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On the Efficient Evaluation of the Azimuthal Fourier Components of the Green's Function for Helmholtz's Equation in Cylindrical Coordinates

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arXiv 2021年

作者： Garritano, James Kluger, Yuval Rokhlin, Vladimir Serkh, Kirill Program in Applied Mathematics Yale University New HavenCT06511 United States Yale School of Medicine New HavenCT06511 United States Dept. of Mathematics Yale University New HavenCT06511 United States Dept. of Math. and Computer Science University of Toronto TorontoONM5S 2E4 Canada

In this manuscript, we develop an efficient algorithm to evaluate the azimuthal Fourier components of the Green's function for the Helmholtz equation in cylindrical coordinates. A computationally efficient algorithm for this modal Green's function is essential for solvers for electromagnetic scattering from bodies of revolution (e.g., radar cross sections, antennas). Current algorithms to evaluate this modal Green's function become computationally intractable when the source and target are close or when the wavenumber is large. Furthermore, most state of the art methods cannot be easily parallelized. In this manuscript, we present an algorithm for evaluating the modal Green's function that has performance independent of both source-to-target proximity and wavenumber, and whose cost grows as $O(m)$, where $m$ is the Fourier mode. Furthermore, our algorithm is embarrassingly parallelizable. © 2021, CC BY.

关键词： Bodies of revolution

Exploring the Hubble Tension and Spatial Curvature from the Ages of Old Astrophysical Objects

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arXiv 2022年

作者： Wei, Jun-Jie Melia, Fulvio Purple Mountain Observatory Chinese Academy of Sciences Nanjing210033 China Guangxi Key Laboratory for Relativistic Astrophysics Nanning530004 China School of Astronomy and Space Sciences University of Science and Technology of China Hefei230026 China Department of Physics The Applied Math Program The University of Arizona TucsonAZ85721 United States Department of Astronomy The University of Arizona TucsonAZ85721 United States

We use the age measurements of 114 old astrophysical objects (OAO) in the redshift range 0 z 8 to explore the Hubble tension. The age of the Universe at any z is inversely proportional to the Hubble constant, H0, so requiring the Universe to be older than the OAO it contains at any z will lead to an upper limit on H0. Assuming flat ΛCDM and setting a Gaussian prior on the matter density parameter Ωm = 0.315 ± 0.007 informed by Planck, we obtain a 95% confidence-level upper limit of H0 −1 Mpc−1, representing a 2σ tension with the measurement using the local distance ladder. We find, however, that the inferred upper limit on H0 depends quite sensitively on the prior for Ωm, and the Hubble tension between early-time and local measurements of H0 may be due in part to the inference of both Ωm and H0 in Planck, while the local measurement uses only H0. The age-redshift data may also be used for cosmological model comparisons. We find that the Rh = ct universe accounts well for the data, with a reasonable upper limit on H0, while Einstein-de Sitter fails to pass the cosmic-age test. Finally, we present a model-independent estimate of the spatial curvature using the ages of 61 galaxies and the luminosity distances of 1,048 Pantheon Type Ia supernovae. This analysis suggests that the geometry of the Universe is marginally consistent with spatial flatness at a confidence level of 1.6σ, characterized as Ωk = 0.43+0.27−0.27 © 2022, CC BY.

关键词： Galaxies

Hint of a truncated primordial spectrum from the CMB large-scale anomalies

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arXiv 2021年

作者： Melia, Fulvio Ma, Qingbo Wei, Jun-Jie Yu, Bo Department of Physics The Applied Math Program Department of Astronomy The University of Arizona TucsonAZ85721 United States Guizhou Provincial Key Laboratory of Radio Astronomy and Data Processing School of Physics and Electronic Science Guizhou Normal University Guiyang550001 China PMO Nanjing210023 China Guangxi Key Laboratory for Relativistic Astrophysics Guangxi University Nanning530004 China University of Chinese Academy of Sciences Beijing100049 China

