MSTuD13
Analysis and algorithm for coupling of kinetic and fluid equations  Part III of III
For Part I, see MSMoD13
For Part II, see MSMoE13
Date: August 11
Time: 13:3015:50
Room: 32
(Note: Click title to show the abstract.)
Organizer:
Lu, Jianfeng (Duke Univ.)
Sun, Weiran (Simon Fraser Univ.)
Abstract: Kinetic equations are widely used to model complex systems occurring in gas dynamics and transport phenomenon, as examples. In these applications, it is common that dense and dilute parts coexist in the system. This leads to multiple spatiotemporal scales which introduce difficulties in both analysis and numerics. Kineticfluid coupling hence has received intensive studies in recent years. This minisymposium aims to bring together experts in analysis and algorithm in kinetic equations to discuss the current status and future developments of the field. It also provides a platform for further interaction and collaboration for researchers in this and related areas.
MSTuD131
13:3014:00
Hydrodynamic limits from kinetic equations in bounded domain
Jiang, Ning (Tsinghua Univ., Beijing)
Abstract: In this talk I will review the hydrodynamic limits from kinetic equations in domain with boundary. Incompressible NavierStokes equations can be derived from Boltzmann equation with Maxwell reflection boundary condition. The boundary conditions for the NS equation depends on the relative sizes of the Knudsen number and accommodation number. We also will discuss the incompressible Euler limit, in particular the relation with Prandtl boundary layer.
MSTuD132
14:0014:30
Uncertainty quantification for kinetic equations
Jin, Shi (Univ. of WisconsinMadison & Shanghai Jiao Tong Univ.)
Abstract: In this talk we will study the generalized polynomial chaos (gPC) approach to
hyperbolic and kinetic equations
with uncertain coefficients/inputs, and multiple time or space scales, and show\
that they can be made
asymptoticpreserving or wellbalanced, in the sense
that the gPC scheme preserves various asymptotic limits in the discrete space. \
This allows the implemention
of the gPC methods for these problems without numerically resolving (by space, \
time, and gPC modes)
the small scales.
CPTuD133
14:3014:50
A multilevel Monte Carlo method for the kinetic equations of plasma dynamics
Ricketson, Lee (New York Univ.)
Abstract: The multilevel Monte Carlo (MLMC) method  introduced by Giles for rapid valuation of financial assets modeled by SDEs  has found numerous applications in other fields, where it frequently accelerates computations by multiple orders of magnitude. An outstanding challenge, however, is the application of the method to McKeanVlasov equations  SDEs featuring interaction with a mean field determined by an average over the underlying stochastic dynamics. Such equations are ubiquitous in statistical models of physical phenomena. Of particular interest are kinetic equations, whose high dimensionality makes Monte Carlo particularly attractive. We present a generalization of MLMC to a class of McKeanVlasov equations, with particular emphasis on applications to the acceleration of the particleincell (PIC) codes that are ubiquitous in the kinetic plasma simulation community. Both theoretical results establishing the efficiency of the method and results from numerical tests will be discussed.
CPTuD134
14:5015:10
A robust numerical method for a multiscale dynamical system
Patidar, Kailash C. (Univ. of the Western Cape)
Abstract: In this talk, we will consider a multiscale dynamical system arising in mathematical biology. The various parameters involved in the models that very at different time scales make such governing problems very difficult to be solved analytically. One can gather semiqualitative information about the solutions using standard analytical techniques. However, a full description about the behavior of solutions is hardly obtainable. To this end, we will discuss a class of numerical methods that can better suit such models. Proposed method will be explored on a number of test examples.
CPTuD135
15:1015:30
A kinetic model of wealth distribution and migration phenomena
Knopoff, Damian (Universidad Nacional de Cordoba)
Torres, German Ariel (Facultad de Matematica, Astronomia y Fisica  Universidad Nacional de Cordoba  CIEM  CONICET)
Abstract: A kinetic model for wealth distribution within a population based on the kinetic theory for active particles is presented, where individuals are characterized by a microscopic variable (the activity) describing their state and are subdivided into classes, including the eventual migration of individuals between populations. In contrast to previous models, it is assumed that interactions among individuals (viewed as trades) are nonconservative and that an external agent (e.g. the State) implements certain distribution policies, since it is clear that wealth can be created and destroyed within a society and consequently the total wealth and the mean wealth per capita evolves in time.
The model is stated in terms of a system of differential equations modelling the time evolution of a distribution function that represents the proportion of individuals in each class. Existence and uniqueness of solutions are shown and some selected simulations representing different scenarios and a parameter
CPTuD136
15:3015:50
Escaping an infestation of parasites by outrunning them: insights from a simple stochastic model
Dong, JiaJia (Bucknell Univ.)
Abstract: Coexistence of multiple species abounds in ecological systems as a consequence of various interactions. We study a parasitehost model, in which the parasites wander randomly and die, giving birth only when they land on the host. For a stationary host with certain boundary conditions, the stochastic process can be solved and the results match well to Monte Carlo simulations. In nontrivial stationary states, the characteristics of the ˇ°parasitecloudˇ± around the host are well understood. If the host moves with uniform velocity, solving the problem becomes much more challenging. Instead, we consider a stationary host with parasites performing biased diffusion, for which our theoretical predictions also agree with simulation. In the appropriate continuum limit, the two processes are identical but interesting differences emerge in our lattice model. The most notable phenomenon is that the stationary parasite population generally increases with the bias, reaching a maximum before vanishing at some critical value.
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Footnote: Code: TypeDateTimeRoom No.
Type : IL=Invited Lecture, SL=Special Lectures, MS=Minisymposia, IM=Industrial Minisymposia, CP=Contributed Papers, PP=Posters
Date: Mo=Monday, Tu=Tuesday, We=Wednesday, Th=Thursday, Fr=Friday
Time : A=8:309:30, B=10:0011:00, C=11:1012:10, BC=10:0012:10, D=13:3015:30, E=16:0018:00, F=19:0020:00, G=12:1013:30, H=15:3016:00
Room No.: TBA
