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Monday: October 18th, 1999

No News.

Tuesday: October 19th, 1999

PDE Seminar: Greg Eyink, Assistant Professor, Department of Mathematics, University of Arizona, will speak on "Self-Similar Decay Solutions for Generalized Stochastic Flows, Part III", at 12:30PM in Math 402. (Brown bag lunches are appropriate).
Abstract: R. H. Kraichnan in 1968 introduced a soluble model of turbulent scalar advection, in which the advecting incompressible velocity is a "synthetic turbulence field" which is Gaussian and white-in-time. Mathematically, the model is given by stochastic advection-diffusion equations or by Brownian motion in a function space of flows (Kunita, 1990), but with velocities only H"older in space not Lipschitz.
Traditional turbulence theory leads one to believe that the stochastic equations in this case should have dissipative weak solutions in the zero diffusion limit, for which the scalar energy decreases. Furthermore, the decay of the statistical correlation functions is traditionally believed to be asymptotically self-similar. In this first talk we will introduce the model and discuss the traditional statistical theory of turbulent scalar decay. In Part II we will describe work of the speaker with J. Xin in which all self-similar decay solutions for the 2-point covariance are found (in terms of confluent hypergeometric functions), their statistical realizability analyzed, and domains of attraction established. Existence of dissipative weak solutions of the hyperbolic stochastic PDE's will follow as a corollary.

Algebra & Number Theory Seminar: Carl Lienert, Department of Mathematics, University of Arizona, will speak on "Representation Numbers of Quadratic Forms", at 2:00PM in Math 402.
Abstract: We will investigate the average representation numbers of positive definite quadratic forms associated with lattices of even or odd rank and even level. In the odd rank case we give an explicit formula and in the even rank case a relationship among the representation numbers. We build operators that reflect certain sublattices and consider their actions on Eisenstein series to obtain the results.

Geometry Seminar: Maciej Wojtkowski, Department of Mathematics, University of Arizona, will speak on "Weyl Manifolds, W-flows and Gaussian Thermostats", at 4:00PM in Math 402.
Abstract: A Weyl structure is a generalization of the Riemannian metric, which describes a space in which the scale changes when we move around. We discovered that Weyl structures are closely related to Gaussian thermostats which were introduced 15 years ago in molecular dynamics. In this talk we will discuss this connection.

Biomathematics Seminar: Math 596A - 3:45 5:30pm, Mathematics Teaching Lab 124. Assistant Professor Koen Visscher, Department of Physics, University of Arizona, will speak on "A Single Modecule Study of Kinesin Displacement Under Load, Part II".
Abstract: Kinesin is a two-headed, ATP-driven motor protein that moves processively along microtubules in discrete steps of ~8 nm, probably by advancing each of its heads alternately. Molecular details of how the chemical energy stored in ATP is coupled to mechanical displacement remain obscure, especially when the molecule experiences an opposing force. To shed light on this question, a force clamp was constructed based on feedback-driven optical tweezers capable of maintaining constant loads on single kinesin molecules moving along microtubules. This instrument provides unprecedented, nanometer-scale, resolution of molecular motion and permits mechanochemical studies under controlled external loads. Experimental techniques and analysis methods will be discussed. Analysis of records of kinesin motion under variable ATP concentrations and loads revealed that kinesin stepping is tightly coupled to ATP hydrolysis over a wide range of forces, with only a single hydrolysis per 8 nm mechanical advance. Increased loads reduce the maximum velocity as anticipated, but also raise the apparent Michaelis-Menten constant. Therefore, the kinesin cycle most likely contains two load-dependent biochemical transitions, one of which also depends upon ATP concentration.The kinesin stall force depends upon the ATP concentration. Like transcription by RNA polymerase (RNAP), the kinesin mechanism involves thermally activated transitions within a free energy landscape. We will present a model that facilitates a simple 'tightly-coupled' mechanism, in which this coupling ratio stays fixed at 1:1. The mechanism: (i) pinpoints the primary effect of load to a conformational change immediately following ATP binding; (ii) naturally leads to tight-coupling, as found experimentally, because hydrolysis occurs only after a motor domain undergoes this conformational change; (iii) provides a quantitative account of velocity data over a wide range of loads and ATP levels; (iv) makes new predictions that are testable with current experimental methods.

