks, which generate less surplus value on average than later first-round picks, a phenomenon known as the loser’s curse. Their conclusion hinges on the assumption that general managers should use expected surplus value as their utility function for evaluating draft picks. This assumption, however, is neither explicitly justified nor necessarily aligned with the strategic complexities of constructing a National Football League roster. In this paper, we challenge their framework by considering alternative utility functions, particularly those that emphasize the acquisition of transformational players––those capable of dramatically increasing a team’s chances of winning the Super Bowl. Under a decision rule that prioritizes the probability of acquiring elite players, which we construct from a novel Bayesian hierarchical Beta regression model, general managers’ draft trade behavior appears rational rather than systematically flawed. More broadly, our findings highlight the critical role of carefully specifying a utility function when evaluating the quality of decisions. © 2024, CC BY.

关键词： Hierarchical systems

Deep learning inter-atomic potential for thermal and phonon behaviour of silicon carbide with quantum accuracy

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arXiv 2021年

作者： Fu, Baoqin Sun, Yandong Zhang, Linfeng Wang, Han Xu, Ben Key Laboratory of Radiation Physics and Technology of the Ministry of Education Institute of Nuclear Science and Technology Sichuan University Chengdu610064 China Graduate School China Academy of Engineering Physics Beijing100193 China Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing100088 China

Silicon carbide (SiC) is an essential material for next generation semiconductors and components for nuclear plants. It’s applications are strongly dependent on its thermal conductivity, which is highly sensitive to microstructures. Molecular dynamics (MD) simulation is the most used methods to address thermal transportation mechanisms in devices or microstructures of nano-meters. However, the implementation of MD is limited in SiC because of lacking accurate inter-atomic potentials. In this work, using the Deep Potential (DP) methodology, we developed two inter-atomic potentials (DP-*Corresponding author. IAPs) for SiC based on two adaptively generated datasets within the density functional approximations at the local density and the generalized gradient levels. These two DP-IAPs manifest their speed with quantum accuracy in lattice dynamics simulations as well as scattering rate analysis of phonon transportation. Combining with molecular dynamics simulations, the thermal transport and mechanical properties were systematically investigated. The presented methodology and the inter-atomic potentials pave the way for a systematic approach to model heat transport in SiC related devices using multiscale modelling. Copyright © 2021, The Authors. All rights reserved.

关键词： Silicon carbide

AUTOAMG(θ): AN AUTO-TUNED AMG METHOD BASED ON DEEP LEARNING FOR STRONG THRESHOLD

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arXiv 2023年

作者： Zou, Haifeng Xu, Xiaowen Zhang, Chen-Song Mo, Zeyao Graduate School of China Academy of Engineering Physics China Academy of Engineering Physics China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics China Academy of Mathematics and Systems Science Chinese Academy of Sciences China

Algebraic Multigrid (AMG) is one of the most used iterative algorithms for solving large sparse linear equations Ax = b. In AMG, the coarse grid is a key component that affects the efficiency of the algorithm, the construction of which relies on the strong threshold parameter θ. This parameter is generally chosen empirically, with a default value in many current AMG solvers of 0.25 for 2D problems and 0.5 for 3D problems. However, for many practical problems, the quality of the coarse grid and the efficiency of the AMG algorithm are sensitive to θ;the default value is rarely optimal, and sometimes is far from it. Therefore, how to choose a better θ is an important question. In this paper, we propose a deep learning based auto-tuning method, AutoAMG(θ) for multiscale sparse linear equations, which are widely used in practical problems. The method uses Graph Neural Networks (GNNs) to extract matrix features, and a Multilayer Perceptron (MLP) to build the mapping between matrix features and the optimal θ, which can adaptively output θ values for different matrices. Numerical experiments show that AutoAMG(θ) can achieve significant speedup compared to the default θ value. Copyright © 2023, The Authors. All rights reserved.

关键词： Linear equations

CONVERGENCE SPEED AND APPROXIMATION ACCURACY OF NUMERICAL MCMC

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arXiv 2022年

作者： Cui, Tiangang Dong, Jing Jasra, Ajay Tong, Xin T. School of Mathematics Monash University Australia Graduate School of Business Columbia University United States Applied Mathematics and Computational Science Program Computer Electrical Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Saudi Arabia Department of Mathematics National University of Singapore Singapore

When implementing Markov Chain Monte Carlo (MCMC) algorithms, perturbation caused by numerical errors is sometimes inevitable. This paper studies how perturbation of MCMC affects the convergence speed and Monte Carlo estimation accuracy. Our results show that when the original Markov chain converges to stationarity fast enough and the perturbed transition kernel is a good approximation to the original transition kernel, the corresponding perturbed sampler has similar convergence speed and high approximation accuracy as well. We discuss two different analysis frameworks: ergodicity and spectral gap, both are widely used in the literature. Our results can be easily extended to obtain non-asymptotic error bounds for MCMC estimators. We also demonstrate how to apply our convergence and approximation results to the analysis of specific sampling algorithms, including Random walk Metropolis and Metropolis adjusted Langevin algorithm with perturbed target densities, and parallel tempering Monte Carlo with perturbed densities. Finally we present some simple numerical examples to verify our theoretical claims. Copyright © 2022, The Authors. All rights reserved.

关键词： Inverse problems