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arXiv 2025年

作者： Emami, Razieh Liska, Matthew Chatterjee, Koushik Bower, Geoffrey C. Benbow, Wystan Finkbeiner, Douglas Wielgus, Maciek Hernquist, Lars Smith, Randall Tremblay, Grant Ricarte, Angelo Steiner, James F. Broderick, Avery E. Saurabh Davelaar, Jordy Grindlay, Josh Vogelsberger, Mark Chan, Chi-Kwan Center for Astrophysics Harvard & Smithsonian 60 Garden Street CambridgeMA02138 United States Center for Relativistic Astrophysics Georgia Institute of Technology Howey Physics Bldg 837 State Street NW AtlantaGA30332 United States Department of Physics University of Maryland College ParkMD United States Academia Sinica Institute of Astronomy and Astrophysics 645 N. A’ohoku Place HiloHI96720 United States Instituto de Astrofísica de Andalucía-CSIC Glorieta de la Astronomía s/n GranadaE-18008 Spain Black Hole Initiative Harvard University 20 Garden Street CambridgeMA02138 United States Perimeter Institute for Theoretical Physics 31 Caroline Street North WaterlooONN2L 2Y5 Canada Department of Physics and Astronomy University of Waterloo 200 University Avenue West WaterlooONN2L 3G1 Canada Max-Planck-Institut für Radioastronomie Auf dem Hügel 69 BonnD-53121 Germany Department of Astrophysical Sciences Peyton Hall Princeton University PrincetonNJ08544 United States NASA Hubble Fellowship Program Department of Physics Kavli Institute for Astrophysics and Space Research Massachusetts Institute of Technology CambridgeMA02139 United States Department of Astronomy and Steward Observatory University of Arizona 933 North Cherry Avenue TucsonAZ85721 United States Data Science Institute University of Arizona 1230 N. Cherry Ave. TucsonAZ85721 United States Program in Applied Mathematics University of Arizona 617 N. Santa Rita TucsonAZ85721 United States

Recent multi-wavelength observations of M87* (Algaba et al. 2024) revealed a high-energy γ-ray flare without a corresponding millimeter counterpart. We present a theoretical polarimetric study to evaluate the presence and nature of a potential millimeter flare in M87*, using a suite of general relativistic magnetohydrodynamical simulations with varying black hole (BH) spins and magnetic field configurations. We find that the emergence of a millimeter flare is strongly influenced by both spin and magnetic structure, with limited sensitivity to the electron distribution (thermal vs. non-thermal). We model the intensity light curve with a damped random walk (DRW) and compare the characteristic timescale (τ) with recent SMA observations, finding that the simulated τ exceeds observed values by over an order of magnitude. In a flaring case with BH spin a=+0.5, we identify a distinct millimeter flare followed by an order-of-magnitude flux drop. All Stokes parameters show variability near the flare, including a sign reversal in the electric vector position angle. While most βm modes remain stable, the EB-correlation phase is highly sensitive to both the flare peak and decay. We examine polarimetric signatures in photon sub-rings, focusing on modes ns=0 and ns=1. The ns=0 signal closely matches the full image, while ns=1 reveals distinct behaviors, highlighting the potential of space VLBI to isolate sub-ring features. Finally, we analyze the magnetic and velocity field evolution during the flare, finding that magnetic reconnection weakens during the flux decay, and the clockwise velocity flow transitions into an outflow-dominated regime. These results suggest that transient radio variability near flares encodes key information about BH spin and magnetic field structure, offering a novel probe into the physics of active galactic nuclei. © 2025, CC BY.

关键词： Magnetohydrodynamics

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Publisher's Note: “Reacting and non-reacting, three-dimensional shear layers with spanwise stretching” [Phys. Fluids 34, 123602 (2022)]

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Physics of Fluids 2023年第1期35卷

作者： Jonathan L. Palafoutas William A. Sirignano 1Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08540 USA 2Department of Mechanical and Aerospace Engineering University of California Irvine Irvine California 92697 USA

This article was published online on 2 December 2022 with errors throughout the paper. All the derivative terms had the wrong denominator; the denominators were

