Fri, 28 May 2021

15:00 - 16:00
Virtual

The applications and algorithms of correspondence modules - Haibin Hang

Haibin Hang
(University of Delaware)
Abstract

 In this work we systematically introduce relations to topological data analysis (TDA) in the categories of sets, simplicial complexes and vector spaces to characterize and study the general dynamical behaviors in a consistent way. The proposed framework not only offers new insights to the classical TDA methodologies, but also motivates new approaches to interesting applications of TDA in dynamical metric spaces, dynamical coverings, etc. The associated algorithm which produces barcode invariants, and relations in more general categories will also be discussed.

Mon, 10 Nov 2014
17:00
L2

Non-Newtonian Flows: The mathematics of surfactant mixtures

Pam Cook
(University of Delaware)
Abstract

In highly concentrated surfactant solutions the surfactant molecules self-assemble into long flexible "wormy" structures. Properties of these wormlike micellar solutions make them ideal for use in oil recovery and in body care products (shampoo). These properties depend strongly on temperature and concentration conditions.   In solution the "worms" entangle, forming a network, but also continuously break and reform, thus earning the name ‘living polymers’. In flow these fluids exhibit spatial inhomogeneities,  shear-banding, and dynamic elastic recoil. In this talk a rheological equation of state that is capable of describing these fluids is described   The resultant governing  macroscale equations consist of a coupled nonlinear partial differential equation system.  Model predictions are presented, contrasted with experimental results, and contrasted with predictions of other existing models.  Generalizations of the model to allow the capturing of  behaviors under changing concentration or temperature conditions, namely power law and stretched exponential relaxation as opposed to exponential relaxation, will be discussed and  particularly a mesoscale stochastic simulation network model will be presented.  

Tue, 05 Nov 2013

14:00 - 14:30
L5

Optimal domain splitting in Chebyshev collocation

Toby Driscoll
(University of Delaware)
Abstract
Chebfun uses a simple rule, essentially a binary search, to automatically split an interval when it detects that a piecewise Chebyshev polynomial representation will be more efficient than a global one. Given the complex singularity structure of the function being approximated, one can find an optimal splitting location explicitly. It turns out that Chebfun really does get the optimal location in most cases, albeit not in the most efficient manner. In cases where the function is expensive to evaluate, such as the solution to a differential equation, it can be preferable to use Chebyshev-Padé approximation to locate the complex singularities and split accordingly. 

 

Thu, 18 Jan 2007

14:00 - 15:00
Comlab

Radial basis function methods for meshless PDE computation

Prof Toby Driscoll
(University of Delaware)
Abstract

Radial basis functions have been used for decades for the interpolation of scattered,

high-dimensional data. Recently they have attracted interest as methods for simulating

partial differential equations as well. RBFs do not require a grid or triangulation, they

offer the possibility of spectral accuracy with local refinement, and their implementation

is very straightforward. A number of theoretical and practical breakthroughs in recent years

has improved our understanding and application of these methods, and they are currently being

tested on real-world applications in shallow water flow on the sphere and tear film evolution

in the human eye.

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