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arXiv 2025年

作者： Ruangkriengsin, Tachin Brandão, Rodolfo Wu, Katie Hwang, Jonghyun Boyko, Evgeniy Stone, Howard A. Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States School of Mathematics University of Bristol Fry Building Woodland Road BristolBS8 1UG United Kingdom Department of Mechanical and Aerospace Engineering Princeton University PrincetonNJ08544 United States Faculty of Mechanical Engineering Technion – Israel Institute of Technology Haifa3200003 Israel

The Weissenberg effect, or rod-climbing phenomenon, occurs in non-Newtonian fluids where the fluid interface ascends along a rotating rod. Despite its prominence, theoretical insights into this phenomenon remain limited. In earlier work, Joseph & Fosdick (Arch. Rat. Mech. Anal., vol. 49, 1973, pp. 321–380) employed domain perturbation methods for second-order fluids to determine the equilibrium interface height by expanding solutions based on the rotation speed. In this work, we investigate the time-dependent interface height through asymptotic analysis with dimensionless variables and equations using the Oldroyd-B model. We begin by neglecting surface tension and inertia to focus on the interaction between gravity and viscoelasticity. In the small-deformation scenario, the governing equations indicate the presence of a boundary layer in time, where the interface rises rapidly over a short time scale before gradually approaching a steady state. By employing a stretched time variable, we derive the transient velocity field and corresponding interface profile on this short time scale and recover the steady-state profile on a longer time scale. Subsequently, we reintroduce small but finite inertial effects to investigate their interplay with viscoelasticity and propose a criterion for determining the conditions under which rod-climbing occurs. © 2025, CC BY.

关键词： Non Newtonian liquids

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From Dyson models to many-body quantum chaos

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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

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

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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

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DYNAMICS OF VORTEX SURFACES IN 3 DIMENSIONS - THEORY AND SIMULATIONS

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PHYSICA D-NONLINEAR PHENOMENA 1989年第1期40卷 91-118页

作者： AGISHTEIN, ME MIGDAL, AA Department of Physics University of California at San Diego La Jolla CA 92093 USA1 1 Current address: Program in Applied and Computational Mathematics Princeton University Fine Hall Washington Road Princeton NY 08544-100 USA.

The dynamics of vortex surfaces in an ideal fluid is considered. The Hamiltonian and the action are constructed and topological conservation laws are discussed. The axially symmetric case is reduced to an effective 2d problem and studied numerically. There is qualitative correspondence with the results of Moore and Krasny for the purely 2d problem. The general case is approximated by means of a triangulated surface and a corresponding computer model is constructed, taking into account the topological conservation laws. The axially symmetric motion of the triangulated surface agrees with the 2d model, but there are some angular instabilities, which may lead to new vortex structures. The large-scale asymmetric 3d simulations with fairly developed instabilities are reported. The results agree with the general scenario of hierarchy of vortex structures.

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Computing Optimal Interfacial Structure of Modulated Phases

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Communications in computational Physics 2017年第1期21卷 1-15页

作者： Jie Xu Chu Wang An-Chang Shi Pingwen Zhang LMAM and School of Mathematical Sciences Peking UniversityBeijing 100871China Program in Applied and Computational Mathematics Princeton UniversityPrincetonNew Jersey 08544USA Department of Physics and Astronomy McMaster UniversityHamiltonOntario L8S4M1Canada

We propose a general framework of computing interfacial structures between two modulated *** we propose to use a computational box consisting of two half spaces,each occupied by a modulated phase with given position and *** boundary conditions and basis functions are chosen to be commensurate with the bulk *** observe that the ordered nature of modulated structures stabilizes the interface,which enables us to obtain optimal interfacial structures by searching local minima of the free energy *** framework is applied to the Landau-Brazovskii model to investigate interfaces between modulated phases with different relative positions and *** types of novel complex interfacial structures emerge from the calculations.

关键词： Interface modulated phase metastable state compatibility Landau-Brazovskiimodel

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Nuclear Neural Networks: Emulating Late Burning Stages in Core Collapse Supernova Progenitors

arXiv

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arXiv 2025年

作者： Grichener, Aldana Renzo, Mathieu Kerzendorf, Wolfgang E. Farmer, Rob de Mink, Selma E. Bellinger, Earl Patrick Chan, Chi-Kwan Chen, Nutan Farag, Ebraheem Justham, Stephen Steward Steward Observatory Department of Astronomy University of Arizona 933 North Cherry Avenue TucsonAZ85721 United States Max Planck Institute for Astrophysics Karl-Schwarzschild-Str. 1 Garching85748 Germany Department of Physics Technion Haifa3200003 Israel Department of Computational Mathematics Science and Engineering Michigan State University East LansingMI48824 United States Department of Physics and Astronomy Michigan State University East LansingMI48824 United States Ludwig-Maximilians-Universitat Munchen Geschwister-Scholl-Platz 1 Munchen80539 Germany Department of Astronomy Yale University New HavenCT06511 United States Steward Observatory Department of Astronomy University of Arizona 933 North Cherry Avenue TucsonAZ85721 United States Data Science Institute University of Arizona 1230 N. Cherry Avenue TucsonAZ85721 United States Program in Applied Mathematics University of Arizona 617 North Santa Rita TucsonAZ85721 United States Machine Learning Research Lab Volkswagen AG Munich38440 Germany

