Joint Solid Mechanics/Material Science Seminar
Abstract: Carbon-based structures have been at the forefront of materials technology for over a decade. Vapor deposited diamond, for example, has been targeted for coatings and microelectronic device applications, while nanotubules are being pursued for use in nanocomposites and in nanoelectronic devices. This talk will focus on two research areas being pursued in our group in which computational methods are used to predict the properties and applications of carbon-based materials systems. In the first part of the talk, a modeling paradigm will be presented that combines results from density functional calculations, molecular modeling, and mesoscale continuum theory to predict macroscale properties such as fracture toughness of polycrystalline diamond films from first principles. The second part of the talk will focus on properties of fullerene nanotubules, including predictions of enhanced reactivity at buckles, a rolling-to-sliding transition of nanotubules moving on graphite, and electronic properties of novel configurations being explored theoretically for various nanoelectronic device applications.
(Rescheduled) -- Statistical Science Seminar
Abstract: Studies that investigate the effect of human teratogens on fetal development typically record the presence or absence of a multitude of birth defects for each infant, resulting in data of multivariate binary form. Such studies typically have three objectives: (1) estimate an overall effect of exposure across outcomes, (2) identify subjects affected by exposure, and (3) identify those outcomes that constitute the syndrome so that these can be used as diagnostic tools during future physical examinations. We propose the use of a logistic regression model with crossed random effect structure to address all three questions simultaneously. Special cases of the model refer to order-restricted exposure effects, exposure effects clustered according to location (face, head, hands, feet or body), and estimation of exposure effects via techniques analogous to the lasso. We use the proposed models to analyze data from a study investigating the effects of in utero antiepileptic drug exposure on fetal development. This is joint work with Jim Hobert, Louis Ryan, and Lewis Holmes. Reception following seminar at 167 Angell St., 2nd floor Conference Room.
Stochastic Systems Seminar
Abstract: We consider the exponential decay rate of the stationary tail probabilities of reflected Brownian motion $X$ in the $N$-dimensional orthant. Under a stability condition, it is known that the exponential decay rate has a variational representation $V(x)$. We will discuss a new representation for $V(x)$ in terms of a time-reversed optimal control problem, and indicate how it can be solved in certain cases.
Abstract: Decorated characters are widely used in various documents. Practical optical character reader (OCR) is required to deal with not only common fonts but also complex designed fonts. However, since appearances of decorated characters are complicated, most general character recognition systems cannot give good performances on such decorated characters.
In this talk, we will propose an algorithm that can extract a character's essential structure from a decorated character. The algorithm is applied in preprocessing of character recognition, and the extracted image can be dealt with by existing character recognition systems.
The proposed algorithm consists of three procedures: (i) global structure extraction, (ii) interpolation of structure and (iii) smoothing. By using multi-scale images, topographical features such as ridges and ravines are detected for structure extraction. Ridges are used for extracting global structure, and ravines are used for interpolation. Experimental results show character structures are clearly extracted from very complex decorated characters.
Brown Applied Mathematics Pattern Theory and Vision Seminar
Abstract: We address the problem of how to reinforcement learn in ultra-complex environments with huge state spaces, where on must learn to exploit compact structure of the problem domain. The approach we propose is to simulate the evolution of an artificial economy of computer programs. The economy is constructed based on two simple principles so as to assign credit to the individual programs for collaborating on problem solutions. We find empirically that, starting from programs that are random computer code, we are able to evolve systems that solve hard problems. In particular our economy has learned to solve arbitrary block stacking problems, to unscramble about half a randomly scrambled Rubik's cube, and to solve several among a collection of commercially sold puzzles. Joint work with Igor Durdanovic.
* Special Scientific Computing Seminar *
* Special Scientific Computing Seminar *
Abstract: We present a finite element scheme, first or second order, for multi-dimensional hyperbolic systems of conservation laws on unstructured meshes. Convergence problems are studied for scalar equations. Lp strong convergence is proved under some conventional conditions. If the solutions are sufficiently smooth and the meshes are uniform, second order error estimates for the second order scheme in L2 and H1 norms are proved for two and three dimensional cases. Some numerical examples are given.
* Special Joint LCDS/Scientific Computing Seminar *
Abstract: The effects of Rossby wave -- turbulence interactions on particle dispersion are investigated in a Lagrangian analysis of the potential vorticity equation for idealized two dimensional turbulence on a $\beta $--plane. The goal is the development of realizable turbulence models for large scale geophysical flows. A Lagrangian analysis produces several exact statistical results for fluid particle dispersion which have direct consequences for simple eddy-viscosity like approximations. Indeed, it seems plausible that the vanishing of the meridional eddy viscosity plays a large role in the establishment of highly stable zonal jets so often observed. In the inviscid problem the first integral time scale of the meridional velocity is found to be zero and the meridional particle dispersion is bounded. The second integral time scale, which determines the magnitude of the bound, is shown to depend explicitly on $\beta $, the enstrophy and the energy of the meridional velocity. The applicability of these predictions is verified in a series of numerical simulations. For a range of $\beta $ values, the meridional extent of quasi-steady, alternating zonal jets appearing in the numerical solutions is seen to scale with the length scale given by the meridional particle dispersion. The relation between this inherent dispersion scale and the dynamic length given by the Rhines' ``classical'' theory is discussed.
Abstract: The basic equations of Kinetic Theory exhibit vastly different behavior as relativistic corrections are introduced into the classical formulations. "Good" and "bad" effects will be illustrated in several cases, and major open problems will be stated. Recent progress on the convergence of the solution of the two-dimensional relativistic Vlasov-Maxwell system to the classical Vlasov-Poisson system (as the speed of light becomes infinite) will be briefly discussed.
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