Brown Analysis Seminar
Abstract: The log Sobolev inequality, due to L. Gross, is an energy-entropy estimate which takes the place of Sobolev inequalities in contexts where they do not hold (for example, infinite-dimensional manifolds). The best constant in the inequality is strongly related to global geometric properties of the manifold (the spectral gap, the isoperimetric constant, and others). In this talk, I will discuss my recent joint work with J.J. Loeb on log Sobolev inequalities in the category of subharmonic functions. In particular, I will discuss a strong log Sobolev inequality for Gaussian (and Gaussian-like measures) which is quite surprising, along with its applications in Segal-Bargmann analysis.
Center for Fluid Mechanics Seminar
Abstract: We present experimental and theoretical research on manipulation of colloids and biological particles in microfluidic systems using AC electric fields. Navigating the AC frequency-amplitude phase space, we effectively and reversibly tune colloidal interactions to yield various steady-state configurations. The colloidal system response can be predicted using a scaling analysis based on the relative importance of dielectrophoresis, electrophoresis, AC-electroosmosis, gravity and Brownian motion. Particularly we present the following applications: 1. Colloidal Microfluidic Circuits: Electric field-directed assembly of gold nano-particles in a microfluidic system enables modulation of the electrical properties within the circuit. Specifically, regulating the colloidal structures enables a single circuit element to act as a variable resistor, capacitor, or inductor in a reversible and switchable fashion. The colloidal microfluidic circuit has the potential for adaptive control of electromagnetic properties across a surface. 2. Bacterial Spore Concentration Using Dielectrophoresis: We present experimental results for concentration of Clostridium Sporogenes spores from various conductivity media, spanning from DI water to milk. Positive DEP diminishes quickly with increased conductivity, and one needs to design electrodes that amplify the negative DEP effects. We present bacterial spore capture in a wide spectrum of media that exhibit 5-orders of magnitudes variation in conductivity, and discuss utilization of the device for water and food safety applications. Bio: Prof. Ali Beskok received his B.S. in Mechanical Engineering from Middle East Technical University, Ankara, Turkiye in 1988. He received an MS degree in Mechanical Engineering from Indiana University Purdue University in Indianapolis in 1991, and M.S. and Ph.D. degrees from Princeton University, Mechanical and Aerospace Engineering in 1994 and 1996, respectively. Dr. Beskok was a Visiting Scholar at Brown University, Center for Fluid Mechanics from 1994 to 1996, and a Post Doctoral Research Associate at Massachusetts Institute of Technology, Research Laboratory of Electronics from 1996-1998. He joined Texas A&M University Mechanical Engineering Department as an Assistant Professor in 1998, and became an Associate Professor in 2004. Currently, he is the Batten Professor of Computational Engineering, and a professor at Old Dominion University, Aerospace Engineering Department.
Stochastic Systems/Probability Seminar
Abstract: I'll discuss well-known relations between spanning trees, loop-erased random walk (LERW), and perfect matchings on planar graphs. I will present a recent result on the computation of the probability that a LERW on a planar graph contains a given edge.
Lefschetz Center for Dynamical Systems Seminar
Abstract: Recently, differential equations involving both delayed and advanced arguments have appeared in an increasing number of models, originating from a wide variety of scientific disciplines. We present recent theoretical and numerical results concerning bifurcations from homoclinic and periodic solutions to such equations. In particular, we show how Lin's method can still be used in the infinite dimensional setting of MFDEs.
Department of Mathematics Colloquium
Lefschetz Center for Dynamical Systems Seminar
Abstract: We study monotone traveling wave solutions connecting 0 and 1 for a class of N dimensional lattice differential equations of the form $$u_v^' = -u_v + g(u_{v-e_1},u_{v-e_2},\cdots, u_{v-e_N}); v \in Z^N$$ and which contain $$u_n^' = -u_n + (u_{n-1})^2; n \in Z$$ as an example. We establish the existence of a minimum wave speed $c_*$ such that for $c \geq c_*$ there is a unique monotone traveling wave connecting 0 and 1. The critical wave speed $c_*$ depends on the direction of propagation in a higher dimensional lattice as well as the gradient of the convex envelope of the nonlinear coupling function $g$ evaluated at the spatially homogeneous equilibrium $(1,1,\cdots,1)$. Our techniques are grounded in the direct analysis of a differential-delay equation; our intuition is guided by spatial dynamics.
Center for Computational Molecular Biology Seminar Series
Abstract: The ends of eukaryotic chromosomes are protected by telomeres, nucleoprotein structures that are essential for chromosomal stability and integrity. Understanding how telomere length is controlled has significant medical implications, especially in the fields of aging and cancer. Two recent systematic genome-wide surveys measuring the telomere length of deleted mutants in the yeast Saccharomyces cerevisiae have identified hundreds of telomere length maintenance (TLM) genes, which span a large array of functional categories and different localizations within the cell. In my talk I will describe two recent works on integrating large-scale screening mutant data with protein-protein interaction information to rigorously chart the cellular subnetwork underlying the function investigated. I will show their application to the yeast telomere length control data, identifying pathways that connect the TLM proteins to the telomere-processing machinery, and predicting new TLM genes and their effect on telomere length.
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PDE Seminar
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