Center for Computational Molecular Biology Lecture
The Scripps Research Institute, Faculty Candidate | |
Special PDE & Lefschetz Center for Dynamical Systems Seminar
Center for Computational Molecular Biology Lecture
Lefschetz Center for Dynamical Systems Seminar
School of Mathematics, Georgia Tech., Atlanta, GA | |
Abstract: As an experimental law, Darcy's law plays an important role in the investigation on compressible flows through porous medium. It was conjectured that Darcy's law can be verified by basic balance laws of mechanics time asymptotically. Previous attempts are able to justify the conjecture for small smooth flows away from vacuum. I will show a proof to the conjecture valid for all physical isentripic flows. The approch is then generalized to uniformly bounded adiabatic flows.
Cognitive & Linguistic Sciences
Spring 2005 Colloquium and CG233 Speakers
Brown University -
Joint Materials/Solid Mechanics Seminar Series
Abstract: Molecular dynamics investigations of plastic deformation in amorphous silicon (a-Si) as modeled by the Stillinger-Weber potential reveal a number of striking characteristics. Disordered systems of differing densities (created by quenching molten Si at different rates) exhibit a range of yield phenomena, from no unambiguously discernable yield strength to pronounced and distinct yield strengths. The constant volume flow state may be accompanied by a dramatic rise or fall in system pressure. This unusual behavior is explained in terms of coexistence and transformations between two distinct atomic environments of amorphous silicon. One is structurally similar to atomic environments in diamond cubic Si and is therefore termed "solidlike." The other=="liquidlike"-- environments is similar to atomic environments in liquid Si. A mesoscopic analysis shows that liquidlike atomic environments act as plasticity carriers in a-Si and --because of their relatively higher density--account for the drop in pressure during constant volume deformation of slowly quenched a-Si.
Insight into the atomic mechanisms of plasticity is obtained by investigating the discrete stress relaxation events that occur when a-Si is deformed by the effectively zero-temperature method of potential energy minimization. Inelastic transformations in well-localized sections of the simulated systems are seen to accompany such stress relaxations. The size of these transforming regions shows a direct linear correlation with the deviatoric component of the accompanying stress relaxation increment, suggesting the existence of a "unit inelastic shearing event" in a=Si. Recurring atomic bonding arrangements observed in inelastically transforming regions of a-Si as well as in the atomic clusters that trigger relaxations indicate that these unit shearing events involve bond length transitions between the two split peaks of the second nearest neighbor shell of bulk a-Si. Meanwhile, investigation of regions responsible for triggering of individual stress relaxations reveals a local yielding criterion that is met at onset of every such relaxation. This criterion confirms that inelastic relaxation is made easier by the more abundant presence of liguidlike atomic environments. Taken together, these observations indicate that plastic flow in a-Si proceeds through a series of autocatalytic avalanches of unit inelastic events.
The results obtained brom investigations of plastic deformation in bulk a-Si are applied to explaining phenomena observed during plastic flow in quasi-columnar nanocrystalling Si.
Stochastic Systems Seminar
Abstract: In this talk I will consider a singular stochastic control problem with an infinite horizon discounted cost criterion. The cost function, state space and control set are all unbounded. In particular, the state space is a polyhedral cone in R^k and for a control to be admissible the corresponding controlled process must satisfy the state constraint condition. For the cost function we assume that polynomial upper and lowerbounds (of the same order) hold. We show that the value function V is the unique solution of the associated Bellman equation with a state constraint boundary condition, in the sense of viscosity solutions. Such control problems arise in the formal heavy traffic limit analysis of scheduling control in open queuing networks. The connection between the above problem of singular control with state constraints and the Brownian control problems of Harrison (1988) will be described. This is a joint work with Rami Atar.
Applied Mathematics Colloquium
University of Texas | |
Abstract: In the presence of market frictions- such as, among others, stochastic volatility, non-traded assets and event risk- the classical arbitrage free valuation theory becomes inapplicable. Various approaches have been developed for the pricing and risk management of the emerging unhedgeable risks. One of them, known as indifference valuation, stems from partial equilibrium arguments and provides a coherent framework for the integration of derivative pricing and optimal investment in arbitrary market environments. It gives rise to challenging stochastic optimization problems for the prices and the risk monitoring strategies. In this talk, an overview of the indifference valuation theory will be given together with a discussion on various applications and their associated stochastic control problems.
Scientific Computing Seminar
and Department of Mathematics, Humboldt-Universitaet zu Berlin, Germany | |
Abstract: Harmonic maps are stationary points of the Dirichlet energy among functions with values in the unit sphere. Owing to the nonconvex constraint, harmonic maps are non-unique and fail to admit higher regularity properties. Moreover, the constraint prohibits the use of standard tools for the numerical approximation. In this talk we discuss stability and weak convergence of three numerical schemes. The first scheme consists in the minimization of the Dirichlet energy over suitable tangent spaces and a renormalization of the update in each iteration. The second approach penalizes the constraint and leads to a time-dependent Ginzburg-Landau equation. A projection method for the discretization of the harmonic map heat flow is the basis for the third approach. Besides stating sufficient conditions for stability and weak convergence to an exact solution, we indicate generalizations to the approximation of p-harmonic maps. Applications include liquid crystal theory, image processing, and micromagnetics.
Part of this talk is based on joint work with Joy Ko.
Brown University Center for Statistical Sciences Seminar
Abstract: Analysis of incomplete data requires assumptions about the mechanism that divides the complete sample into its observed and missing parts. When two different types of missing values occur in the same data set, one should also consider the process that partitions the missing data into the two groups. This work extends Rubin's (1976) concept of missing at random to two sets of missing values, describing conditions under which the missing-data processes may be completely or partially ignored. Conventional multiple imputation (MI) replaces the missing values in a data set by m>1 sets of simulated values. I explore a two-stage extension of MI in which the missing data are partitioned into two parts and imputed N=mn times in a nested fashion. Two-stage MI divides the missing information into two components of variability, lending insight when the missing values are of two qualitatively different types. Point estimates and standard errors from the $N$ complete-data analyses are consolidated by simple rules derived by analogy to nested analysis of variance. I present simple examples of two-stage MI and discuss a variety of potential applications.
Department of Mathematics Colloquium Lecture
PDE Seminar
Abstract: We consider finite time blowup solutions of the L^{2} -critical cubic focusing nonlinear Schrodinger equation on R^{2}. Such functions, when in H^{1}, are known to concentrate a fixed L^{2}-mass (the mass of the ground state) at the point of blowup. Blowup solutions from initial data that is only in L^{2} are known to concentrate at least a small amount of mass. In this paper we consider the intermediate case of blowup solutions from initial data in H^s, with 1 > s > s_Q, where s_Q 1/5 + 1/5 sqrt {11}. Our main result is that such solutions, when radially symmetric, concentrate at least the mass of the ground state at the origin at blowup time.
Department of Mathematics Colloquium Lecture
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