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Physical Review Research 2019年第3期1卷 033017-033017页

作者： K. Mouloudakis M. Loulakis I. K. Kominis Department of Physics University of Crete Heraklion 71003 Greece School of Applied Mathematical and Physical Sciences National Technical University of Athens 15780 Athens Greece Institute of Applied and Computational Mathematics FORTH 70013 Heraklion Greece Institute of Theoretical and Computational Physics University of Crete Heraklion 70013 Greece

Spin-exchange collisions in alkali-metal vapors underlie several fundamental and applied investigations such as nuclear structure studies and tests of fundamental symmetries, ultrasensitive atomic magnetometers, magnetic resonance, and biomagnetic imaging. Spin-exchange collisions cause a loss of spin coherence and concomitantly produce spin noise, both phenomena being central to quantum metrology. We develop here the quantum-trajectory picture of spin-exchange collisions, consistent with their long-standing ensemble description using density matrices. We then use quantum trajectories to reveal the nature of spin-noise correlations that spontaneously build up in multispecies atomic vapors, frequently utilized in the most sensitive spin measurements.

关键词： Atomic & molecular collisions Quantum metrology Quantum sensing

Nature’s Microfluidic Transporter: Rotational Cytoplasmic Streaming at High Péclet Numbers

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Physical Review Letters 2008年第17期101卷 178102-178102页

作者： Jan-Willem van de Meent Idan Tuval Raymond E. Goldstein Department of Applied Mathematics and Theoretical Physics Centre for Mathematical Sciences University of Cambridge Wilberforce Road Cambridge CB3 0WA United Kingdom Cambridge Computational Biology Institute Centre for Mathematical Sciences University of Cambridge Wilberforce Road Cambridge CB3 0WA United Kingdom

Cytoplasmic streaming circulates the contents of large eukaryotic cells, often with complex flow geometries. A largely unanswered question is the significance of these flows for molecular transport and mixing. Motivated by “rotational streaming” in Characean algae, we solve the advection-diffusion dynamics of flow in a cylinder with bidirectional helical forcing at the wall. A circulatory flow transverse to the cylinder’s long axis, akin to Dean vortices at finite Reynolds numbers, arises from the chiral geometry. Strongly enhanced lateral transport and longitudinal homogenization occur if the transverse Péclet number is sufficiently large, with scaling laws arising from boundary layers.

关键词： Reynolds number

Wellposedness and scattering for the generalized Boussinesq equation

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arXiv 2021年

作者： Chen, Jie Guo, Boling Shao, Jie Institute of Applied Physics and Computational Mathematics Beijing100088 China Department of Mathematics Nanjing University of Science and Technology Nanjing210094 China School of Mathematical Sciences Peking University Beijing100871 China

In this paper, we show the local well-posedness of the generalized Boussinesq equation(gBQ) in L2(Rd),H1(Rd) and obtain the global well-posedness, finite-time blowup and small initial data scattering of gBQ in energy space H1(Rd). Moreover, we obtain the large radial initial data scattering of defocusing case for d ≥ 3 by using the method of Dodson-Murphy. © 2021, CC BY.

关键词： Partial differential equations

A nonlinear three-moment model for radiative transfer in spherical symmetry

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arXiv 2019年

作者： Li, Ruo Li, Weiming Zheng, Lingchao HEDPS & CAPT LMAM & School of Mathematical Sciences Peking University Beijing China Applied and Computational Mathematics Division Beijing Computational Science Research Center Beijing China Department of Mathematics Hong Kong University of Science & Technology Clear Water Bay Kowloon Hong Kong School of Mathematical Sciences Peking University Beijing China

We study the approximation of the radiative transfer equation with a relatively few moments in the spherically symmetric case. We propose a three-moment model based on choosing the beta distribution as the ansatz for the specific intensity. This ansatz enables our model to capture the anisotropy in the distribution function. The characteristic structure of the Riemann problem of the model is studied in detail. Numerical simulations demonstrate its validity in approximating the radiative transfer equation in the spherically symmetric case and its advantage in approximating highly anisotropic distribution functions in comparison to the Pn method. Copyright © 2019, The Authors. All rights reserved.

关键词： Radiative transfer

Deep Potentials for Materials Science

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arXiv 2022年

作者： Wen, Tongqi Zhang, Linfeng Wang, Han Weinan, E. Srolovitz, David J. Department of Mechanical Engineering The University of Hong Kong Hong Kong DP Technology Beijing China AI for Science Institute Beijing China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing China HEDPS CAPT College of Engineering Peking University Beijing China School of Mathematical Sciences Peking University Beijing China Department of Mathematics and Program in Applied and Computational Mathematics Princeton University Princeton United States Shenzhen China

To fill the gap between accurate (and expensive) ab initio calculations and efficient atomistic simulations based on empirical interatomic potentials, a new class of descriptions of atomic interactions has emerged and been widely applied;i.e., machine learning potentials (MLPs). One recently developed type of MLP is the Deep Potential (DP) method. In this review, we provide an introduction to DP methods in computational materials science. The theory underlying the DP method is presented along with a step-by-step introduction to their development and use. We also review materials applications of DPs in a wide range of materials systems. The DP Library provides a platform for the development of DPs and a database of extant DPs. We discuss the accuracy and efficiency of DPs compared with ab initio methods and empirical potentials. Copyright © 2022, The Authors. All rights reserved.

