Center for Fluid Mechanics Seminar
Abstract: The transport phenomena associated with wall-bounded turbulent flows factor prominently in the performance of a large number of engineering applications and observations of natural processes. For this reason, the study of wall-flow dynamics and their scaling behaviors with increasing Reynolds number warrants considerable attention. Attempts to date, however, have primarily focused on questions relating to what scaling behaviors occur, rather than the dynamical reasons why they occur. Given these considerations, the present talk is organized in three parts. In the first part it is shown that the predominant methodology for discerning the dominant mechanisms associated with the mean flow dynamics is problematic, and can lead to erroneous conclusions. In the second part we examine the Millikan-Izakson (inner/outer/overlap) arguments that underpin the widely accepted derivation for a logarithmic mean profile. Rigorous existing results from the theory of functions are outlined. They reveal that the Millikan-Izakson arguments constitute something exceedingly close to a tautology and embody very little physics. The first two parts establish the context for the third. The presentation concludes with a physical interpretation of the mathematical conditions necessary for a logarithmic (or nearly logarithmic) mean profile. The basis for this interpretation is the analysis of Fife et al., (2005 JFM 532}, 165) which reveals that the mean differential statement of Newton's second law rigorously admits a hierarchy of physical layers each having their own characteristic length. These analyses show that the condition for exact logarithmic dependence exists when the normalized equations of motion (normalized using the local characteristic length) attain a self-similar structure, and physically indicate that the von Karman constant will only be truly constant when an exact self-similar structure in the gradient of the turbulent force is attained across a range of layers comprising the hierarchy. These results are discussed relative to the physics of boundary layer Reynolds number dependence and recent data indicating that the von Karman constant varies for varying mean momentum balance.
CCMB Distinguished Lecture Series
Abstract: Standard amino acid substitution matrices are constructed as log-odds ratios from large collections of alignments of related proteins. Any such collection has an implicit "standard" set of amino acid background frequencies. The matrices produced, however, often are used to compare proteins with quite non-standard amino acid compositions. We argue on theoretical grounds that this is inappropriate, and have described a method for transforming a standard matrix into one appropriate for comparing proteins with any non-standard compositions. Compositionally-adjusted matrices yield improved results from the twin perspectives of alignment score and alignment quality when proteins with strongly biased compositions are compared. To what extent are such adjusted matrices of utility for general purpose protein database searches? Using standard test platforms, we compared a standard matrix to compositionally-adjusted matrices, with relative entropy left unconstrained, or constrained in various ways. We found that constraining the relative entropy of the compositionally adjusted matrix to a fixed value in the new compositional context generally produced the best results. We also found that if the sequences compared are not known to have strong compositional biases, then it is still on average advantageous to use an adjusted matrix when the sequences satisfy certain simple length or compositional inequalities. Applying these findings to general-purpose database searches can lead to a significant improvement in retrieval performance, with a minimal increase in execution time.
Abstract: Certain fractals are known to behave like elastic bodies capable of storing intrinsic energy. In our talk we address the question of whether such a fractal is also apt to absorb energy from the surrounding space. As the fractal has a singular embedding in space, this process is not trivial. We show that absorption is possible, while keeping the spectra stable.
Department of Mathematics Colloquium
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