Brown University
Joint Materials/Solid Mechanics Seminar Series
School of Civil and Environmental Engineering, Cornell University | |
Abstract: Introduced by Barenblatt and Dugdale in the 1960's, cohesive fracture postulates that cracks grow because a material's inherent ability to self-cohere degrades when sufficiently high loads are applied at crack sites. In the area of dynamic fracture, we have analyzed adaptive finite element models of cohesive fracture, which are applicable to the case of crack growth in a homogeneous material in which the crack may follow complicated patterns not known in advance. We have shown that finite element analysis is unlikely to converge to any kind of underlying mechanical solution unless the model has a property called time continuity and the spatial discretization is sufficiently rich in element orientations, a condition known to be satisfied by a single class of discretizations (pinwheel meshes). We have also applied cohesive fracture to the prediction of fatigue crack growth by showing that cohesive fracture in this area can be equated to introduction of a damage variable whose evolution describes stiffness degradation as well as crack healing via closure.
Parts of this talk represent joint work with A. Ural, C. Sam, P. Ganguly, V. Krishnan and S. Vavasis.
*Center for Computational Molecular Biology Seminar Series*
Massachusetts Institute of Technology, Cambridge, MA | |
Abstract: Many genome-scale search or comparison projects require the creation of a data-structure which supports the efficient location of nucleotide or amino acid words. Such indices can, for example, provide the seeds for genome alignments (to proteins, ESTs, or other genomes) or an initial set of "overlaps" for assembly. These indices tend to be space intensive. For example, the suffix tree, a popular data structure for this purpose requires more than an order of magnitude more space than the original sequence. This requiring at least some part of the project to be run on a "big memory" machine or a cluster of computers, providing a significant obstacle to resource-poor researchers.
With a recent data-structure, the compressed suffix array (CSA) implemented via the Burrows-Wheeler transform, we can trade time-efficiency for space-efficiency, taking equal or logarithmically more time, but typically taking up less space than that of the indexed sequence. This is more than an order of magnitude trade between the run time and the memory required. If space is more expensive than time, this is an appropriate approach to consider.
I implemented a space-efficient implementation of the CSA on nucleotide data requiring less than 5 bits per nucleotide character to build, and less than 2.5 bits per character, once built. I will present a description of this data structure and how it can used to obtain matches. My implementation was demonstrated by aligning two mammalian genomes on a modest workstation equipped with under 2 GB of free RAM in time superior to that of the implementations of other data structures. I will also give rough comparisons to a few publicly available indexing structures.
Scientific Computing Seminar
e-mail: ag@math.la.asu.edu | |
Abstract: Reconstruction of piecewise smooth functions from their Fourier spectral coefficients is often studied. Applications arise in various scientific fields, in particular, the use of Fourier methods are common in medical magnetic resonance imaging (MRI) because of their relationship to Radon transforms. Such images are not free from Gibbs phenomenon, as various tissue regions can be seen as piecewise smooth functions. Filtering is frequently used to alleviate the ringing in the images. However abnormal developments often begin near the edges of tissues regions, and it is well known that filtering compromises the integrity of the image there. Hence we are motivated to use high order reconstruction techniques for purposes of earlier and better diagnosis.
Recently spectral reprojection methods, notably the Gegenbauer reconstruction method, have been developed to reconstruct piecewise smooth functions in their smooth sub-intervals and restore the exponential properties of spectral methods. Specifically, unlike standard filtering, the convergence rate does not deteriorate as the discontinuities are approached. This talk discusses these methods and demonstrate their capabilities in fields such as MRI reconstruction.
Another type of problem occurs when the given information is discrete (non-uniform) grid point data. Spectral reprojection methods can only be used if the data has a Gaussian type distribution. However, here we show that a similarly designed projection method, based on discrete variable orthogonal polynomials, can reconstruct piecewise smooth functions with spectral accuracy. The method is computationally efficient and robust.
Brown University
Brain Science Program
Ph.D. Thesis Defense
A Multi-Electrode Study in the Awake Monkey | |
This thesis seminar is open to all persons. |
PDE Seminar
Department of Mathematics Colloquium Lecture
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