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PLANAR PSEUDO-GEODESICS AND TOTALLY UMBILIC SUBMANIFOLDS

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arXiv 2021年

作者： Markvorsen, Steen Raffaelli, Matteo Department of Applied Mathematics and Computer Science Technical University of Denmark Matematiktorvet Building 303B Kongens Lyngby2800 Denmark Institute of Discrete Mathematics and Geometry TU Wien Wiedner Hauptstraße 8-10/104 Vienna1040 Austria

We study totally umbilic isometric immersions between Riemannian manifolds. First, we provide a novel characterization of the totally umbilic isometric immersions with parallel normalized mean curvature vector, i.e., those having nonzero mean curvature vector and such that the unit vector in the direction of the mean curvature vector is parallel in the normal bundle. Such characterization is based on a family of curves, called planar pseudo-geodesics, representing a natural extrinsic generalization of both geodesics and Riemannian circles: being planar, their Cartan development in the tangent space is planar in the ordinary sense;being pseudo-geodesics, their geodesic and normal curvatures satisfy a linear relation. We study these curves in detail and, in particular, establish their local existence and uniqueness. Moreover, in the case of codimension-one immersions, we prove the following statement: an isometric immersion ι: M,→ Q is totally umbilic if and only if the extrinsic shape of every geodesic of M is planar. This extends a well-known result about surfaces in 3MSC Codes 53B25 (Primary) 53A04, 53C40, 53C42 (Secondary) © 2021, CC BY.

关键词： Vectors

DISTANCE EVOLUTIONS in GROWING PREFERENTIAL ATTACHMENT GRAPHS

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arXiv 2020年

作者： Jorritsma, Joost Komjáthy, Júlia Department of Mathematics and Computer Science Eindhoven University of Technology Netherlands Delft Institute of Applied Mathematics Delft University of Technology Netherlands

We study the evolution of the graph distance and weighted distance between two fixed vertices in dynamically growing random graph models. More precisely, we consider preferential attachment models with power-law exponent τ ∈ (2, 3), sample two vertices ut, vt uniformly at random when the graph has t vertices, and study the evolution of the graph distance between these two fixed vertices as the surrounding graph grows. This yields a discrete-time stochastic process in t' ≥ t, called the distance evolution. We show that there is a tight strip around the function (Equation presented)that the distance evolution never leaves with |log(τ−2)| high probability as t tends to infinity. We extend our results to weighted distances, where every edge is equipped with an i.i.d. copy of a non-negative random variable *** Codes 05C80, 05C82, 60C05 Copyright © 2020, The Authors. All rights reserved.

关键词： Random processes

A granular model for crowd motion and pedestrian flow

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Journal of the London Mathematical Society 2025年第5期111卷

作者： Igbida, Noureddine Urbano, José Miguel Institut de recherche XLIM UMR-CNRS 7252 Faculté des Sciences et Techniques Université de Limoges Limoges France Applied Mathematics and Computational Sciences (AMCS) Computer Electrical and Mathematical Sciences and Engineering Division (CEMSE) King Abdullah University of Science and Technology (KAUST) Thuwal Saudi Arabia CMUC Department of Mathematics University of Coimbra Coimbra Portugal

We study a granular model for congested crowd motion and pedestrian flow. Our approach is based on an approximation through a Hele-Shaw type equation involving a degenerate operator of (Formula presented.) -Laplacian type and a linear drift, for which we prove existence and uniqueness using nonlinear semigroup methods and the doubling variables technique. Our main result shows that, as (Formula presented.), the weak solutions of the (Formula presented.) -problem converge to a solution of the congested crowd motion problem interpreted in a variational sense. © 2025 The Author(s). The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.

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Rayleigh-Taylor instability under multi-mode perturbation: discrete Boltzmann modeling with tracers

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arXiv 2022年

作者： Li, Hanwei Xu, Aiguo Zhang, Ge Shan, Yiming Laboroatory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing100088 China Center for Applied Physics and Technology MOE Key Center for High Energy Density Physics Simulations College of Engineering Peking University Beijing100871 China State Key Laboratory of Explosion Science and Technology Beijing Institute of Technology Beijing100081 China Energy Resources Engineering Department Stanford University 367 Panama St StanfordCA94305-2220 United States

The Rayleigh-Taylor Instability (RTI) under multi-mode perturbation in compressible flow is probed via the Discrete Boltzmann Modeling (DBM) with tracers. The distribution of tracers provides clear boundaries between light and heavy fluids in the position space. Besides, the position-velocity phase space offers a new perspective for understanding the flow behavior of RTI with intuitive geometrical correspondence. The effects of viscosity, acceleration, compressibility, and Atwood number on the mixing of material and momentum and the mean non-equilibrium strength at the interfaces are investigated separately based on both the mixedness defined by the tracers and the non-equilibrium strength defined by the DBM. The mixedness increases with viscosity during early stage but decreases with viscosity at the later stage. Acceleration, compressibility, and Atwood number show enhancement effects on mixing based on different mechanisms. After the system relaxes from the initial state, the mean non-equilibrium strength at the interfaces presents an initially increasing and then declining trend, which is jointly determined by the interface length and the macroscopic physical quantity gradient. We conclude that the four factors investigated all significantly affect early evolution behavior of RTI system, such as the competition between interface length and macroscopic physical quantity gradient. The results contribute to the understanding of the multi-mode RTI evolutionary mechanism and the accompanied kinetic effects. © 2022, CC BY-NC-ND.