关键词： Calculations

Bayesian Parameter Inference for Partially Observed SDEs driven by Fractional Brownian Motion

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arXiv 2022年

作者： Maama, Mohamed Jasra, Ajay Ombao, Hernando Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955 Saudi Arabia Statistics Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955 Saudi Arabia

In this paper we consider Bayesian parameter inference for partially observed fractional Brownian motion (fBM) models. The approach we follow is to time-discretize the hidden process and then to design Markov chain Monte Carlo (MCMC) algorithms to sample from the posterior density on the parameters given data. We rely on a novel representation of the time discretization, which seeks to sample from an approximation of the posterior and then corrects via importance sampling;the approximation reduces the time (in terms of total observation time T) by O(T). This method is extended by using a multilevel MCMC method which can reduce the computational cost to achieve a given mean square error (MSE) versus using a single time discretization. Our methods are illustrated on simulated and real data. Copyright © 2022, The Authors. All rights reserved.

关键词： Mean square error

OnsagerNet: Learning stable and interpretable dynamics using a generalized Onsager principle

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arXiv 2020年

作者： Yu, Haijun Tian, Xinyuan Weinan, E. Li, Qianxiao NCMIS 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 Department of Mathematics The Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Mathematics National University of Singapore Singapore119077 Singapore Institute of High Performance Computing A*STAR Singapore138632 Singapore

We propose a systematic method for learning stable and physically interpretable dynamical models using sampled trajectory data from physical processes based on a generalized Onsager principle. The learned dynamics are autonomous ordinary differential equations parameterized by neural networks that retain clear physical structure information, such as free energy, diffusion, conservative motion and external forces. For high dimensional problems with a low dimensional slow manifold, an autoencoder with metric preserving regularization is introduced to find the low dimensional generalized coordinates on which we learn the generalized Onsager dynamics. Our method exhibits clear advantages over existing methods on benchmark problems for learning ordinary differential equations. We further apply this method to study Rayleigh-Bénard convection and learn Lorenz-like low dimensional autonomous reduced order models that capture both qualitative and quantitative properties of the underlying dynamics. This forms a general approach to building reduced order models for forced dissipative *** Codes 76E30, 34D20, 68T05/07, 82C35 Copyright © 2020, The Authors. All rights reserved.

关键词： Ordinary differential equations

A comparison of sequential and GPU-accelerated implementations of B-spline signal processing operations for 2-D and 3-D images

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A comparison of sequential and GPU-accelerated implementatio...

Workshops on Image Processing Theory, Tools and Applications, IPTA

作者： Alex Karantza Sonia Lopez Alarcon Nathan D. Cahill Department of Computer Engineering Rochester Institute of Technology Rochester NY USA Center for Applied and Computational Mathematics School of Mathematical Sciences Rochester Institute of Technology Rochester NY USA

ISBN: (纸本)9781467325851

B-spline signal processing operations are widely used in the analysis of two and three-dimensional images. In this paper, we investigate and compare some of these basic operations (direct transformations, indirect transformations, and computation of partial derivatives) by (1) recursive filter based implementations in MATLAB and C++, and (2) GPU-accelerated implementations in CUDA. All operations are compared at a variety of resolution levels on a 2-D panoramic image as well as a 3-D magnetic resonance (MR) image. Results indicate significant improvements in efficiency for the CUDA implementations. A MATLAB toolkit implementing the various B-spline signal processing tasks as well as the C++ and CUDA implementation described here is currently publicly available.

关键词： Splines (mathematics) Graphics processing units MATLAB Laplace equations Kernel Convolution Transforms

On the use of multiple compartment epidemiological models to describe the dynamics of inuenza in Europe

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arXiv 2019年

作者： Seroussi, Inbar Levy, Nir Paolotti, Daniela Sochen, Nir Yom-Tov, Elad Department of Microsoft Herzeliya46733 Israel Computational Epidemiology Laboratory Institute for Scientific Interchange Turin Department of Applied Mathematics School of Mathematical Sciences University of Tel Aviv Tel Aviv Israel

We develop a multiple compartment Susceptible-Infected-Recovered (SIR) model to analyze the spread of several infectious diseases through different geographic areas. Additionally, we propose a data-quality sensitive optimization framework for fitting this model to observed data. We fit the model to the temporal profile of the number of people infected by one of six inuenza strains in Europe over 7 inuenza seasons. In addition to describing the temporal and spatial spread of inuenza, the model provides an estimate of the inter-country and intra-country infection and recovery rates of each strain and in each season. We find that disease parameters remain relatively stable, with a correlation greater than 0:5 over seasons and stains. Clustering of inuenza strains by the inferred disease parameters is consistent with genome sub-types. Surprisingly, our analysis suggests that inter-country human mobility plays a negligible role in the spread of inuenza in Europe. Finally, we show that the model allows the estimation of disease load in countries with poor or none existent data from the disease load in adjacent countries. Our findings reveal information on the spreading mechanism of inuenza and on disease parameters. These can be used to assist in disease surveillance and in control of inuenza as well as of other infectious pathogens in a heterogenic environment. Copyright © 2019, The Authors. All rights reserved.

关键词： Disease control

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