检索结果-内蒙古大学图书馆

Interior electroneutrality in nernst-planck-navier-stokes systems

学校读者我要写书评

暂无评论

arXiv 2020年

作者： Constantin, Peter Ignatova, Mihaela Lee, Fizay-Noah DEPARTMENT OF MATHEMATICS PRINCETON UNIVERSITY PRINCETONNJ08544 United States DEPARTMENT OF MATHEMATICS TEMPLE UNIVERSITY PHILADELPHIAPA19122 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

We consider the limit of vanishing Debye length for ionic diffusion in fluids, described by the Nernst-Planck-Navier-Stokes system. In the asymptotically stable cases of blocking (vanishing normal flux) and uniform selective (special Dirichlet) boundary conditions for the ionic concentrations, we prove that the ionic charge density ρ converges in time to zero in the interior of the domain, in the limit of vanishing Debye length (ǫ → 0). For the unstable regime of Dirichlet boundary conditions for the ionic concentrations, we prove bounds that are uniform in time and ǫ. We also consider electroneutral boundary conditions, for which we prove that electroneutrality ρ → 0 is achieved at any fixed ǫ > 0, exponentially fast in time in Lp, for all 1 ≤ p MSC Codes 35Q30, 35Q35, 35Q92 Copyright © 2020, The Authors. All rights reserved.

关键词： Boundary conditions

Emergent spaces for coupled oscillators

学校读者我要写书评

暂无评论

arXiv 2020年

作者： Thiem, Thomas N. Kooshkbaghi, Mahdi Bertalan, Tom Laing, Carlo R. Kevrekidis, Ioannis G. Department of Chemical and Biological Engineering Princeton University United States Program in Applied and Computational Mathematics Princeton University United States Department of Mechanical Engineering Massachusetts Institute of Technology United States School of Natural and Computational Sciences Massey University New Zealand Department of Applied Mathematics and Statistics Johns Hopkins University United States

Systems of coupled dynamical units (e.g. oscillators or neurons) are known to exhibit complex, emergent behaviors that may be simplified through coarse-graining: a process in which one discovers coarse variables and derives equations for their evolution. Such coarse-graining procedures often require extensive experience and/or a deep understanding of the system dynamics. In this paper we present a systematic, data-driven approach to discovering "bespoke" coarse variables based on manifold learning algorithms. We illustrate this methodology with the classic Kuramoto phase oscillator model, and demonstrate how our manifold learning technique can successfully identify a coarse variable that is one-to-one with the established Kuramoto order parameter. We then introduce an extension of our coarse-graining methodology which enables us to learn evolution equations for the discovered coarse variables via an artificial neural network architecture templated on numerical time integrators (initial value solvers). This approach allows us to learn accurate approximations of time derivatives of state variables from sparse flow data, and hence discover useful approximate differential equation descriptions of their dynamic behavior. We demonstrate this capability by learning ODEs that agree with the known analytical expression for the Kuramoto order parameter dynamics at the continuum limit. We then show how this approach can also be used to learn the dynamics of coarse variables discovered through our manifold learning methodology. In both of these examples, we compare the results of our neural network based method to typical finite differences complemented with geometric harmonics. Finally, we present a series of computational examples illustrating how a variation of our manifold learning methodology can be used to discover sets of "effective" parameters, reduced parameter combinations, for multi-parameter models with complex coupling. We conclude with a discussion of possible ext

关键词： Neural networks

Structural Effects and Aggregation in a Social-Network Model of Natural Resource Consumption

学校读者我要写书评

暂无评论

IFAC-PapersOnLine 2017年第1期50卷 7675-7680页

作者： Manzoor T. Rovenskaya E. Muhammad A. Department of Electrical Engineering Lahore University of Management Sciences (LUMS) Lahore Pakistan Center for Water Informatics & Technology (WIT) Lahore University of Management Sciences (LUMS) Pakistan Advanced Systems Analysis Program International Institute for Applied Systems Analysis (IIASA) Laxenburg Austria Faculty of Computational Mathematics and Cybernetics Lomonosov Moscow State University Moscow Russian Federation

