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A DISCRETE MODEL FOR COMPETING STAGE-STRUCTURED SPECIES

THEORETICAL POPULATION BIOLOGY 1992年第3期41卷 372-387页

作者： CUSHING, JM Department of Mathematics Interdisciplinary Program in Applied Mathematics Building 89 University of Arizona Tucson Arizona 85721 USA

This paper deals with the problem of relating physiological properties of individual organisms to the dynamics at the total population level. A general nonlinear matrix difference equation is described which accounts for the dynamics of stage-structured populations under the assumption that individuals in the populations can be placed into well defined descriptive stages. Density feedback is modeled through an assumption that (stage-specific) fertilities and transitions are proportional to a resource uptake functional which is dependent upon a total weighted population size. It is shown how, if stage-specific differences in mortality are insignificant compared to stage-specific differences in fertility and inter-stage transitions, a nonlinear version of the strong ergodic theorem of demography mathematically separates the population level dynamics from the dynamics of the stage distribution vector, which is shown to stabilize independently of the population level dynamics. The nonlinear dynamics at the population level are governed by a key parameter π that encapsulates the stage-specific parameters and thereby affords a means by which population level dynamics can be linked to properties of individual organisms. The method is applied to a community of stagestructured populations competing for a common limiting resource, and it is seen how the parameter π determines the competitively superior species. An example of size structured competitors illustrates how the method can relate the competitive success of a species to such size-specific properties as resource conversion efficiencies and allocation fractions for individual growth and reproduction, largest adult body size, and size at birth and maturation.

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ANN-based analysis of thin film Maxwell fluid dynamics with electro-osmotic and nonlinear thermal effects

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Alexandria Engineering Journal 2025年 127卷 392-410页

作者： Irfan Saif Ud Din Imran Siddique Zohaib Zahid Muhammad Nadeem S. Islam Department of Mathematics University of Management and Technology Lahore 54770 Pakistan Department of Mathematics University of Sargodha Sargodha 40100 Pakistan Mathematics in Applied Sciences and Engineering Research Group Scientific Research Center Al-Ayen University Nasiriyah 64001 Iraq Federal University of Technology Paran UTFPR Mechanical Engineering Department DAMEC Postgraduate Program in Mechanical and Materials Engineering PPGEM Research Center for Rheology and Non-Newtonian Fluids CERNN R. Deputado Heitor Alencar Furtado 5000 - Bloco N - Ecoville Curitiba PR 81280-340 Brazil Department of Mechanical Engineering Prince Mohammad Bin Fahd University P.O Box 1664 Al Khobar 31952 Saudi Arabia

An intelligent Levenberg-Marquardt Technique (LMT) with artificial neural network (ANN) backpropagation (BP) has been used to analyze the thermal heat and mass transfer of unsteady magnetohydrodynamics (MHD) thin film Maxwell fluid flow in a porous inclined sheet with an emphasis on the influence of electro-osmosis. The activation energy, chemical reaction, mixed convection, melting heat, joule heating, nonlinear thermal radiation, variable thermal conductivity and thermal source/sink effect are taken into account for transport expressions. Appropriate similarity transformations were used to translate partial differential equations (PDEs) into ordinary differential equations (ODEs). After that, the built-in MATLAB BVP4C method was used for a data set assessed using the LMT-ANN strategy to solve these ODEs. The physical significance of the designed parameters is thoroughly discussed in both tabular and graphical form. The observed R -squared value is 1, and the mean square error up to 10 − 15 demonstrates the LMT-ANN's precise and accurate computing capability. The model’s validity is also confirmed by the strong agreement between the obtained predicted findings and numerical results, which shows a high degree of accuracy within the range of 10 − 8 to 10 − 11 . It was revealed that radiative heat considerably increases surface heat energy through accumulation, improving heat transfer qualities, whereas fluid temperature is raised by Joule dissipation, variable thermal conductivity, and heat source. Electro-osmosis and magnetic fields reduce fluid velocity by generating opposing forces that resist the flow. This problem works best in microscale fluid transport systems and drilling operations, where magnetic and electro-osmotic control are crucial. These systems include micro-electromechanical systems, lab-on-a-chip devices, porous geological formations, and thin film coating technologies.

关键词： Maxwell fluid Magnetic effect Electro-osmosis effect Variable thermal conductivity Heat source Chemical reaction

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Boundary Layer Theory and the Zero-Viscosity Limit of the Navier-Stokes Equation

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Acta Mathematica Sinica,English Series 2000年第2期16卷 207-218页

作者： Weinan E department of mathematics and program in applied and Computational mathematics,Princeton University,USA Department of Mathematics and Program in Applied and Computational Mathematics Princeton University Princeton USA

A central problem in the mathematical analysis of fluid dynamics is the asymptotic limit of the fluid flow as viscosity goes to *** is particularly important when boundaries are present since vorticitv is typically generated at the boundary as a result of boundary layer *** boundary laver theory,developed by Prandtl about a hundred years ago,has become a standard tool in addressing these *** at the mathematical level,there is still a lack of fundamental understanding of these questions and the validity of the boundary layer *** this article,we review recent progresses on the analysis of Prandtl’s equation and the related issue of the zero-viscosity limit for the solutions of the Navier-Stokes *** also discuss some directions where progress is expected in the near future.