Context. Several satellite missions have uncovered a series of potential anomalies in the fluctuation spectrum of the cosmic microwave background temperature, including: (1) an unexpectedly low level of correlation at large angles, manifested via the angular correlation function, C(θ);and (2) missing power in the low multipole moments of the angular power spectrum, C. Aims. Their origin is still debated, however, due to a persistent lack of clarity concerning the seeding of quantum fluctuations in the early Universe. A likely explanation for the first of these appears to be a cutoff, kmin = (3.14 ± 0.36) × 10−4 Mpc−1, in the primordial power spectrum, P(k). Our goal in this paper is twofold: (1) we examine whether the same kmin can also self-consistently explain the missing power at large angles, and (2) we confirm that the introduction of this cutoff in P(k) does not adversely affect the remarkable consistency between the prediction of Planck-ΛCDM and the Planck measurements at > 30. Methods. We use the publicly available code CAMB to calculate the angular power spectrum, based on a line-of-sight approach. The code is modified slightly to include the additional parameter (i.e., kmin) characterizing the primordial power spectrum. In addition to this cutoff, the code optimizes all of the usual standard-model parameters. Results. In fitting the angular power spectrum, we find an optimized cutoff, (Equation presented), when using the whole range of 's, and (Equation presented), when fitting only the range ≤ 30, where the Sachs-Wolfe effect is dominant. Conclusions. These are fully consistent with the value inferred from C(θ), suggesting that both of these large-angle anomalies may be due to the same truncation in P(k). © 2021, CC BY.

关键词： Cosmology

Individuality and slow dynamics in bacterial growth homeostasis

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arXiv 2018年

作者： Susman, Lee Kohram, Maryam Vashistha, Harsh Nechleba, Jeffrey T. Salman, Hanna Brenner, Naama Network Biology Research Laboratory Technion-Israel Institute of Technology Haifa32000 Israel Interdisciplinary Program of Applied Math Technion-Israel Institute of Technology Haifa32000 Israel Department of Physics and Astronomy University of Pittsburgh PittsburghPA15260 United States Department of Computational and Systems Biology University of Pittsburgh PittsburghPA15260 United States Department of Chemical Engineering Technion-Israel Institute of Technology Haifa32000 Israel

Microbial growth and division are fundamental processes relevant to many areas of life science. Of particular interest are homeostasis mechanisms, which buffer growth and division from accumulating fluctuations over multiple cycles. These mechanisms operate within single cells, possibly extending over several division cycles. However, all experimental studies to date have relied on measurements pooled from many distinct cells. Here, we disentangle long-term measured traces of individual cells from one another, revealing subtle differences between temporal and pooled statistics. By analyzing correlations along up to hundreds of generations, we find that the parameter describing effective cell-size homeostasis strength varies significantly among cells. At the same time, we find an invariant cell size which acts as an attractor to all individual traces, albeit with different effective attractive forces. Despite the common attractor, each cell maintains a distinct average size over its finite lifetime with suppressed temporal fluctuations around it, and equilibration to the global average size is surprisingly slow (> 150 cell cycles). To demonstrate a possible source of variable homeostasis strength, we construct a mathematical model relying on intracellular interactions, which integrates measured properties of cell size with those of highly expressed proteins. Effective homeostasis strength is then influenced by interactions and by noise levels, and generally varies among cells. A predictable and measurable consequence of variable homeostasis strength appears as distinct oscillatory patterns in cell size and protein content over many generations. We discuss the implications of our results to understanding mechanisms controlling division in single cells and their characteristic timescales. Copyright © 2018, The Authors. All rights reserved.