In this paper we consider a networked system of natural-resource consumption, where the agents are governed by a recently reported model of consumer psychology Dynamics of the consumption for each agent are influenced by the state of the resource and consumption of her neighbors. The process is parameterized by the psychological characteristics of each agent. This study extends the original model to incorporate the underlying network topology and explores the effects of aggregation via densely-connected communities present in the network. The exercise yields new interpretations of the predictions made by the original model in context of the influence network. We present aggregation mechanisms first for certain canonical structures of the consuming population and later on for a class of non-canonically structured populations. In the end we present an approximate aggregation scheme for populations where only some inaccurate information of the consumer characteristics is available. © 2017

关键词： Control in economics identification of environmental systems Modeling Multi-agent systems Natural resources management Social Networks

Existence and Stability of Nonequilibrium Steady States of Nernst-Planck-Navier-Stokes Systems

学校读者我要写书评

暂无评论

arXiv 2022年

作者： Constantin, Peter Ignatova, Mihaela Lee, Fizay-Noah Department of Mathematics Princeton University PrincetonNJ08544 United States Department of Mathematics Temple University PhiladelphiaPA19122 United States Program In Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

MSC Codes 35Q30, 35Q35, 35Q92We consider the Nernst-Planck-Navier-Stokes system in a bounded domain of Rd, d = 2, 3 with general nonequilibrium Dirichlet boundary conditions for the ionic concentrations. We prove the existence of smooth steady state solutions and present a sufficient condition in terms of only the boundary data that guarantees that these solutions have nonzero fluid velocity. We show that time evolving solutions are ultimately bounded uniformly, independently of their initial size. In addition, we consider one dimensional steady states with steady nonzero currents and show that they are globally nonlinearly stable as solutions in a three dimensional periodic strip, if the currents are sufficiently weak. © 2022, CC BY.

关键词： Navier Stokes equations

Nernst-Planck-Navier-stokes systems far from equilibrium

学校读者我要写书评

暂无评论

arXiv 2020年

作者： Constantin, Peter Ignatova, Mihaela Lee, Fizay-Noah Department of Mathematics Princeton University PrincetonNJ08544 United States Department of Mathematics Temple University PhiladelphiaPA19122 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

We consider ionic electrodiffusion in fluids, described by the Nernst-Planck-Navier-Stokes system. We prove that the system has global smooth solutions for arbitrary smooth data: aribitrary positive Dirichlet boundary conditions for the ionic concentrations, arbitrary Dirichlet boundary conditions for the potential, arbitrary positive initial concentrations, and arbitrary regular divergence-free initial velocities. The result holds for any positive diffusivities of ions, in bounded domains with smooth boundary in three space dimensions, in the case of two ionic species, coupled to Stokes equations for the fluid. The result also holds in the case of Navier-Stokes coupling, if the velocity is regular. The global smoothness of solutions is also true for arbitrarily many ionic species, if all their diffusivities are the *** Codes 35Q30, 35Q35, 35Q92 Copyright © 2020, The Authors. All rights reserved.

关键词： Navier Stokes equations

Pre-processing and classification of hyperspectral imagery via selective inpainting

学校读者我要写书评

暂无评论

Pre-processing and classification of hyperspectral imagery v...

IEEE International Conference on Acoustics, Speech and Signal Processing

作者： Victoria Chayes Kevin Miller Rasika Bhalerao Jiajie Luo Wei Zhu Andrea L. Bertozzi Wenzhi Liao Stanley Osher California Research Training Program in Computational and Applied Mathematics United States of America University of California Los Angeles Department of Mathematics United States of America Ghent University Department of Telecommunications and Information Processing Belgium

ISBN: (纸本)9781509041183

We propose a semi-supervised algorithm for processing and classification of hyperspectral imagery. For initialization, we keep 20% of the data intact, and use Principal Component Analysis to discard voxels from noisier bands and pixels. Then, we use either an Accelerated Proximal Gradient algorithm (APGL), or a modified APGL algorithm with a penalty term for distance between inpainted pixels and endmembers (APGL Hyp), on the initialized datacube to inpaint the missing data. APGL and APGL Hyp are distinguished by performance on datasets with full pixels removed or extreme noise. This inpainting technique results in band-by-band datacube sharpening and removal of noise from individual spectral signatures. We can also classify the inpainted cube by assigning each pixel to its nearest endmember via Euclidean distance. We demonstrate improved accuracy in classification over data-mining techniques like k-means, unmixing techniques like Hierarchical Non-Negative Matrix Factorization, and graph-based methods like Non-Local Total Variation.