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An immersed peridynamics model of fluid-structure interaction accounting for material damage and failure

arXiv

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arXiv 2022年

作者： Kim, Keon Ho Bhalla, Amneet P.S. Griffith, Boyce E. Department of Mathematics University of North Carolina Chapel HillNC United States Department of Mechanical Engineering San Diego State University San DiegoCA United States Departments of Mathematics Applied Physical Sciences and Biomedical Engineering University of North Carolina Chapel HillNC United States Carolina Center for Interdisciplinary Applied Mathematics University of North Carolina Chapel HillNC United States Computational Medicine Program University of North Carolina Chapel HillNC United States McAllister Heart Institute University of North Carolina Chapel HillNC United States

This paper develops and benchmarks an immersed peridynamics method to simulate the deformation, damage, and failure of hyperelastic materials within a fluid-structure interaction framework. The immersed peridynamics method describes an incompressible structure immersed in a viscous incompressible fluid. It expresses the momentum equation and incompressibility constraint in Eulerian form, and it describes the structural motion and resultant forces in Lagrangian form. Coupling between Eulerian and Lagrangian variables is achieved by integral transforms with Dirac delta function kernels, as in standard immersed boundary methods. The major difference between our approach and conventional immersed boundary methods is that we use peridynamics, instead of classical continuum mechanics, to determine the structural forces. We focus on non-ordinary state-based peridynamic material descriptions that allow us to use a constitutive correspondence framework that can leverage well-characterized nonlinear constitutive models of soft materials. The convergence and accuracy of our approach are compared to both conventional and immersed finite element methods using widely used benchmark problems of nonlinear incompressible elasticity. We demonstrate that the immersed peridynamics method yields comparable accuracy with similar numbers of structural degrees of freedom for several choices of the size of the peridynamic horizon. We also demonstrate that the method can generate grid-converged simulations of fluid-driven material damage growth, crack formation and propagation, and rupture under large deformations. © 2022, CC BY-SA.

关键词： Continuum mechanics

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IGA using Offset-based Overlapping Domain Parameterizations

arXiv

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arXiv 2023年

作者： Kargaran, Somayeh Jüttler, Bert Takacs, Thomas Doctoral Program Computational Mathematics Johannes Kepler University Linz Altenberger Straße 69 Linz4040 Austria Hagenberg Austria Institute of Applied Geometry Johannes Kepler University Linz Altenberger Straße 69 Linz4040 Austria Austrian Academy of Sciences Altenberger Straße 69 Linz4040 Austria

Isogeometric analysis (IGA) is a numerical method, proposed in [1], that connects computer-aided design (CAD) with finite element analysis (FEA). In CAD the computational domain is usually represented by B-spline or NURBS patches. Given a B-spline or NURBS parameterization of the domain, an isogeometric discretization is defined on the domain using the same B-spline or NURBS basis as for the domain parameterization. Ideally, such an isogeometric discretization allows an exact representation of the underlying CAD model. CAD models usually represent only the boundary of the object. For planar domains, the CAD model is given as a collection of curves representing the boundary. Finding a suitable parameterization of the interior is one of the major issues for IGA, similar to the mesh generation process in the FEA setting. The objective of this isogeometric parameterization problem is to obtain a set of patches, which exactly represent the boundary of the domain and which are parameterized regularly and without self-intersections. This can be achieved by segmenting the domain into patches which are matching along interfaces, or by covering the domain with overlapping patches. In this paper we follow the second approach. To construct from a given boundary curve a planar parameterization suitable for IGA, we propose an offset-based domain parameterization algorithm. Given a boundary curve, we obtain an inner curve by generalized offsetting. The inner curve, together with the boundary curve, naturally defines a ring-shaped patch with an associated parameterization. By definition, the ring-shaped patch has a hole, which can be covered by a multi-cell domain. Consequently, the domain is represented as a union of two overlapping subdomains which are regularly parameterized. On such a configuration, one can employ the overlapping multi-patch (OMP) method, as introduced in [2], to solve PDEs on the given domain. The performance of the proposed method is reported in several numer

关键词： Parameterization

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An Immersed Peridynamics Model of Fluid-Structure Interaction Accounting for Material Damage and Failure

