检索结果-内蒙古大学图书馆

MODERN PHYSICS LETTERS A 1991年第11期6卷 1023-1043页

作者： MIGDAL, AA Physics Department and Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 USA

A time-independent field theoretical framework for turbulence is suggested, based upon a variational principle for a stationary solution of the Fokker-Planck equation. We obtain a functional equation for the effective Action of this spatial field theory and investigate its general properties and some numerical solutions. The equation is completely universal, and allows for the scale invariant solutions in the inertial range. The critical indices are not fixed at the kinematical level, but rather should be found from certain eigenvalue conditions, as in the field theory of critical phenomena. Unlike the Wyld field theory, there are no divergences in our Feynman integrals, due to some magic cancellations. The simplest possible Gaussian approximation yields crude but still reasonable results (there are deviations from Kolmogorov scaling in 3 dimensions, but at 2.7544 dimensions it would be exact). Our approach allows us to study some new problems, such as spontaneous parity breaking in 3d turbulence. It turns out that with the appropriate helicity term added to the velocity correlation function, logarithmic infrared divergences arise in our field theory which effectively eliminates these terms. In order to build a quantitative theory of turbulence, one should consider more sophisticated Ansatz for the effective Action, which would require serious numerical work.

关键词：

来源：评论

学校读者我要写书评

暂无评论

A Simple Framework of Conservative Algorithms for the Coupled Nonlinear Schrdinger Equations with Multiply Components

引用

Communications in Theoretical Physics 2014年第6期61卷 703-709页

作者：钱旭宋松和李伟斌 Department of Mathematics and Systems Science National University of Defense Technology Program in Applied and Computational Mathematics Princeton University State Key Laboratory of High Performance Computing National University of Defense Technology

Considering the coupled nonlinear Schr¨odinger system with multiply components, we provide a novel framework for constructing energy-preserving algorithms. In detail, based on the high order compact finite difference method, Fourier pseudospectral method and wavelet collocation method for spatial discretizations, a series of high accurate conservative algorithms are presented. The proposed algorithms can preserve the corresponding discrete charge and energy conservation laws exactly, which would guarantee their numerical stabilities during long time ***, several analogous multi-symplectic algorithms are constructed as comparison. Numerical experiments for the unstable plane waves will show the advantages of the proposed algorithms over long time and verify the theoretical analysis.

关键词： conservative algorithm coupled nonlinear SchrSdinger equation multiply components unstablewave

来源：评论

学校读者我要写书评

暂无评论

A comparative analysis of optimization and generalization properties of two-layer neural network and random feature models under gradient descent dynamics

引用

Science China mathematics 2020年第7期63卷 1235-1258页

作者： Weinan E Chao Ma Lei Wu Department of Mathematics Princeton UniversityPrincetonNJ 08544USA The Program in Applied and Computational Mathematics Princeton UniversityNJ 08544USA Beijing Institute of Big Data Research Beijing 100871China

A fairly comprehensive analysis is presented for the gradient descent dynamics for training two-layer neural network models in the situation when the parameters in both layers are *** initialization schemes as well as general regimes for the network width and training data size are *** the overparametrized regime,it is shown that gradient descent dynamics can achieve zero training loss exponentially fast regardless of the quality of the *** addition,it is proved that throughout the training process the functions represented by the neural network model are uniformly close to those of a kernel *** general values of the network width and training data size,sharp estimates of the generalization error are established for target functions in the appropriate reproducing kernel Hilbert space.

关键词： two-layer neural network random feature model Gram matrix generalization error

来源：评论

学校读者我要写书评

暂无评论

Machine learning from a continuous viewpoint,I

引用

Science China mathematics 2020年第11期63卷 2233-2266页

作者： Weinan E Chao Ma Lei Wu Department of Mathematics Princeton UniversityPrincetonNJ 08544USA The Program in Applied and Computational Mathematics Princeton UniversityPrincetonNJ 08544USA Beijing Institute of Big Data Research Beijing 100871China

We present a continuous formulation of machine learning,as a problem in the calculus of variations and differential-integral equations,in the spirit of classical numerical *** demonstrate that conventional machine learning models and algorithms,such as the random feature model,the two-layer neural network model and the residual neural network model,can all be recovered(in a scaled form)as particular discretizations of different continuous *** also present examples of new models,such as the flow-based random feature model,and new algorithms,such as the smoothed particle method and spectral method,that arise naturally from this continuous *** discuss how the issues of generalization error and implicit regularization can be studied under this framework.

