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Eulerian method for computing multivalued solutions of the Euler-Poisson equations and applications to wave breaking in klystrons

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Physical Review E 2004年第1期70卷 016502-016502页

作者： Xiantao Li John G. Wöhlbier Shi Jin John H. Booske The Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA Department of Electrical and Computer Engineering University of Wisconsin Madison Wisconsin 53706 USA Department of Mathematics University of Wisconsin Madison Wisconsin 53706 USA

We provide methods of computing multivalued solutions to the Euler-Poisson system and test them in the context of a klystron amplifier. An Eulerian formulation capable of computing multivalued solutions is derived from a kinetic description of the Euler-Poisson system and a moment closure. The system of the moment equations may be closed due to the special structure of the solution in phase space. The Eulerian moment equations are computed for a velocity modulated electron beam, which has been shown by prior Lagrangian theories to break in a finite time and form multivalued solutions. The results of the Eulerian moment equations are compared to direct computation of the kinetic equations and a Lagrangian method also developed in the paper. We use the Lagrangian formulation for the explicit computation of wave breaking time and location for typical velocity modulation boundary conditions.

关键词： Klystrons

Algorithms for Solving High Dimensional PDEs: From Nonlinear Monte Carlo to Machine Learning

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arXiv 2020年

作者： Weinan, E. Han, Jiequn Jentzen, Arnulf Department of Mathematics Princeton University United States Program in Applied and Computational Mathematics Princeton University United States Faculty of Mathematics and Computer Science University of Münster Germany

In recent years, tremendous progress has been made on numerical algorithms for solving partial differential equations (PDEs) in a very high dimension, using ideas from either nonlinear (multilevel) Monte Carlo or deep learning. They are potentially free of the curse of dimensionality for many different applications and have been proven to be so in the case of some nonlinear Monte Carlo methods for nonlinear parabolic PDEs. In this paper, we review these numerical and theoretical advances. In addition to algorithms based on stochastic reformulations of the original problem, such as the multilevel Picard iteration and the Deep BSDE method, we also discuss algorithms based on the more traditional Ritz, Galerkin, and least square formulations. We hope to demonstrate to the reader that studying PDEs as well as control and variational problems in very high dimensions might very well be among the most promising new directions in mathematics and scientific computing in the near *** Codes 65C05, 65K10, 65M75, 90C06 Copyright © 2020, The Authors. All rights reserved.

关键词： Monte Carlo methods

The impact of cosmic ray feedback during the epoch of reionisation

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arXiv 2025年

作者： Farcy, Marion Rosdahl, Joakim Dubois, Yohan Blaizot, Jérémy Martin-Alvarez, Sergio Haehnelt, Martin Kimm, Taysun Teyssier, Romain Institute for Physics Laboratory for Galaxy Evolution and Spectral Modelling EPFL Observatoire de Sauverny Chemin Pegasi 51 Versoix1290 Switzerland Centre de Recherche Astrophysique de Lyon CNRS UMR 5574 Univ. Lyon Ens de Lyon 9 avenue Charles André Saint-Genis-LavalF-69230 France Institut d’Astrophysique de Paris CNRS UMR 7095 Sorbonne Université 98 bis bd Arago Paris75014 France Stanford University StanfordCA94305 United States Kavli Institute for Cosmology Institute of Astronomy Madingley Road CambridgeCB3 0HA United Kingdom Department of Astronomy Yonsei University 50 Yonsei-ro Seodaemun-gu Seoul03722 Korea Republic of Department of Astrophysical Sciences Princeton University Peyton Hall PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University Fine Hall Washington Road PrincetonNJ08544-1000 United States

Galaxies form and evolve via a multitude of complex physics. In this work, we investigate the role of cosmic ray (CR) feedback in galaxy evolution and reionisation, by examining its impact on the escape of ionising radiation from galaxies. For this purpose, we present two sphinx cosmological radiation-magneto-hydrodynamics simulations, allowing for the first time a study of the impact of CR feedback on thousands of resolved galaxies during the Epoch of Reionisation (EoR). The simulations differ in their feedback prescriptions: one adopts a calibrated strong supernova (SN) feedback, while the other simulation reduces the strength of SN feedback and includes CR feedback instead. We show that both comparably regulate star formation, reasonably match observations of high-redshift UV luminosity functions, and produce a similar amount of hydrogen ionising photons. In contrast to the model with strong SN feedback, the model with CRs lead to incomplete reionisation, which is in strong disagreement with observational estimates of the reionisation history. This is due to CR feedback shaping the ISM differently, filling with gas the low density cavities otherwise carved by SN explosions. As a result, this reduces the escape of ionising photons, at any halo mass, and primarily in the close vicinity of the stars. Our study indicates that CR feedback regulates galaxy growth during the EoR, but negatively affects reionisation, a tension which paves the way for further exploration and refinement of existing galaxy formation and feedback models. Such improvements are crucial in order to capture and understand the process of reionisation and the underlying evolution of galaxies through cosmic time. © 2025, CC BY.

关键词： Cosmic rays

A trace theorem for sobolev spaces on the sierpinski gasket

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arXiv 2019年

作者： CAO, SHIPING LI, SHUANGPING STRICHARTZ, ROBERT S. TALWAI, PREM Department of Mathematics Cornell University Ithaca14853 United States Program in Applied and Computational Mathematics Princeton University NJ08544-1000 United States

We give a discrete characterization of the trace of a class of Sobolev spaces on the Sierpinski gasket to the bottom line. This includes the L2 domain of the Laplacian as a special case. In addition, for Sobolev spaces of low orders, including the domain of the Dirichlet form, the trace spaces are Besov spaces on the *** Codes 28A80 Copyright © 2019, The Authors. All rights reserved.