Mathematics Instruction Colloquium: Cecilia Taylor, Department of Mathematics, University of Arizona, will speak on "Families of Parabolas: Locus of the Vertices" at 4:15PM in Math 501. Refreshments will be served beforehand.

Wednesday: October 20th, 1999

Graduate Student Seminar: Matthias Lesch, Department of Mathematics, University of Arizona, will speak on "Dirac Operators", at 12:00PM in Math 402. Please see Grad Colloquium posters/website.

Mathematical Physics Seminar: John Lapeyre, Department of Physics, University of Arizona, will speak on "Random Walks on Lattices with Fluctuating Bond Disorder, Part II", at 2:00PM in Math 402.

Thursday: October 21st, 1999

Modelling Seminar: Professor Michael W. Marcellin, Department of Electrical and Computer Engineering, University of Arizona, will speak on "Overview of JPEG 2000", at 12:30PM in MTL124. (Brown Bag lunches are appropriate).
Abstract: JPEG 2000 is an emerging standard for next generation compression of still imagery. It is projected that JPEG 2000 will be published as an ISO (International Standards Organization) standard in late 2000. Currently, JPEG 2000 exists in "working draft" form, and algorithm technical details are about ninety-five percent complete. JPEG 2000 provides many features available previously only from multiple algorithms/compressed bit streams. JPEG 2000 provides both lossy and lossless decompression, progressive transmission by quality, progressive transmission by resolution, random codestream access, and region of interest encoding/decoding all from a single compressed bit stream. The essential ingredients of JPEG 2000 are wavelets and binary arithmetic coding. The talk will provide an overview of the theoretical and practical issues of JPEG 2000, and will describe how such a rich feature set is possible from a single algorithm/compressed codestream.

Mathematics Colloquium: Prof. Brent Gordon, University of Oklahoma, Norman, Oklahoma, will speak on "Fourier Transforms in Algebraic Geometry", at 4:00PM in Math 501. Refreshments at 3:30PM in Math 401N.

Friday: October 22nd, 1999

Brown Bag Seminar: Jens Eriksen, Visitor to Deparment of Mathematics - ACMS, University of Arizona, will speak on "Pulse Propagation in Kerr Bulk Media."at 12:00PM in Math 402.
Abstract: The topic of the talk is pulse propagation through kerr bulk media. The decomposition of the electrical field into a slowly varying envelope function and a rapidly oscillating carrier wave is reviewed. The role of diffraction, temporal dispersion and cubic nonlinearity is discussed. In particular examples of self-focusing and pulse splitting are shown.

Applied Mathematics Colloquium: Professor Guenter Ahlers, Center for Nonlinear Science and Department of Physics, University of California at Santa Barbara, will speak on "The Pattern Formation Near Onset on Rayleigh-B/enard Convection: Some Simple Unexplained Results", at 4:00PM in Math 501. Refreshments at 3:30PM in Math 401N.
Abstract: Our goals as experimentalists in the field of pattern formation fall into three categories: 1) Test already existing theoretical predictions; 2) Find qualitatively new phenomena which are simple enough to be understood in the not too distant future; and 3) Design simple "idealized" experiments illustrating important general phenomena. This talk will illustrate how these goals are pursued, by discussing a number of studies of pattern formation under carefully controlled conditions near the onset of convection in a shallow horizontal layer of a fluid heated from below. The first part of the talk will be devoted to experimental results for convection-roll selected in a cylindrical sample which had an interior section of uniform spacing. For Rayleigh numbers above the critical value in the interior, straight or slightly curved rolls were selected. It is observed that in some regimes, the pattern repeatedly formed defects. The defects moved in the direction of the perturbation associated with the instability responsible for their formation. In the second half of the talk, the effect of a Coriolis force due to rotation of a sample with rigid sidewalls (no ramp) about a vertical axis will be considered. At small dimensionless rotation rates appropriate Prandtl numbersdomain chaos was found immediately above a supercritical bifurcation. The dependence of the time and length scales of the chaotic state on the Rayleigh number differed from the theoretically expected dependence. For other values, the patterns differed from the theoretically expected chaotic state. Instead, rotating square patterns were found. Finally, some opportunities for future work will be mentioned.

Departmental Announcements

No Announcements.