关键词： Boundary layer Blow-up Zero-viscosity limit Prandtl’s equation

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Impact of the relativistic Cowling approximation on shear and interface modes of neutron stars

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Physical Review D 2025年第6期111卷 063029-063029页

作者： Christian J. Krüger Hajime Sotani Theoretical Astrophysics IAAT University of Tübingen 72076 Tübingen Germany Department of Mathematics and Physics Kochi University Kochi 780-8520 Japan Astrophysical Big Bang Laboratory RIKEN Saitama 351-0198 Japan Interdisciplinary Theoretical and Mathematical Science Program (iTHEMS) RIKEN Saitama 351-0198 Japan

We investigate shear and interface modes excited in neutron stars with an elastic crust in the full general relativistic framework and compare them to the results obtained within the relativistic Cowling approximation. We observe that the Cowling approximation has virtually no impact on the frequencies or the eigenfunctions of the shear modes; in contrast, the interface modes that arise due to the discontinuities of the shear modulus experience a considerable shift in frequency when applying the Cowling approximation. Furthermore, we extend a scheme based on the properties of the phase of amplitude ratios, which allows us to estimate the damping times of slowly damped modes; our extension can provide an estimation of the damping time even if the features of the amplitude ratio are incomplete or if some of them violate the underlying linearity assumption. The proposed scheme is also computationally less expensive and numerically more robust and we provide accurate estimates as well as lower bounds for damping times of shear and interface modes. We estimate the damping times also via the quadrupole formula and find that it provides good order-of-magnitude estimates.

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Effective Dimension Aware Fractional-Order Stochastic Gradient Descent for Convex Optimization Problems

arXiv

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arXiv 2025年

作者： Partohaghighi, Mohammad Marcia, Roummel Chen, YangQuan Electrical Engineering and Computer Science graduate program University of California Merced United States Department of Applied Mathematics University of California Merced MercedCA United States Lab Department of Mechanical Engineering School of Engineering University of California MercedCA95343 United States

Fractional-order stochastic gradient descent (FOSGD) leverages a fractional exponent to capture long-memory effects in optimization, yet its practical impact is often constrained by the difficulty of tuning and stabilizing this exponent. In this work, we introduce 2SED Fractional-Order Stochastic Gradient Descent (2SEDFOSGD), a novel method that synergistically combines the Two-Scale Effective Dimension (2SED) algorithm with FOSGD to automatically calibrate the fractional exponent in a data-driven manner. By continuously gauging model sensitivity and effective dimensionality, 2SED dynamically adjusts the exponent to curb erratic oscillations and enhance convergence rates. Theoretically, we demonstrate how this dimension-aware adaptation retains the benefits of fractional memory while averting the sluggish or unstable behaviors frequently observed in naive fractional SGD. Empirical evaluations across multiple benchmarks confirm that our 2SED-driven fractional exponent approach not only converges faster but also achieves more robust final performance, suggesting broad applicability for fractional-order methodologies in large-scale machine learning and related domains. © 2025, CC BY.

关键词： Convex optimization

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THE DYNAMICS OF HIERARCHICAL AGE-STRUCTURED POPULATIONS

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JOURNAL OF MATHEMATICAL BIOLOGY 1994年第7期32卷 705-729页

作者： CUSHING, JM 1. Department of Mathematics Interdisciplinary Program on Applied Mathematics Building 89 University of Arizona 85721 Tucson AZ USA

An age-structured population is considered in which the birth and death rates of an individual of age a is a function of the density of individuals older and/or younger than a. An existence/uniqueness theorem is proved for the McKendrick equation that governs the dynamics of the age distribution function. This proof shows how a decoupled ordinary differential equation for the total population size can be derived. This result makes a study of the population's asymptotic dynamics (indeed, often its global asymptotic dynamics) mathematically tractable. Several applications to models for intra-specific competition and predation are given.

