[00060] Mathematical approaches to collective phenomena
Session Time & Room : 3C (Aug.23, 13:20-15:00) @E803
Type : Proposal of Industrial Minisymposium
Abstract : The contributions of the mathematics to understanding of collective phenomena such as the fluid dynamics are certainly conspicuous. In particular, developments of the numerical method to solve PDE, PDE analysis of the hydrodynamic equation or Boltzmann equation by applied mathematicians are quite significant in the industry. This minisymposium invites four eminent researchers, who study various types of collective phenomena such as the gas dynamics, biological swarming, electrically charged fluids and so on. Their presentations will indicate new insights and inspirations in the future applied mathematics.
[04763] Multi-fidelity method for a class of kinetic equations with uncertainties
Format : Talk at Waseda University
Author(s) :
Liu Liu (The Chinese University of Hong Kong )
Lorenzo Pareschi (University of Ferrara)
xueyu zhu (University of Iowa)
Abstract : In this talk, we will discuss some recent development on the topic of multi-fidelity methods for solving a class of kinetic equations with uncertainties and multiple scales. The Boltzmann equation, linear transport equation and epidemic transport system will be particularly studied, together with formal error estimates. We will also briefly discuss application of deep learning approaches to study kinetic problems.
[04788] Brownian HydroDynamics for Confined Electrolyte Solutions
Format : Talk at Waseda University
Author(s) :
Aleksandar Donev (Courant Institute, New York University)
Abstract : Electrolyte solutions appear in many engineering systems and processes, such as desalination, microfluidic pumps, and batteries. For confined electrolytes, (quasistatic) long-ranged electrostatic interactions among the particles play a crucial role in the static structure. Similarly, hydrodynamic interactions (HIs) mediated by the solvent are also long-ranged and affect the dynamics in crucial ways. Confinement in slit channel geometries is of particular importance, especially for electrohydrodynamics and electrochemistry near electrodes in devices and batteries. In particular, very thin electric (Debye) double layers with complex structure form near dielectric or metallic boundaries and many important electro-hydrodynamic phenomena occur in this layer. I will discuss the limitations of the classical Poisson-Nernst-Planck-Stokes equations for non-dilute electrolytes, in which the Debye scale is molecular, and present an alternative Brownian HydroDynamics (BD-HI) approach that uses fluctuating hydrodynamics for the solvent but represents the ions as explicit Brownian particles. By using BD-HI we are able to reach much longer (diffusive) time scales than molecular dynamics because of the implicit overdamped solvent, at the expense of loosing some microscopic details.
[04809] Delay Models of Collective Behavior with Biological and Industrial Applications
Format : Talk at Waseda University
Author(s) :
Jan Haskovec (King Abdullah University of Science and Technology)
Abstract : The talk will give an overview of recent results for models of collective behavior governed by delay differential equations. It will focus on models of interacting agents with applications in biology (flocking, swarming), social sciences (opinion formation) and engineering (swarm robotics), where latency (delay) plays a significant role. We will explain that there are two main sources of delay - inter-agent communications and information processing - and show that they have qualitatively different impacts on the group dynamics. We will give an ovierview of analytical methods for studying the asymptotic behavior of the models and their mean-field limits. Finally, motivated by situations where finite speed of information propagation is significant, we will introduce an interesting class of problems where the delay depens nontrivially and nonlinearly on the state of the system, and discuss the available analytical results and open problems here.
[04973] Model Cascades for Dilute Gases Based on Moment Equations
Format : Talk at Waseda University
Author(s) :
Manuel Torrilhon (RWTH Aachen)
Abstract : Dilute gas flows show thermal non-equilibrium due to lack of particle collisions. This requires modeling using the statistical description of kinetic gas theory. Moment equations extend the classical fluid dynamic equations for processes with moderate Knudsen numbers. We will present non-equilibrium models based on moment approximations, which provide a hierarchy of models in a cascading nature. This can be used to estimate model errors and perform model-adaptive simulations.