关键词： machine learning continuous formulation flow-based model gradient flow particle approximation

来源：评论

学校读者我要写书评

暂无评论

From Dyson models to many-body quantum chaos

引用

Physical Review B 2025年第3期111卷 035147-035147页

作者： Alexei Andreanov Matteo Carrega Jeff Murugan Jan Olle Dario Rosa Ruth Shir Center for Theoretical Physics of Complex Systems Institute for Basic Science (IBS) Daejeon 34126 Korea Basic Science Program Korea University of Science and Technology (UST) Daejeon 34113 Korea CNR-SPIN Via Dodecaneso 33 16146 Genova Italy The Laboratory for Quantum Gravity & Strings Department of Mathematics and Applied Mathematics University of Cape Town Cape Town 7701 South Africa The National Institute for Theoretical and Computational Sciences Private Bag X1 Matieland 7602 South Africa Max Planck Institute for the Science of Light 91058 Erlangen Germany ICTP South American Institute for Fundamental Research Instituto de Física Teórica UNESP—University of Estadual Paulista Rua Dr. Bento Teobaldo Ferraz 271 01140-070 São Paulo SP Brazil Department of Physics and Materials Science University of Luxembourg L-1511 Luxembourg Luxembourg

A deep understanding of the mechanisms underlying many-body quantum chaos is one of the big challenges in contemporary theoretical physics. We tackle this problem in the context of a set of perturbed quadratic Sachdev-Ye-Kitaev (SYK) Hamiltonians defined on graphs. This allows us to disentangle the geometrical properties of the underlying single-particle problem and the importance of the interaction terms, showing that the former is the dominant feature ensuring the single-particle to many-body chaotic transition. Our results are verified numerically with state-of-the-art numerical techniques, capable of extracting eigenvalues in a desired energy window of very large Hamiltonians. Our approach essentially provides a new way of viewing many-body chaos from a single-particle perspective.

关键词： Quantum chaos

来源：评论

学校读者我要写书评

暂无评论

Accurate Formula for the Effective Conductivity of Highly Clustered Two-Phase Materials

arXiv

引用

arXiv 2025年

作者： Skolnick, Murray Torquato, Salvatore Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Chemistry Department of Physics Princeton Materials Institute and Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Two-phase heterogeneous materials arising in a variety of natural and synthetic situations exhibit a wide-variety of microstructures and thus display a broad-spectrum effective physical properties. Given that such properties of disordered materials generally depend on an infinite-set of microstructural correlation functions that are typically unobtainable, in practice, one must consider rigorous bounds and approximations on the effective properties that depend on a limited set of nontrivial microstructural information. Torquato derived [Random Heterogeneous Materials, Microstructure and Macroscopic Properties (2002)] such an approximation for the effective thermal/electrical conductivity of two-phase microstructures that perturb about those that realize the well-known self-consistent formula;a key feature of such microstructures being phase-inversion symmetry which can be observed in certain cellular, bicontinuous, and porous materials. Here, we show via extensive numerical simulations that this virtually unexamined approximation, which depends on up to three-point correlations, predicts accurately the effective conductivities of various two- and three-dimensional two-phase microstructures across phase volume fractions in which both phases can form large and well-connected clusters;including certain phase-inversion symmetric microstructures as well as phase-inversion asymmetric dispersions of certain fully penetrable particles. We also highlight the accurate sensitivity of this approximation to phase-connectedness properties by showing that it predicts percolation thresholds that are in good quantitative and/or qualitative agreement with known thresholds for the models considered here. Finally, we discuss how this formula can be used to design materials with desirable effective conductivity properties and thus aid in materials by design. © 2025, CC BY-SA.

关键词： Porous materials

来源：评论

学校读者我要写书评

暂无评论

Semi-Eulerian and High Order Gaussian Beam Methods for the Schrödinger Equation in the Semiclassical Regime

引用

Communications in computational Physics 2011年第3期9卷 668-687页

作者： Shi Jin Hao Wu Xu Yang Department of Mathematics University of WisconsinMadisonWI 53706USA Department of Mathematical Sciences Tsinghua UniversityBeijing 10084China Program in Applied and Computational Mathematics Princeton UniversityNJ 08544USA

A novel Eulerian Gaussian beam method was developed in[8]to compute the Schrödinger equation efficiently in the semiclassical *** this paper,we introduce an efficient semi-Eulerian implementation of this *** new algorithm inherits the essence of the Eulerian Gaussian beam method where the Hessian is computed through the derivatives of the complexified level set functions instead of solving the dynamic ray tracing *** difference lies in that,we solve the ray tracing equations to determine the centers of the beams and then compute quantities of interests only around these *** yields effectively a local level set implementation,and the beam summation can be carried out on the initial physical space instead of the phase *** a consequence,it reduces the computational cost and also avoids the delicate issue of beam summation around the caustics in the Eulerian Gaussian beam ***,the semi-Eulerian Gaussian beam method can be easily generalized to higher order Gaussian beam methods,which is the topic of the second part of this *** numerical examples are provided to verify the accuracy and efficiency of both the first order and higher order semi-Eulerian methods.

