Hydrodynamic fluctuations in quasi-two dimensional diffusion
DateFriday, October 5, 2018 - 3:00pm
AbstractWe study diffusion of colloids on a fluid-fluid interface using particle simulations and fluctuating hydrodynamics. Diffusion on a two-dimensional interface with three-dimensional hydrodynamics is known to be anomalous, with the collective diffusion coefficient diverging like the inverse of the wavenumber. This unusual collective effect arises because of the compressibility of the fluid flow in the plane of the interface, and leads to a nonlinear nonlocal convolution term in the diffusion equation for the ensemble-averaged concentration. We study the magnitude and dynamics of density and color density fluctuations using a novel Brownian dynamics algorithm, as well as fluctuating hydrodynamics theory and simulation. We also examine nonequilibrium fluctuations in systems with two-dimensional hydrodynamics, such as thin smectic films in vacuum. We find that nonequilibrium fluctuations are colossal and comparable in magnitude to the mean, and can be accurately modeled using numerical solvers for the nonlinear equations of fluctuating hydrodynamics.
Analyzing Scalar Data with Computational Topology and TTK
DateFriday, October 12, 2018 - 3:00pm
AbstractIn this talk, I will discuss and demonstrate recent work with collaborators at UPMC Sorbonne on the creation of the Topological ToolKit (TTK), an open source software platform for topological data analysis of piecewise linear scalar fields. TTK is built on top of VTK and ParaView, and provides access points for developers, end users, and researchers across a wide of range of experience levels. Two key advantages of TTK are that it (1) provides a unified platform for topological analysis, allowing a modular approach to analyzing data under a consistent set of mathematical abstractions and (2) offers an efficient triangulation data structure that caches queries for repeated use. TTK is available on the web at https://topology-tool-kit.github.io/ Bio: Joshua A. Levine is an assistant professor in the Department of Computer Science at University of Arizona (http://www.cs.arizona.edu/~josh). Prior to starting at Arizona in 2016, he was an assistant professor at Clemson University from 2012 to 2016, and before that a postdoctoral research associate at the University of Utah’s SCI Institute from 2009 to 2012. He received his PhD in Computer Science from The Ohio State University in 2009 after completing BS degrees in Computer Engineering and Mathematics in 2003 and an MS in Computer Science in 2004 from Case Western Reserve University. His research interests include visualization, geometric modeling, topological analysis, mesh generation, vector fields, performance analysis, and computer graphics.
High Order Mimetic Difference Operators
DateFriday, October 19, 2018 - 3:00pm
AbstractMimetic Difference Operators satisfy a discrete analog of the divergence theorem and they are used to create/design conservative/reliable numerical representations to continuous models. We will present mimetic versions of the divergence and gradient operators which exhibit high order of accuracy at the grid interior as well as at the boundaries. As a case of study, we will show fourth order operators Divergence and Gradient in a one-dimensional staggered grid. Mimetic conditions on discrete operators are stated using matrix analysis and the overall high order of accuracy determines the bandwidth of the matrices. This contributes to a marked clarity with respect to earlier approaches of construction. As test cases, we will solve 2-D elliptic equations with full tensor coefficients. Additionally, applications to elastic wave propagation under free surface and shear rupture boundary conditions will be given.
Mathematical Models, Parameter Identification, and Uncertainty
DateFriday, October 26, 2018 - 3:00pm
Abstract: Many mathematical models, such as those commonly used to quantitatively describe various biological processes, contain a large number of rate constants. The components of the state vector usually are not directly observable, and first-principles estimates of the rate constants rarely are available. Instead, one relies on time series that are functions of the state vector to validate the model. This talk will discuss the following question: if values of model parameters can be found that fit the observed data, then what confidence can we place in predictions from the model? The predictions depend on the model parameters, for which there may or may not be unique estimates that correspond to a given set of observations; this is the identifiability problem. I will give examples from simple SIR models to more complicated models of prostate cancer.