关键词： Sobolev spaces

Level sets of quantum control landscapes

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Level sets of quantum control landscapes

International Symposium on Communications Control and Signal Processing (ISCCSP)

作者： Vincent Beltrani Jason Dominy Tak-San Ho Herschel Rabitz Department of Chemistry Princeton University NJ USA Program in Applied and Computational Mathematics Princeton University NJ USA

A controlled quantum system possesses a search landscape defined by the observable value as a functional of the control field. Within the search landscape, there exist level sets of controls giving the same observable value. This paper focuses on level sets of the transition probability P i¿f . For transition probabilities 0 < P i¿f < 1, a first order diffeomorphic modulation observable response preserving homotopy (D-MORPH) algorithm is utilized to investigate level sets. At the top of the control landscape, P i¿f = 1, a second order D-MORPH algorithm is presented that can explore the perfect control level set. D-MORPH is utilized to identify level set members that exhibit certain desirable secondary characteristics, e.g., minimal pulse fluence. Numerical simulations for finite level systems are presented to illustrate the variety of control behavior found across level set members.

关键词： Level set Communication system control Control systems Optimal control Topology Signal processing algorithms Centralized control Relativistic quantum mechanics Process control Signal processing

A trace bound for the hereditary discrepancy 00

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A trace bound for the hereditary discrepancy

Proceedings of the sixteenth annual symposium on computational geometry

作者： Bernard Chazelle Alexey Lvov Department of Computer Science Princeton University and NEC Research Institute Program in Applied and Computational Mathematics Princeton University

Covariance estimation using conjugate gradient for 3D classification in CRYO-EM

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Covariance estimation using conjugate gradient for 3D classi...

IEEE International Symposium on Biomedical Imaging

作者： Joakim Andén Eugene Katsevich Amit Singer Program in Applied and Computational Mathematics Princeton University Princeton NJ Department of Statistics Stanford University Stanford CA

Classifying structural variability in noisy projections of biological macromolecules is a central problem in Cryo-EM. In this work, we build on a previous method for estimating the covariance matrix of the three-dimensional structure present in the molecules being imaged. Our proposed method allows for incorporation of contrast transfer function and non-uniform distribution of viewing angles, making it more suitable for real-world data. We evaluate its performance on a synthetic dataset and an experimental dataset obtained by imaging a 70S ribosome complex.

关键词： Covariance matrices Eigenvalues and eigenfunctions Microscopy Image reconstruction Biology Image resolution

Cryo-EM reconstruction of continuous heterogeneity by Laplacian spectral volumes

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arXiv 2019年

作者： Moscovich, Amit Halevi, Amit Andén, Joakim Singer, Amit Program in Applied & Computational Mathematics Princeton University Princeton NJ United States Center for Computational Mathematics Flatiron Institute New YorkNY United States Department of Mathematics Princeton University Princeton NJ United States

Single-particle electron cryomicroscopy is an essential tool for high-resolution 3D reconstruction of proteins and other biological macromolecules. An important challenge in cryo-EM is the reconstruction of non-rigid molecules with parts that move and deform. Traditional reconstruction methods fail in these cases, resulting in smeared reconstructions of the moving parts. This poses a major obstacle for structural biologists, who need high-resolution reconstructions of entire macromolecules, moving parts included. To address this challenge, we present a new method for the reconstruction of macromolecules exhibiting continuous heterogeneity. The proposed method uses projection images from multiple viewing directions to construct a graph Laplacian through which the manifold of three-dimensional conformations is analyzed. The 3D molecular structures are then expanded in a basis of Laplacian eigenvectors, using a novel generalized tomographic reconstruction algorithm to compute the expansion coefficients. These coefficients, which we name spectral volumes, provide a high-resolution visualization of the molecular dynamics. We provide a theoretical analysis and evaluate the method empirically on several simulated data *** Codes 62P10, 65R32, 94A08 Copyright © 2019, The Authors. All rights reserved.

关键词： Macromolecules

The knowledge gradient for sequential decision making with stochastic binary feedbacks 33

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The knowledge gradient for sequential decision making with s...

33rd International Conference on Machine Learning, ICML 2016

作者： Wang, Yingfei Wang, Chu Powell, Warren Department of Computer Science Princeton University PrincetonNJ08540 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Operations Research and Financial Engineering Princeton University PrincetonNJ08544 United States

ISBN: (纸本)9781510829008

We consider the problem of sequentially making decisions that are rewarded by "successes" and "failures" which can be predicted through an unknown relationship that depends on a partially controllable vector of attributes for each instance. The learner takes an active role in selecting samples from the instance pool. The goal is to maximize the probability of success, either after the offline training phase or minimizing regret in online learning. Our problem is motivated by real-world applications where observations are time consuming and/or expensive. With the adaptation of an online Bayesian linear classifier, we develop a knowledge-gradient type policy to guide the experiment by maximizing the expected value of information of labeling each alternative, in order to reduce the number of expensive physical experiments. We provide a finite-time analysis of the estimated error and demonstrate the performance of the proposed algorithm on both synthetic problems and benchmark UCI datasets.

关键词： Benchmarking