SSRN

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SSRN 2022年

作者： Kim, Keon Ho Bhalla, Amneet Pal Singh Griffith, Boyce E. Department of Mathematics University of North Carolina Chapel HillNC United States Department of Mechanical Engineering San Diego State University San DiegoCA United States Departments of Mathematics Applied Physical Sciences and Biomedical Engineering University of North Carolina Chapel HillNC United States Carolina Center for Interdisciplinary Applied Mathematics University of North Carolina Chapel HillNC United States Computational Medicine Program University of North Carolina Chapel HillNC United States McAllister Heart Institute University of North Carolina Chapel HillNC United States

This paper develops and benchmarks an immersed peridynamics method to simulate the deformation, damage, and failure of hyperelastic materials within a fluid-structure interaction framework. The immersed peridynamics method describes an incompressible structure immersed in a viscous incompressible fluid. It expresses the momentum equation and incompressibility constraint in Eulerian form, and it describes the structural motion and resultant forces in Lagrangian form. Coupling between Eulerian and Lagrangian variables is achieved by integral transforms with Dirac delta function kernels, as in standard immersed boundary (IB) methods. The major difference between our approach and conventional IB methods is that we use peridynamics, instead of classical continuum mechanics, to determine the structural forces. We focus on non-ordinary state-based peridynamic material descriptions that allow us to use a constitutive correspondence framework that can leverage well characterized nonlinear constitutive models of soft materials. The convergence and accuracy of our approach are compared to both conventional and immersed finite element methods using widely used benchmark problems of nonlinear incompressible elasticity. We demonstrate that the immersed peridynamics method yields comparable accuracy with similar numbers of structural degrees of freedom for several choices of the size of the peridynamic horizon. We also demonstrate that the method can generate grid-converged simulations of fluid-driven material damage growth, crack formation and propagation, and rupture under large deformations. © 2022, The Authors. All rights reserved.

关键词： Fluid structure interaction

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Erratum: ‘‘A direct interaction approximation treatment of high Rayleigh number convective turbulence and comparison with experiment’’ [Phys. Fluids 31, 256 (1988)]

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Physics of Fluids 1988年第8期31卷

作者： Gregory J. Hartke V. M. Canuto William P. Dannevik NASA Goddard Space Flight Center Institute for Space Studies 2880 Broadway New York New York 10025 Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544

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Erratum: “Effect of dimensionality on the continuum percolation of overlapping hyperspheres and hypercubes. II. Simulation results and analyses” [J. Chem. Phys. 137, 074106 (2012)]

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The Journal of Chemical Physics 2014年第15期141卷

作者： S. Torquato Y. Jiao 1Department of Chemistry Department of Physics Princeton Center for Theoretical Science and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA 2Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA

In Table I and the caption of Fig. 8 of Ref. 1, the numerical value of the percolation threshold ηc of three-dimensional overlapping spheres as determined via t

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Spectral neighbor joining for reconstruction of latent tree models

arXiv

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arXiv 2020年

作者： Jaffe, Ariel Amsel, Noah Nadler, Boaz Chang, Joseph T. Kluger, Yuval Program in Applied Mathematics Yale University New HavenCT06511 United States Department of Computer Science Weizmann Institute of Science Rehovot76100 Israel Department of Statistics Yale University New HavenCT06520 United States Interdepartmental Program in Computational Biology and Bioinformatics New HavenCT06511 Singapore Department of Pathology New HavenCT06511 United States

A key assumption in multiple scientific applications is that the distribution of observed data can be modeled by a latent tree graphical model. An important example is phylogenetics, where the tree models the evolutionary lineages of various organisms. Given a set of independent realizations of the random variables at the leaves of the tree, a common task is to infer the underlying tree topology. In this work we develop Spectral Neighbor Joining (SNJ), a novel method to recover latent tree graphical models. In contrast to distance based methods, SNJ is based on a spectral measure of similarity between all pairs of observed variables. We prove that SNJ is consistent, and derive a sufficient condition for correct tree recovery from an estimated similarity matrix. Combining this condition with a concentration of measure result on the similarity matrix, we bound the number of samples required to recover the tree with high probability. We illustrate via extensive simulations that SNJ requires fewer samples to accurately recover trees in regimes where the tree contains a large number of leaves or long edges. We provide theoretical support for this observation by analyzing the model of a perfect binary tree. Copyright © 2020, The Authors. All rights reserved.