关键词： Schrödinger equation semi-Eulerian Gaussian beam method high order methods

来源：评论

学校读者我要写书评

暂无评论

A NUMERICAL STUDY OF THE GAUSSIAN BEAM METHODS FOR SCHR(O|¨)DINGER-POISSON EQUATIONS

引用

Journal of computational mathematics 2010年第2期28卷 261-272页

作者： Shi Jin Hao Wu Xu Yang Department of Mathematics University of Wisconsin Madison W1 53706 USA Department of Mathematical Sciences Tsinghua University Beijing 100084 China Department of Mathematics University of Wisconsin Madison WI 53706 USA Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544USA

As an important model in quantum semiconductor devices, the SchrSdinger-Poisson equations have generated widespread interests in both analysis and numerical simulations in recent years. In this paper, we present Gaussian beam methods for the numerical simulation of the one-dimensional Schrodinger-Poisson equations. The Gaussian beam methods for high frequency waves outperform the geometrical optics method in that the former are accurate even around caustics. The purposes of the paper are first to develop the Gaussian beam methods, based on our previous methods for the linear SchrSdinger equation, for the Schrodinger-Poisson equations, and then check their validity for this weakly-nonlinear system.

关键词： Schrodinger-Poisson equations Gaussian beam methods Vlasov-Poisson equations

来源：评论

学校读者我要写书评

暂无评论

mathematics for cryo-electron microscopy

Mathematics for cryo-electron microscopy

引用

2018 International Congress of Mathematicians, ICM 2018

作者： Singer, Amit Department of Mathematics Program in Applied and Computational Mathematic Princeton University United States

ISBN: (纸本)9789813272934

Single-particle cryo-electron microscopy (cryo-EM) has recently joined X-ray crystallography and NMR spectroscopy as a high-resolution structural method for biological macromolecules. Cryo-EM was selected by Nature Methods as Method of the Year 2015, large scale investments in cryo-EM facilities are being made all over the world, and the Nobel Prize in Chemistry 2017 was awarded to Jacques Dubochet, Joachim Frank and Richard Henderson "for developing cryo-electron microscopy for the high-resolution structure determination of biomolecules in solution". This paper focuses on the mathematical principles underlying existing algorithms for structure determination using single particle cryo-EM. © ICM *** rights reserved.

关键词： X ray crystallography

来源：评论

学校读者我要写书评

暂无评论

The complex interplay between risk tolerance and the spread of infectious diseases

引用

Journal of the Royal Society Interface 2025年第225期22卷 20240486页

作者： Nguyen, Maximilian M. Freedman, Ari S. Cheung, Matthew A. Saad-Roy, Chadi M. Espinoza, Baltazar Grenfell, Bryan T. Levin, Simon A. Lewis-Sigler Institute Princeton University PrincetonNJ United States Department of Ecology and Evolutionary Biology Princeton University PrincetonNJ United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Miller Institute for Basic Research in Science University of California Berkeley BerkeleyCA United States Department of Integrative Biology University of California BerkeleyCA United States Biocomplexity Institute University of Virginia CharlottesvilleVA United States

Risk-driven behaviour provides a feedback mechanism through which individuals both shape and are collectively affected by an epidemic. We introduce a general and flexible compartmental model to study the effect of heterogeneity in the population with regard to risk tolerance. The interplay between behaviour and epidemiology leads to a rich set of possible epidemic dynamics. Depending on the behavioural composition of the population, we find that increasing heterogeneity in risk tolerance can either increase or decrease the epidemic size. We find that multiple waves of infection can arise due to the interplay between transmission and behaviour, even without the replenishment of susceptibles. We find that increasing protective mechanisms such as the effectiveness of interventions, the fraction of risk-averse people in the population and the duration of intervention usage reduce the epidemic overshoot. When the protection is pushed past a critical threshold, the epidemic dynamics enter an underdamped regime where the epidemic size exactly equals the herd immunity threshold and overshoot is eliminated. Finally, we can find regimes where epidemic size does not monotonically decrease with a population that becomes increasingly risk-averse. © 2025 The Author(s).

关键词： epidemic size heterogeneous behaviour intervention adoption and usage risk tolerance

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：