关键词： Hyperspectral imagery (HSI) data preprocessing image inpainting image classification image enhancement Data preprocessing hyperspectral imagery Image classification image enhancement pixel Pretreatment matrix decomposition initialization Euclidean distance

Pair correlation function characteristics of nearly jammed disordered and ordered hard-sphere packings

学校读者我要写书评

暂无评论

Physical Review E 2005年第1期71卷 011105-011105页

作者： Aleksandar Donev Salvatore Torquato Frank H. Stillinger Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA PRISM Princeton University Princeton New Jersey 08544 USA Department of Chemistry Princeton University Princeton New Jersey 08544 USA

We study the approach to jamming in hard-sphere packings and, in particular, the pair correlation function g2(r) around contact, both theoretically and computationally. Our computational data unambiguously separate the narrowing δ-function contribution to g2 due to emerging interparticle contacts from the background contribution due to near contacts. The data also show with unprecedented accuracy that disordered hard-sphere packings are strictly isostatic: i.e., the number of exact contacts in the jamming limit is exactly equal to the number of degrees of freedom, once rattlers are removed. For such isostatic packings, we derive a theoretical connection between the probability distribution of interparticle forces Pf(f), which we measure computationally, and the contact contribution to g2. We verify this relation for computationally generated isostatic packings that are representative of the maximally random jammed state. We clearly observe a maximum in Pf and a nonzero probability of zero force, shedding light on long-standing questions in the granular-media literature. We computationally observe an unusual power-law divergence in the near-contact contribution to g2, persistent even in the jamming limit, with exponent −0.4 clearly distinguishable from previously proposed inverse-square-root divergence. Additionally, we present high-quality numerical data on the two discontinuities in the split-second peak of g2 and use a shared-neighbor analysis of the graph representing the contact network to study the local particle clusters responsible for the peculiar features. Finally, we present the computational data on the contact contribution to g2 for vacancy-diluted fcc crystal packings and also investigate partially crystallized packings along the transition from maximally disordered to fully ordered packings. We find that the contact network remains isostatic even when ordering is present. Unlike previous studies, we find that ordering has a significant impact on the sh

关键词： MOLECULAR-DYNAMICS SIMULATION DISK PACKINGS CRYSTALLIZATION DISTRIBUTIONS GENERATION PARTICLES PRESSURE

Unexpected Density Fluctuations in Jammed Disordered Sphere Packings

学校读者我要写书评

暂无评论

Physical Review Letters 2005年第9期95卷 090604-090604页

作者： Aleksandar Donev Frank H. Stillinger Salvatore Torquato Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA PRISM Princeton University Princeton New Jersey 08544 USA Department of Chemistry Princeton University Princeton New Jersey 08544 USA

We computationally study jammed disordered hard-sphere packings as large as a million particles. We show that the packings are saturated and hyperuniform, i.e., that local density fluctuations grow only as a logarithmically augmented surface area rather than the volume of the window. The structure factor shows an unusual nonanalytic linear dependence near the origin, S(k)∼|k|. In addition to exponentially damped oscillations seen in liquids, this implies a weak power-law tail in the total correlation function, h(r)∼−r−4, and a long-ranged direct correlation function c(r).

关键词： .saturated power-law structure factor hard-sphere damped sphere packings jammed hyperuniform local density fluctuations nonanalytic direct correlation function

ON THE GLOBAL WELL-POSEDNESS AND GEVREY REGULARITY OF SOME ELECTRODIFFUSION MODELS

学校读者我要写书评

暂无评论

arXiv 2022年

作者： Abdo, Elie Lee, Fizay-Noah Wang, Weinan Department of Mathematics Temple University PhiladelphiaPA19122 United States Program In Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Mathematics University of Arizona TucsonAZ85712 United States

We consider the Nernst-Planck equations describing the nonlinear time evolution of multiple ionic concentrations in a two-dimensional incompressible fluid. The velocity of the fluid evolves according to either the Euler or Darcy’s equations, both forced nonlinearly by the electric forces generated by the presence of charged ions. We address the global well-posedness and Gevrey regularity of the resulting electrodiffusion models in the periodic setting. © 2022, CC BY.

关键词： Nonlinear equations