Apr

12

2011

The incompressible Navier-Stokes equations provide an adequate physical model of a variety of physical phenomena. However, when the fluid speeds are not too low, the equations possess very complicated solutions making both mathematical theory and numerical work challenging. If time is discretized by treating the inertial term explicitly, each time step of the solver is a linear boundary value problem. We show how to solve this linear boundary value problem using Green's functions, assuming the channel and plane Couette geometries. The advantage of using Green's functions is that numerical derivatives are replaced by numerical integrals. However, the...

Apr

12

2011

Soft and biological materials often exhibit disordered and heterogeneous microstructure. In most cases, the transmission and distribution of stresses through these complex materials reflects their inherent heterogeneity. We are developing a set of techniques that provide the ability to apply to quantify the connection between microstructure and local stresses. We subject soft and biological materials to precise deformations while measuring real space information about the distribution and redistribution of stress.
Using our custom confocal rheometer platform we can determine the role of shear stress in a variety...

Apr

11

2011

Abstract: Suppose that x(t) is a signal generated by a chaotic system and that the signal has been recorded in the interval [0,T]. We ask: What is the largest value t_f such that the signal can be predicted in the interval (T,T+t_f] using the history of the signal and nothing more? We show that the answer to this question is contained in a major result of modern information theory proved by Wyner, Ziv, Ornstein, and Weiss. All current algorithms for predicting chaotic series assume that if a pattern of events in some interval in the past is similar to the pattern of events leading up to the present moment, the...

Apr

07

2011

The 1:1 forced complex Ginzburg-Landau equation (FCGL) is a non-variational system that exhibits bistability between equilibria and thus admits traveling front solutions. A localized state consisting of an inner equilibrium embedded in an outer equilibrium can be formed by assembling two identical fronts back-to-back. In this talk, I will first describe the bifurcation structure of 1D steady localized states that takes the form of collapsed snaking (CS) if the inner equilibrium is temporally stable, and defect-mediated snaking (DMS) if the inner equilibrium is modulationally unstable. Outside their existence ranges, the steady localized states undergo time evolutions...

Apr

04

2011

We consider dynamics of Bose-Einstein condensates with long-range attractive interaction proportional to 1/r^b and arbitrary angular dependence. It is shown exactly that collapse of Bose-Einstein condensate without contact interactions is possible only for b greater or equal to 2. Case b=2 is critical and requires number of particles to exceed critical value to allow collapse. Case b>2 is supercritical with expected weak collapse which traps rapidly decreasing number of particles during approach to collapse. For b

Mar

31

2011

Join us for the first Blended Research @ the Library panel discussion, Post-Shuttle Age: The Future of NASA. Panelists are David Ballantyne, Assistant Professor in the School of Physics and the Center for Relativistic Astrophysics (CRA); Ashley Korzun, graduate student in the Daniel Guggenheim School of Aerospace Engineering; John Krige, Kranzberg Professor in the School of History, Technology and Society; and David Spencer, Professor in the School of Aerospace Engineering and Director of the Center for Space Systems. They will be discussing the future of NASA after the end of the space shuttle program, touching on topics...

Mar

30

2011

Dr. Feigenbaum received his Ph.D. in theoretical high energy physics from the Massachusetts Institute of Technology in 1970, under Francis E. Low. He was a research associate at Cornell University from 1970 to 1972 and a research associate at Virginia Polytechnic Institute from 1972 to 1974. He then moved to Los Alamos National Laboratory, where he was a staff member from 1974 to 1981 and a fellow from 1981 to 1982. (Dr. Feigenbaum, while creating his work on chaos, shared his office with Murray Gell-Mann in 1976.) From 1982 to 1986 he was a...

Mar

17

2011

nce the realm of philosophers, black holes have now been shown to exist. Indeed, black holes as massive as 1 million to 1 billion Suns populate the cores of essentially all massive galaxies. Contrary to popular thought, these super-massive black holes are messy eaters, spewing out nearly as much (in the form of mass and energy) as they consume. This "feedback" process has been postulated to be the valve that controls the growth and evolution of their host galaxies, shaping the very evolution of our Universe. I will discuss how statistical analyses of active galactic nuclei and quasars from the Sloan Digital Sky Survey (SDSS) can be used to test the hypothesis that...

Mar

16

2011

The discovery by Meissner and Ochsenfeld in 1933 that the magnetic field inside a conductor is expelled when it is cooled down to become superconducting was considered very surprising at the time. Meissner wrote that this has no classical explanation. Since then virtually every textbook stresses that this means that a superconductor is in fact not just a zero resistivity perfect conductor but in addition has the mysterious property that it can expel internal magnetic flux. In this colloquium I will present evidence that this is all a misunderstanding based on insufficient knowledge of what classical physics in fact predicts about the...