关键词： Cells

A Stochastic MPEC Approach for Grid Tariff Design with Demand Side Flexibility

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TechRxiv

TechRxiv 2019年

作者： Askeland, Magnus Burandt, Thorsten Gabriel, Steven A. SINTEF Energy Research Department of Electric Power Engineering Norwegian University of Science and Technology Trondheim Norway Technical University of Berlin The Energy Transportation Environment Department German Institute for Economic Research DIW Berlin Berlin Germany Department of Industrial Economics and Technology Management Norwegian University of Science and Technology Trondheim Norway Department of Mechanical Engineering Applied Math & Statistics Scientific Computation Program University of Maryland College Park Maryland United States

As the end-users increasingly can provide flexibility to the power system, it is important to consider how this flexibility can be activated as a resource for the grid. Electricity network tariffs are one option that can be used to activate this flexibility. Therefore, by designing efficient grid tariffs, it might be possible to reduce the total costs in the power system by incentivizing a change in consumption patterns. This paper provides a methodology for optimal grid tariff design under decentralized decision-making and uncertainty in demand, power prices, and renewable generation. A bilevel model is formulated to adequately describe the interaction between the end-users and a distribution system operator. In addition, a centralized decision-making model is provided for benchmarking purposes. The bilevel model is reformulated as a mixed-integer linear problem solvable by branch-and-cut techniques. Results for a deterministic example and a stochastic case study are presented and discussed. © 2019, CC BY-SA.

关键词： Decision making

Neural FIM for learning Fisher information metrics from point cloud data

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arXiv 2023年

作者： Fasina, Oluwadamilola Huguet, Guillaume Tong, Alexander Zhang, Yanlei Wolf, Guy Nickel, Maximilian Adelstein, Ian Krishnaswamy, Smita Applied Math Program Yale University New HavenCT United States Mila - Quebec AI Institute MontrealQC Canada Department of Mathematics and Statistics Université de Montréal MontrealQC Canada Department of Computer Science and Operations Research Université de Montréal MontrealQC Canada FAIR Meta AI United States Department of Math Yale University New HavenCT United States Department of Computer Science Yale University New HavenCT United States Department of Genetics Yale University New HavenCT United States

Although data diffusion embeddings are ubiquitous in unsupervised learning and have proven to be a viable technique for uncovering the underlying intrinsic geometry of data, diffusion embeddings are inherently limited due to their discrete nature. To this end, we propose neural FIM, a method for computing the Fisher information metric (FIM) from point cloud data - allowing for a continuous manifold model for the data. Neural FIM creates an extensible metric space from discrete point cloud data such that information from the metric can inform us of manifold characteristics such as volume and geodesics. We demonstrate Neural FIM's utility in selecting parameters for the PHATE visualization method as well as its ability to obtain information pertaining to local volume illuminating branching points and cluster centers embeddings of a toy dataset and two single-cell datasets of IPSC reprogramming and PBMCs (immune cells). Copyright © 2023, The Authors. All rights reserved.

关键词： Embeddings

Crouzeix’s Conjecture and Related Problems

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arXiv 2020年

作者： Bickel, Kelly Gorkin, Pamela Greenbaum, Anne Ransford, Thomas Schwenninger, Felix Wegert, Elias Department of Mathematics Bucknell University LewisburgPA17837 United States Department of Mathematics Bucknell University LewisburgPA17837 United States Department of Applied Mathematics University of Washington Département de mathématiques et de statistique Université Laval QuébecQCG1V 0A6 Canada Department of Mathematics Universität Hamburg Department of Applied Mathematics University of Twente Netherlands Department of Mathematics and Computer Science Technische Universität Bergakademie Freiberg Division of Mathematical Sciences National Science Foundation United States NSERC and the Canada Research Chairs program

In this paper, we establish several results related to Crouzeixs conjecture. We show that the conjecture holds for contractions with eigenvalues that are sufficiently well-separated. This separation is measured by the so-called separation constant, which is defined in terms of the pseudohyperbolic metric. Moreover, we study general properties of related extremal functions and associated vectors. Throughout, compressions of the shift serve as illustrating examples which also allow for refined *** Codes 47A25, 47A12, 15A60, 47A20, 30J10 Copyright © 2020, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions

A model of fluid-structure and biochemical interactions for applications to subclinical leaflet thrombosis

