Lefschetz Center for Dynamical Systems Seminar
Brown University Center for Statistical Sciences Seminar
Abstract: Functional magnetic resonance imaging (fMRI) is a non-invasive technique that provides high resolution information about brain blood flow and oxygenation. This allows researchers to study which localized regions of the brain are activated by various stimuli and cognitive processes. Measuring brain activity is accomplished through very indirect means, resulting in very noisy (although rather large) data sets. The analysis of such data involves a multitude of statistical challenges. Some basic approaches to making statistical inference will be introduced, along with a discussion of current problems that remain.
LEMS and Electrical Science Seminar
Abstract: During the last few years, the complexity and size of digital systems has increased so drastically that guaranteeing correctness is no longer a trivial task. Formal verification provides a framework that allows to reason formally about the behavior of a system. The implementation is checked against a set of properties that have to be satisfied. Typically, a digital system is modeled as a collection of interacting subsystems. As new subsystems are added the number of states may grow exponentially. This is known as the "state domain explosion" problem. Abstract interpretation is one approach to alleviate the state domain explosion problem. The main idea is to interpret the behavior of a system in a different abstracted (and therefore simplified) system with fewer states. The challenges for these techniques are the range of applicability and the degree of automation provided to the designer. So far, automatic abstraction techniques have been applied in very specific examples, and usually require the user intervention to guide the process. This presentation proposes an automatic abstraction paradigm to verify generic digital systems, as well as a practical implementation.
Biography: Abelardo Pardo received his BS and MS degrees in Computer Science at the Polytechnic University of Catalonia, Barcelona, Spain, in 1991 and his Ph.D. at the University of Colorado at Boulder in 1997. His areas of interest include formal verification of reactive systems and algorithms for automatic abstraction for verification. He is currently working at the Boston Advanced Development Labs of Mentor Graphics in Billerica, MA.
Joint Center for Fluid Mechanics & Division of Engineering Seminar
Abstract: The swirling pipe flow is of interest from a point of view of fundamentals as much as from that of engineering applications. The difficulties associated with this flow are both of an experimental and of a theoretical nature. For example, the difficulties in the proper modelling of turbulent swirling flows are well known. The susceptibility of these flows to probes introduced for measurements is equally well known. A major difficulty, that is met with in these flows is also regarding experimental realization of a well defined distribution of angular momentum in the swirling flows, which, it is known, is difficult with conventional vanes.
Our present work is an attempt to generate a swirling flow with a distribution of angular momentum close to solid body rotation over some length in a pipe in the turbulent regime. We report on Laser-Doppler measurements of the velocity vector and turbulence quantities in this flow.
Our apparatus for creating the well defined swirl consists of a long pipe rotating about its own axis with a honeycomb structure inside. The individual channels of the honeycomb have a length to diameter ratio 90:1.
Three-dimensional LDA measurements of the flow downstream of the rotating honeycomb are performed utilizing a refractive index matching technique, wherein the flowing fluid, the pipe, the surrounding viewing box, and the fluid inside the box all have the same refractive index. Hence, all refraction effects due to curved walls are avoided. To prevent change of the refractive index by thermal effects the temperature of the medium is controlled.
Preliminary measurements of the velocity and turbulence behaviour in this flow will be presented.
Stochastic Systems Seminar
Abstract: Let $\{\omega_i\}$ denote a sequence of i.i.d. random variables, and let $X_n$ denote the random walk which, when at site $i$, jumps right with probability $\omega_i$. Recurrence and transience criteria for $X_n$ were provided by Solomon (1975), and sub-diffusive behaviour in the recurrent case was demonstrated by Sinai (1982). Large deviations, conditioned on the environment, were derived by Greven and den Hollander (1994).
It turns out that the behaviour of the probabilities $P(X_n/n\sim v)$ sharply differs from the standard random walk, and sub-exponential regimes coexist with large deviation type asymptotics. I will review in this talk an approach to this problem, yielding both the LDP and the sub-exponential regime, and some surprising identities between the process and its time reversal.
Brown Analysis Seminar
Brown University Graduate School Dissertation Defense
Scientific Computing Seminar
Abstract: Krylov subspace methods are iterative methods that are widely used for numerically solving large-scale linear systems, especially those arising in PDE applications. A Newton-Krylov method is an implementation of Newton's method in which the linear systems that characterize Newton steps are solved approximately using a Krylov subspace method. Newton-Krylov methods have enjoyed considerable success on large-scale nonlinear systems, notably those associated with CFD problems. In this talk, I will first review Krylov subspace methods and their implementation in Newton-Krylov methods, focussing on globalization and other issues that must be considered for practical effectiveness. I will then report on extensive experiments aimed at evaluating the effectiveness of Newton-Krylov methods in solving problems involving steady-state fluid flow coupled with heat and mass transfer. This experimental work is joint with J. N. Shadid and R. S. Tuminaro at Sandia National Laboratories.
PDE Seminar
Department of Mathematics Colloquium
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