One of the main challenges in modeling massive stars to the onset of core collapse is the computational bottleneck of nucleosynthesis during advanced burning stages. The number of isotopes formed requires solving a large set of fully-coupled stiff ordinary differential equations (ODEs), making the simulations computationally intensive and prone to numerical instability. To overcome this barrier, we design a nuclear neural network (NNN) framework with multiple hidden layers to emulate nucleosynthesis calculations and conduct a proof-of-concept to evaluate its performance. The NNN takes the temperature, density and composition of a burning region as input and predicts the resulting isotopic abundances along with the energy generation and loss rates. We generate training sets for initial conditions corresponding to oxygen core depletion and beyond using large nuclear reaction networks, and compare the predictions of the NNNs to results from a commonly used small net. We find that the NNNs improve the accuracy of the electron fraction by 280 − 660 % and the nuclear energy generation by 250 − 750 %, consistently outperforming the small network across all timesteps. They also achieve significantly better predictions of neutrino losses on relatively short timescales, with improvements ranging from 100 − 106 %. While further work is needed to enhance their accuracy and applicability to different stellar conditions, integrating NNN trained models into stellar evolution codes is promising for facilitating large-scale generation of core-collapse supernova (CCSN) progenitors with higher physical fidelity. © 2025, CC BY.

关键词： Nucleosynthesis

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Second-order Sigma-Delta (ΣΔ) quantization of finite frame expansions

Second-order Sigma-Delta (ΣΔ) quantization of finite frame...

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作者： Benedetto, John J. Powell, Alexander M. Yilmaz, Özgür Department of Mathematics University of Maryland College Park MD 20742 United States Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 United States Department of Mathematics University of British Columbia Vancouver BC V6T 1Z2 Canada

The second-order Sigma-Delta (ΣΔ) scheme with linear quantization rule is analyzed for quantizing finite unit-norm tight frame expansions for Rd. Approximation error estimates are derived, and it is shown that for certain choices of frames the quantization error is of order 1/N2, where N is the frame size. However, in contrast to the setting of bandlimited functions there are many situations where the second-order scheme only gives approximation error of order 1/N. For example, this is the case when quantizing harmonic frames of odd length in even dimensions. An important component of the error analysis involves extending existing stability results to yield smaller invariant sets for the linear second-order ΣΔ scheme. © 2005 Elsevier Inc. All rights reserved.

关键词： Estimation

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Efficient Monolithic Solvers for Fluid-Structure Interaction applied to Flapping Membranes 26th

Efficient Monolithic Solvers for Fluid-Structure Interaction...

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26th International Conference on Domain Decomposition Methods, 2020

作者： Jodlbauer, D. Langer, U. Wick, T. Doctoral Program "Computational Mathematics" Johannes Kepler University Linz Altenberger Str. 69 LinzA-4040 Austria Johann Radon Institute for Computational and Applied Mathematics Austrian Academy of Sciences Altenberger Str. 69 LinzA-4040 Austria Institut für Angewandte Mathematik Leibniz Universität Hannover Welfengarten 1 Hannover30167 Germany

ISBN: (纸本)9783030950248

This work is devoted to the efficient solution of variational-monolithic fluid-structure interaction (FSI) initial-boundary value problems. Solvers for such monolithic systems were developed, e.g., in [2, 3, 5, 7, 9, 11–13, 15]. Due to the interface coupling conditions, the development of robust scalable parallel solvers remains a challenging task, and to the best of our knowledge only semi-cost optimal parallel approaches could be derived [4, 9]. The main purpose of this work consists in further numerical studies of the solver, developed in [9], for a benchmark problem that is motivated by hemodynamic applications. Specifically, we consider channel flow with elastic membranes and elastic solid walls. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Fluid structure interaction

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computational Methods for Single-Particle Electron Cryomicroscopy

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Biomedical Data Science 1000年第1期3卷 163-190页

作者： Amit Singer Fred J. Sigworth 1Department of Mathematics and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA email: amits@math.princeton.edu 2Departments of Cellular and Molecular Physiology Biomedical Engineering and Molecular Biophysics and Biochemistry Yale University New Haven Connecticut 06520 USA email: fred.sigworth@yale.edu

Single-particle electron cryomicroscopy (cryo-EM) is an increasingly popular technique for elucidating the three-dimensional (3D) structure of proteins and other biologically significant complexes at near-atomic resolution. It is an imaging method that does not require crystallization and can capture molecules in their native states. In single-particle cryo-EM, the 3D molecular structure needs to be determined from many noisy 2D tomographic projections of individual molecules, whose orientations and positions are unknown. The high level of noise and the unknown pose parameters are two key elements that make reconstruction a challenging computational problem. Even more challenging is the inference of structural variability and flexible motions when the individual molecules being imaged are in different conformational states. This review discusses computational methods for structure determination by single-particle cryo-EM and their guiding principles from statistical inference, machine learning, and signal processing, which also play a significant role in many other data science applications.

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Nucleation of Ordered Phases in Block Copolymers

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Physical Review Letters 2010年第14期104卷 148301-148301页

作者： Xiuyuan Cheng Ling Lin Weinan E Pingwen Zhang An-Chang Shi School of Mathematical Sciences and The Key Laboratory of Mathematics and Applied Mathematics Peking University Beijing 100871 China Department of Mathematics and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544-1000 USA Department of Physics and Astronomy McMaster University Hamilton Ontario L8S 4M1 Canada

Nucleation of various ordered phases in block copolymers is studied by examining the free-energy landscape within the self-consistent field theory. The minimum energy path (MEP) connecting two ordered phases is computed using a recently developed string method. The shape, size, and free-energy barrier of critical nuclei are obtained from the MEP, providing information about the emergence of a stable ordered phase from a metastable phase. In particular, structural evolution of embryonic gyroid nucleus is predicted to follow two possible MEPs, revealing an interesting transition pathway with an intermediate perforated layered structure.

关键词： Nucleation

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