关键词： Recovery

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Time-stepping approach for solving upper-bound problems: Application to two-dimensional Rayleigh-Bénard convection

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Physical Review E 2015年第4期92卷 043012-043012页

作者： Baole Wen Gregory P. Chini Rich R. Kerswell Charles R. Doering Program in Integrated Applied Mathematics University of New Hampshire Durham New Hampshire 03824 USA Center for Fluid Physics University of New Hampshire Durham New Hampshire 03824 USA The Institute for Computational Engineering and Sciences The University of Texas at Austin Austin Texas 78712 USA Department of Mechanical Engineering University of New Hampshire Durham New Hampshire 03824 USA School of Mathematics University of Bristol University Walk Bristol BS8 1TW United Kingdom Department of Physics University of Michigan Ann Arbor Michigan 48109-1040 USA Department of Mathematics University of Michigan Ann Arbor Michigan 48109-1043 USA Center for the Study of Complex Systems University of Michigan Ann Arbor Michigan 48109-1107 USA

An alternative computational procedure for numerically solving a class of variational problems arising from rigorous upper-bound analysis of forced-dissipative infinite-dimensional nonlinear dynamical systems, including the Navier-Stokes and Oberbeck-Boussinesq equations, is analyzed and applied to Rayleigh-Bénard convection. A proof that the only steady state to which this numerical algorithm can converge is the required global optimal of the relevant variational problem is given for three canonical flow configurations. In contrast with most other numerical schemes for computing the optimal bounds on transported quantities (e.g., heat or momentum) within the “background field” variational framework, which employ variants of Newton's method and hence require very accurate initial iterates, the new computational method is easy to implement and, crucially, does not require numerical continuation. The algorithm is used to determine the optimal background-method bound on the heat transport enhancement factor, i.e., the Nusselt number (Nu), as a function of the Rayleigh number (Ra), Prandtl number (Pr), and domain aspect ratio L in two-dimensional Rayleigh-Bénard convection between stress-free isothermal boundaries (Rayleigh's original 1916 model of convection). The result of the computation is significant because analyses, laboratory experiments, and numerical simulations have suggested a range of exponents α and β in the presumed Nu∼PrαRaβ scaling relation. The computations clearly show that for Ra≤1010 at fixed L=22,Nu≤0.106Pr0Ra5/12, which indicates that molecular transport cannot generally be neglected in the “ultimate” high-Ra regime.

关键词： RAYLEIGH-Benard convection RESEARCH BOUNDS (mathematics) CONVECTIVE flow (Fluid dynamics) NATURAL heat convection NUSSELT number

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ReLSO: A Transformer-based Model for Latent Space Optimization and Generation of Proteins

arXiv

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arXiv 2022年

作者： Castro, Egbert Godavarthi, Abhinav Rubinfien, Julian Givechian, Kevin Bhaskar, Dhananjay Krishnaswamy, Smita Computational Biology and Bioinformatics Program Yale University New HavenCT06511 United States Department of Applied Mathematics Yale University New HavenCT06511 United States Department of Genetics Yale University New HavenCT06511 United States Department of Computer Science Yale University New HavenCT06511 United States

The development of powerful natural language models have increased the ability to learn meaningful representations of protein sequences. In addition, advances in high-throughput mutagenesis, directed evolution, and next-generation sequencing have allowed for the accumulation of large amounts of labeled fitness data. Leveraging these two trends, we introduce Regularized Latent Space Optimization (ReLSO), a deep transformer-based autoencoder which features a highly structured latent space that is trained to jointly generate sequences as well as predict fitness. Through regularized prediction heads, ReLSO introduces a powerful protein sequence encoder and novel approach for efficient fitness landscape traversal. Using ReLSO, we explicitly model the sequence-function landscape of large labeled datasets and generate new molecules by optimizing within the latent space using gradient-based methods. We evaluate this approach on several publicly-available protein datasets, including variant sets of anti-ranibizumab and GFP. We observe a greater sequence optimization efficiency (increase in fitness per optimization step) by ReLSO compared to other approaches, where ReLSO more robustly generates high-fitness sequences. Furthermore, the attention-based relationships learned by the jointly-trained ReLSO models provides a potential avenue towards sequence-level fitness attribution information. © 2022, CC BY-NC-ND.

关键词： Proteins

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