关键词： Interface states

Covariance-Based Activity Detection in Cooperative Multi-Cell Massive MIMO: Scaling Law and Efficient Algorithms

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arXiv 2023年

作者： Wang, Ziyue Liu, Ya-Feng Wang, Zhaorui Yu, Wei The State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China The School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China Guangdong Provincial Key Laboratory of Future Networks of Intelligence The Chinese University of Hong Kong Shenzhen518172 China The Edward S. Rogers Sr. Department of Electrical and Computer Engineering University of Toronto TorontoONM5S 3G4 Canada

This paper focuses on the covariance-based activity detection problem in a multi-cell massive multiple-input multiple-output (MIMO) system. In this system, active devices transmit their signature sequences to multiple base stations (BSs), and the BSs cooperatively detect the active devices based on the received signals. While the scaling law for the covariance-based activity detection in the single-cell scenario has been extensively analyzed in the literature, this paper aims to analyze the scaling law for the covariance-based activity detection in the multi-cell massive MIMO system. Specifically, this paper demonstrates a quadratic scaling law in the multi-cell system, under the assumption that the path-loss exponent of the fading channel γ > 2. This finding shows that, in the multi-cell massive MIMO system, the maximum number of active devices that can be correctly detected in each cell increases quadratically with the length of the signature sequence and decreases logarithmically with the number of cells (as the number of antennas tends to infinity). Moreover, in addition to analyzing the scaling law for the signature sequences randomly and uniformly distributed on a sphere, the paper also establishes the scaling law for signature sequences based on a finite alphabet, which are easier to generate and store. Finally, this paper proposes two efficient accelerated coordinate descent (CD) algorithms with a convergence guarantee for solving the device activity detection problem. The first algorithm reduces the complexity of CD by using an inexact coordinate update strategy. The second algorithm avoids unnecessary computations of CD by using an active set selection strategy. Simulation results show that the proposed algorithms exhibit excellent performance in terms of computational efficiency and detection error probability. Copyright © 2023, The Authors. All rights reserved.

关键词： Fading channels

Application of hill climbing algorithm in determining the characteristic objects preferences based on the reference set of alternatives 12th

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Application of hill climbing algorithm in determining the ch...

12th KES International Conference on Intelligent Decision Technologies, KES-IDT 2020

作者： Więckowski, Jakub Kizielewicz, Bartlomiej Kolodziejczyk, Joanna Research Team on Intelligent Decision Support Systems Department of Artificial Intelligence and Applied Mathematics Faculty of Computer Science and Information Technology West Pomeranian University of Technology in Szczecin Żolnierska 49 Szczecin71-210 Poland

ISBN: (纸本)9789811559242

Random processes are a frequent issue when trying to solve problems in various areas. The randomness factor makes it difficult to clearly define the input parameters of a system in maximizing its effects. The solution to this problem may be the usage of stochastic optimization methods. In the following article, the Hill Climbing method has been used to solve the problem of optimization, which in combination with the COMET method gave satisfactory results by determining the relationship between the preference assessment of already existing alternatives to the newly determined alternatives. The motivation to conduct the study was the desire to systematize knowledge on the effective selection of input parameters for stochastic optimization methods. The proposed solution indicates how to select the grid size in an unknown problem and the step size in the Hill Climbing method. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd 2020.

关键词： Random processes

A quantum wavelet uncertainty principle

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arXiv 2021年

作者： Arfaoui, Sabrine Alshehri, Maryam G. Mabrouk, Anouar Ben Laboratory of Algebra Number Theory and Nonlinear Analysis LR18ES15 Department of Mathematics Faculty of Sciences Monastir5000 Tunisia Department of Mathematics Faculty of Sciences University of Tabuk Saudi Arabia Department of Mathematics Higher Institute of Applied Mathematics and Computer Science Street of Assad Ibn Alfourat Kairouan3100 Tunisia Laboratory of Algebra Number Theory and Nonlinear Analysis LR18ES15 Department of Mathematics Faculty of Sciences Monastir5000 Tunisia

In the present paper, a new uncertainty principle is derived for the generalized q-Bessel wavelet transform studied earlier in [55]. In this paper, an uncertainty principle associated with wavelet transforms in the q-calculus framework has been established. A two-parameters extension of the classical Bessel operator is applied to generate a wavelet function which is exploited next to explore a wavelet uncertainty principle already in the q-calculus *** Codes 42C40, 33C10 © 2021, CC0.

