Eric Sembrat's Test Bonanza

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<2 singularity at r=0 is not strong enough to allow collapse but attractive 1/r^b interaction admits stable self-trapping even in absence of external trapping potential.

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 collectively referred to as depinning dynamics. Moving on to 2D, I will first introduce the temporal dynamics of quasi-1D periodic stripes leading to planar localized hexagons. In exploring fully 2D steady solutions, the bifurcation structure of radially symmetric localized states again depends on whether the inner equilibrium is temporally stable or modulationally unstable. The time evolution of these fully 2D localized states leads to either radially expanding or contracting fronts or to localized hexagons bounded by an axisymmetric front. At the end, I will describe the case when the inner equilibrium becomes Hopf unstable in time, which in turn yields localized spatiotemporal chaos that bears some resemblance to turbulent spots in shear flows.

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 mere use of Green's functions does not result in a good solver. Numerical derivatives can come in through the nonlinear inertial term or the incompressibility constraint, even if the linear boundary value problem is tackled using Green's functions. In addition, the boundary value problem will be singularly perturbed at high Reynolds numbers. We show how to eliminate all numerical derivatives in the wall-normal direction and to cast the integrals into a form that is robust in the singularly perturbed limit. [This talk is based on joint work with Tobasco].

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 pattern from the past can be used to predict the chaotic signal. Unfortunately, this intuitively reasonable idea is fundamentally deficient and all current predictors fall well short of the Wyner-Ziv bound. We explain why the current methods are deficient and develop some ideas for deriving an optimal predictor. [This talk is based on joint work with X. Liang and K. Serkh].

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NIST-F1, a cesium fountain frequency standard which serves as the US primary frequency standard has been operating for several years with fractional frequency uncertainties of  .  The uncertainties in NIST-F1 are limited primarily by the blackbody radiation shift caused by the room temperature environment of the fountain.  We have begun operation of NIST-F2 with preliminary uncertainties in the region of  .  NIST-F2 uses a novel cryogenic structure to reduce the blackbody radiation shift to negligible levels and should be capable of operation at the  level.  Recent comparisons between NIST F1&F2 show no significant disagreement at the  level, which serves as the best measurement to date of the blackbody radiation shift.  We will review the operation of both cesium fountains and present preliminary results of comparisons between the two.

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 of materials. First, I will describe our  
recent results on the nonlinear rheology of in vitro collagen networks.  We apply precisely controlled shear strains to collagen networks that are adhered to a thin elastic polyacrylamide gel substrate embedded with fiduciary markers.  By utilizing a modified version of traction force microscopy we can calculate the distribution of forces as a function of the applied strain. We find that the signatures of yielding in these materials follow a universal form.  Second, I will discuss how the application of a cyclic load can determine the mechanical strength of a biopolymer system.  We observe that when actin networks are cyclicly strained, they either work harden, or soften depending on the specifics of the cross-linking protein.

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 super-massive black holes are so all-powerful. We'll find that the answer requires pushing even the currently most expansive dataset to its limits, providing an important argument for the next generation of astronomical surveys, including the LSST project.

Upcoming seminars: http://www.cra.gatech.edu/events/seminars.shtml

Graphene has been proposed as a viable replacement for silicon on a number of electronic applications due to its high mobility. At Georgia Tech we have been studying charge transport through graphene junctions contacted to two normal metal contacts, aiming for a quantitatively accurate description. In this talk I will present an overview of the problem, making an emphasis on crucial differences between theory and experiment, that so far preclude quantitative modeling. Then I will present our results, including some very recent developments concerning graphene junctions attached to titanium contacts (titanium has been the metal of choice for contacting graphene in experiments). Charge leakage from the metal contacts will become an issue for small-scale devices.

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 such as the future of payload delivery, the exploration of Mars, the commercialization of space, funding issues and much more.  Come be part of the discussion!

Soil harbors a huge number of microbial species interacting through secretion of antibiotics and other chemicals. What patterns of species interactions allow for this astonishing biodiversity to be sustained, and how do these interactions evolve? I used a combined experimental-theoretical approach to tackle these questions. Focusing on bacteria from the genus Steptomyces, known for their diverse secondary metabolism and production of antibiotics, I isolated 64 natural strains from several individual grains of soil and systematically measured all pairwise interactions among them. Quantitative measurements on such scale were never possible before. They were enabled by a novel experimental platform based on robotic handling, a unique self-built scanner array and automatic image analysis. This unique platform allowed the simultaneous capturing of ~15,000 time-lapse movies of growing colonies of each isolate on media conditioned by each of the other isolates. The data revealed a rich network of strong negative (inhibitory) and positive (stimulating) interactions. Analysis of this network and the phylogeny of the isolates, together with mathematical modeling of microbial communities, revealed that: 1) The network of interactions has three special properties: “balance”, “bi- modality” and “reciprocity”; 2) The interaction network is fast evolving; 3) Mathematical modeling explains how rapid evolution gives rise to the three special properties through an interplay between ecology and evolution. These properties are not a result of stable co-existence, but rather of continuous evolutionary turnover of strains with different production and resistance capabilities.