Lefschetz Center for Dynamical Systems Seminar
Academia Sinica-Taipei and Stanford University | |
Center for Fluid Mechanics
And
The Fluids, Thermal and Chemical Processes Group
Of
The Division of Engineering
Seminar Series
Abstract: Most practical flows in engineering take place at very high Reynolds number, while most existing scaling laws for wall-bounded turbulence are based on data obtained at low to moderate Reynolds numbers. Consequently, a long-standing challenge has been to understand if and how the scaling laws and fundamental mechanisms in wall-bounded turbulent flows change with increasing Reynolds number. Towards this aim, experiments have been conducted over the past six years in the near-neutral atmospheric surface layer at the SLTEST facility in Utah's western desert. Combined with complementary multi-plane PIV, and arrays of hot-wire anemometers in laboratory wind-tunnel facilities, instantaneous and statistically averaged quantities are compared over three orders of magnitude change in Reynolds number. Laboratory facilities include those at the University of Minnesota, and the high Reynolds number wind tunnel at the University of Melbourne, Australia.
The experiments show strong evidence for an increased influence, with increasing Reynolds number, of outer-scaled motions on the near-wall inner-scaled region, which is contrary to that predicted by classic scaling laws. Moreover, the outer-scaled motions are found to be dominated by very long streamwise structures, termed "superstructures". Their role and influence in turbulent boundary layers will be discussed.
Special Seminar
Mathematics Department, Brown University
Abstract: Motivated by Carleman's proof of isoperimetric inequality in the plane and Jacobs' isoperimetric inequality for functions analytic in multiply connected domains, we discuss a problem of maximizing the isoperimetric ratio among all scalar flat conformal metrics on a higher dimensional Euclidean domain. First we will describe some sharp integral inequalities for harmonic functions on the unit ball or upper halfspace and a Liouville type theorem. Then we discuss the existence and regularity of extremal functions for a general domain (joint work with Xiaodong Wang and Xiaodong Yan).
Special Colloquium
Mathematics Department, Brown University
Abstract: Sobolev maps are basic objects in the study of variational problems between manifolds. We will discuss the topological information of a Sobolev map and issues in calculus of variations related to the "topological singularity" of a Sobolev map.
Brown University -
Center for Computational Molecular Biology Seminar Series Lecture
University of California, San Diego | |
Abstract: With the appearance of large networks of protein-protein and protein-DNA interactions as a new type of biological measurement, methods are needed for constructing cellular pathway models using interaction data as the central framework. The key idea is that, by comparing the molecular interaction network with other biological data sets, it will be possible to organize the network into modules representing the repertoire of distinct functional processes in the cell. Three distinct types of network comparisons will be discussed, including those to identify:
(1) Protein interaction networks that are conserved across species
(2) Networks in control of gene expression changes
(3) Networks correlating with systematic phenotypes and synthetic
lethals
Using these computational modeling and query tools, we are constructing network models to explain the physiological response of yeast to DNA damaging agents.
Brown University -
Division of Applied Mathematics
Transatlantic Seminar
Scientific Computing Seminar
Brown University | |
Modeling Blood Flow in Tissue | |
Abstract: Micromorphic fluids (i.e. Eringen fluids) are an extension of classical continuum fluids. The structure of the theory allows for the particles to rotate and deform in addition to the usual translation. The particulate structure of blood is mainly due to the presence of the red blood cells; the effects of these structures can be significant in microcirculation. The main focus of this presentation will be on model development. It will include an introduction to micromorphic fluids, their previous use in modeling blood flow as well as an introduction to the upscaling technique used to develop the final model equations. The model equations will be discussed relative to previous models of blood flow. The results include a generalized Fickian law with a Brinkman type correction term. The hope is to not only introduce the audience to the micromorphic fluids and the upscaling technique used (hybrid mixture theory), but to begin a dialogue on numerical issues related to this problem and connections to other models for blood flow.
Department of Mathematics Colloquium
Abstract: 50 years have gone by since the late Professor Eugene Wigner (Nobel Laureate in Physics, 1963) surmised that the distribution of adjacent spacings between neutron-induced resonances in nuclei has the form
p(x)dx = (pi x / 2) exp(-pi x^{2}/4)dx,
where x = spacing/average spacing.
His argument was based on the properties of matrices in which the elements are chosen randomly and independently from some probability distribution. Random Matrix Theory is now applied in many fields, including Chaos Theory, Quantum Chromo-Dynamics, String Theory and Quantum Gravity, mesoscopic systems in Condensed Matter, traffic flow patterns, communication networks, stock price fluctuations, and Number Theory. The pioneering experimental and theoretical developments of the subject that took place in the 1950's are discussed from a personal perspective.
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