关键词： Calculations

Asymptotic spectral properties and preconditioning of an approximated nonlocal Helmholtz equation with fractional Laplacian and variable coefficient wave number μ

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arXiv 2024年

作者： Adriani, Andrea Sormani, Rosita L. Tablino-Possio, Cristina Krause, Rolf Serra-Capizzano, Stefano Department of Science and High Technology University of Insubria Via Valleggio 11 Como22100 Italy Department of Theoretical and Applied Sciences University of Insubria Via Dunant 3 Varese21100 Italy Department of Mathematics and Applications University of Milano - Bicocca via Cozzi 53 Milano20125 Italy Center for Computational Medicine in Cardiology University of Italian Switzerland Via Giuseppe Buffi 13 Lugano6900 Switzerland Division of Scientific Computing Department of Information Technology Uppsala University Lägerhyddsv 2 hus 2 UppsalaSE-751 05 Sweden UniDistance Suisse Schinerstrasse 18 Brig3900 Switzerland

The current study investigates the asymptotic spectral properties of a finite difference approximation of nonlocal Helmholtz equations with a fractional Laplacian and a variable coefficient wave number μ, as it occurs when considering a wave propagation in complex media, characterized by nonlocal interactions and spatially varying wave speeds. More specifically, by using tools from Toeplitz and generalized locally Toeplitz theory, the present research delves into the spectral analysis of nonpreconditioned and preconditioned matrix sequences, with the main novelty regarding a complete picture of the case where μ = μ(x, y) is nonconstant. We report numerical evidence supporting the theoretical findings. Finally, open problems and potential extensions in various directions are presented and briefly *** Codes 65F08, 35R11, 65N22, 15A18, 47B35 © 2024, CC BY.

关键词： Helmholtz equation

Automated control and optimization of laser-driven ion acceleration

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High Power Laser science and Engineering 2023年第3期11卷 32-40页

作者： B.Loughran M.J.V.Streeter H.Ahmed S.Astbury M.Balcazar M.Borghesi N.Bourgeois C.B.Curry S.J.D.Dann S.DiIorio N.P.Dover T.Dzelzainis O.C.Ettlinger M.Gauthier L.Giuffrida G.D.Glenn S.H.Glenzer J.S.Green R.J.Gray G.S.Hicks C.Hyland V.Istokskaia M.King D.Margarone O.McCusker P.McKenna Z.Najmudin C.Parisuaña P.Parsons C.Spindloe D.R.Symes A.G.R.Thomas F.Treffert N.Xu C.A.J.Palmer School of Mathematics and Physics Queen’s University BelfastBelfastUK Central Laser Facility STFC Rutherford Appleton LaboratoryDidcotUK Gérard Mourou Center for Ultrafast Optical Science University of MichiganAnn ArborMIUSA SLAC National Accelerator Laboratory Menlo ParkCAUSA Department of Electrical and Computer Engineering University of AlbertaEdmontonABCanada The John Adams Institute for Accelerator Science Imperial College LondonLondonUK ELI Beamlines Centre Institute of PhysicsCzech Academy of SciencesDolníBˇrežanyCzech Republic Department of Applied Physics Stanford UniversityStanfordCAUSA Department of Physics SUPAUniversity of StrathclydeGlasgowUK Faculty of Nuclear Sciences and Physical Engineering Czech Technical University in PraguePragueCzech Republic Department of Mechanical Engineering Stanford UniversityStanfordCAUSA Institut für Kernphysik Technische Universität DarmstadtDarmstadtGermany

The interaction of relativistically intense lasers with opaque targets represents a highly non-linear,multi-dimensional parameter *** limits the utility of sequential 1D scanning of experimental parameters for the optimization of secondary radiation,although to-date this has been the accepted methodology due to low data acquisition *** repetition-rate(HRR)lasers augmented by machine learning present a valuable opportunity for efficient source ***,an automated,HRR-compatible system produced high-fidelity parameter scans,revealing the influence of laser intensity on target pre-heating and proton generation.A closed-loop Bayesian optimization of maximum proton energy,through control of the laser wavefront and target position,produced proton beams with equivalent maximum energy to manually optimized laser pulses but using only 60%of the laser *** demonstration of automated optimization of laser-driven proton beams is a crucial step towards deeper physical insight and the construction of future radiation sources.

关键词： Bayesian optimization high repetition-rate laser-target interaction laser-driven particle acceleration proton generation