关键词： AGE-STRUCTURED POPULATION DYNAMICS MCKENDRICK EQUATIONS HIERARCHICAL MODELS EXISTENCE/UNIQUENESS ASYMPTOTIC DYNAMICS GLOBAL STABILITY INTRA-SPECIFIC COMPETITION CANNIBALISM

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Following marginal stability manifolds in quasilinear dynamical reductions of multiscale flows in two space dimensions

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Physical Review E 2025年第2期111卷 025105-025105页

作者： Alessia Ferraro Gregory P. Chini T. M. Schneider Emergent Complexity in Physical Systems Laboratory (ECPS) École Polytechnique Fédérale de Lausanne CH-1015 Lausanne Switzerland Nordita Royal Institute of Technology and Stockholm University Stockholm 106 91 Sweden Department of Mechanical Engineering and Program in Integrated Applied Mathematics University of New Hampshire Durham New Hampshire 03824 USA

We derive a two-dimensional (2D) extension of a recently developed formalism for slow-fast quasilinear (QL) systems subject to fast instabilities. The emergent dynamics of these systems is characterized by a slow evolution of (suitably defined) mean fields coupled to marginally stable, fast fluctuation fields. By exploiting this scale separation, an efficient hybrid fast-eigenvalue/slow-initial-value solution algorithm can be developed in which the amplitude of the fast fluctuations is slaved to the slowly evolving mean fields to ensure marginal stability—and temporal scale separation—is maintained. For 2D systems, the fluctuation eigenfunctions are labeled by their Fourier wave numbers characterizing spatial variability in that extended spatial direction, and the marginal mode(s) must coincide with the fastest-growing mode(s) over all admissible Fourier wave numbers. Here we derive an ordinary differential equation governing the slow evolution of the wave number of the fastest-growing fluctuation mode that simultaneously must be slaved to the mean dynamics to ensure the mode has zero growth rate. We illustrate the procedure in the context of a 2D model partial differential equation that shares certain attributes with the equations governing strongly stratified shear flows and other strongly constrained forms of geophysical turbulence in extreme parameter regimes. The slaved evolution follows one or more marginal stability manifolds, which constitute select state-space structures that are not invariant under the full flow dynamics yet capture quasicoherent structures in physical space in a manner analogous to invariant solutions identified in, e.g., transitionally turbulent shear flows. Accordingly, we propose that marginal stability manifolds are central organizing structures in a dynamical systems description of certain classes of multiscale flows in which scale separation justifies a QL approximation of the dynamics.

关键词： Shear flow

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HiPoNet: A Topology-Preserving Multi-View Neural Network For High Dimensional Point Cloud and Single-Cell Data

arXiv

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arXiv 2025年

作者： Viswanath, Siddharth Madhu, Hiren Bhaskar, Dhananjay Kovalic, Jake Johnson, Dave Ying, Rex Tape, Christopher Adelstein, Ian Perlmutter, Michael Krishnaswamy, Smita Department of Computer Science Yale University New Haven United States Department of Genetics Yale University New Haven United States Department of Applied Physics Yale University New Haven United States Program in Computing Boise State University Idaho United States Cell Communication Lab Department of Oncology University College London Cancer Institute London United Kingdom Department of Mathematics Yale University New Haven United States Department of Mathematics Boise State University Idaho United States Computational Biology and Bioinformatics Program Yale University New Haven United States Wu-Tsai Institute Yale University New Haven United States Program for Applied Math Yale University New Haven United States

In this paper, we propose HiPoNet, an end-to-end differentiable neural network for regression, classification, and representation learning on high-dimensional point clouds. Single-cell data can have high dimensionality exceeding the capabilities of existing methods for point clouds which are tailored for 3D data. Moreover, modern single-cell and spatial experiments now yield entire cohorts of datasets (i.e. one on every patient), necessitating models that can process large, high-dimensional point clouds at scale. Most current approaches build a single nearest-neighbor graph, discarding important geometric information. In contrast, HiPoNet forms higher-order simplicial complexes through learnable feature reweighting, generating multiple data views that disentangle distinct biological processes. It then employs simplicial wavelet transforms to extract multiscale features—capturing both local and global topology. We empirically show that these components preserve topological information in the learned representations, and that HiPoNet significantly outperforms state-of-the-art point-cloud and graph-based models on single cell. We also show an application of HiPoNet on spatial transcriptomics datasets using spatial co-ordinates as one of the views. Overall, HiPoNet offers a robust and scalable solution for high-dimensional data analysis. © 2025, CC BY.

关键词： Network topology

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The Elastic Continuum Limit of the Tight Binding Model

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Chinese Annals of mathematics,Series B 2007年第6期28卷 665-676页

作者： Weinan E Jianfeng LU Department of Mathematics and Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 USA

The authors consider the simplest quantum mechanics model of solids, the tight binding model, and prove that in the continuum limit, the energy of tight binding model converges to that of the continuum elasticity model obtained using Cauchy-Born rule. The technique in this paper is based mainly on spectral perturbation theory for large matrices.

关键词： Continuum limit Elasticity theory Cauchy-Born rule Tight binding model

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Transient rod-climbing in an Oldroyd-B fluid

arXiv

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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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