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2023年第5期39卷 e3700-e3700页

作者： Barrett, Aaron Brown, Jordan A. Smith, Margaret Anne Woodward, Andrew Vavalle, John P. Kheradvar, Arash Griffith, Boyce E. Fogelson, Aaron L. Univ Utah Dept Math Salt Lake City UT 84112 USA Univ N Carolina Dept Math Chapel Hill NC USA Univ N Carolina Adv Med Imaging Lab Med Ctr Chapel Hill NC USA Univ N Carolina Sch Med Chapel Hill NC USA Univ N Carolina Dept Med Div Cardiol Chapel Hill NC USA Univ Calif Irvine Dept Biomed Engn Irvine CA USA Univ N Carolina Dept Applied Phys Sci Chapel Hill NC USA Univ N Carolina Dept Biomed Engn Chapel Hill NC USA Univ N Carolina Carolina Ctr Interdisciplinary Appl Math Chapel Hill NC USA Univ N Carolina Computat Med Program Chapel Hill NC USA Univ N Carolina McAllister Heart Inst Chapel Hill NC USA Univ Utah Dept Biomed Engn Salt Lake City UT USA

Subclinical leaflet thrombosis (SLT) is a potentially serious complication of aortic valve replacement with a bioprosthetic valve in which blood clots form on the replacement valve. SLT is associated with increased risk of transient ischemic attacks and strokes and can progress to clinical leaflet thrombosis. SLT following aortic valve replacement also may be related to subsequent structural valve deterioration, which can impair the durability of the valve replacement. Because of the difficulty in clinical imaging of SLT, models are needed to determine the mechanisms of SLT and could eventually predict which patients will develop SLT. To this end, we develop methods to simulate leaflet thrombosis that combine fluid-structure interaction and a simplified thrombosis model that allows for deposition along the moving leaflets. Additionally, this model can be adapted to model deposition or absorption along other moving boundaries. We present convergence results and quantify the model's ability to realize changes in valve opening and pressures. These new approaches are an important advancement in our tools for modeling thrombosis because they incorporate both adhesion to the surface of the moving leaflets and feedback to the fluid-structure interaction.

关键词： cardiac fluid dynamics fluid-structure interaction leaflet thrombosis numerical methods

Scattering of a short electromagnetic pulse from a Lorentz-Duffing film: Theoretical and numerical analysis

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arXiv 2018年

作者： Brio, Moysey Caputo, Jean-Guy Gwirtz, Kyle Liu, Jinjie Maimistov, Andrei Department of Mathematics University of Arizona TucsonAZ85721 United States Laboratoire de Mathématiques INSA Rouen Normandie Saint-Etienne du Rouvray76801 France Program in Applied Mathematics University of Arizona TucsonAZ85721 United States Department of Mathematical Sciences Delaware State University DoverDE19901 United States Department of Solid State Physics and Nanostructures National Research Nuclear University Moscow Engineering Physics Institute Kashirskoe sh. 31 Moscow115409 Russia

We combine scattering theory, Fourier, traveling wave and asymptotic analyses together with numerical simulations to present interesting and practically useful properties of femtosecond pulse interaction with thin films. The dispersive material is described by a single resonance Lorentz model and its nonlinear extension with a cubic Duffing-type nonlinearity. A key feature of the Lorentz dielectric function is that its real part becomes negative between its zero and its pole, generating a forbidden region. We illustrate numerically the linear interaction of the pulse with the film using both scattering theory and Fourier analysis. Outside this region we show the generation of a sequence of pulses separated by round trips in the Fabry-Perot cavity due to multiple reflections. When the pulse spectrum is inside the forbidden region, we observe total reflection. Near the pole of the dielectric function, we demonstrate the slowing down of the pulse (group velocity tending to zero) in the medium that behaves as a high-Q cavity. We use the combination of analysis and simulations in the linear regime to validate the delta function approximation of the thin layer;this collapses the forbidden region to a single resonant point of the spectrum. We also study the single cycle pulse interaction with a thin film and show three distinct types of reflection: half-pulse, sinusoidal wave train and cosine wavelet. Finally we analyze the influence of a strong nonlinearity and observe that the film switches from reflecting to trasparent. Copyright © 2018, The Authors. All rights reserved.

关键词： Thin films