Eric Sembrat's Test Bonanza

A particle undergoing a random walk is a classic physics problem that underlies our understanding of diffusion, the molecular nature of matter, polymer conformations, and the fluctuation-dissipation theorem. In addition to its conceptual importance in physics, a random walk is a surpisingly good model for some biophysical problems. This talk will present several examples, including DNA conformation and protein motion along a biopolymer, that are well described by a biased or unbiased random walk. I will discuss the physical theory and biophysical applications of several problems from our recent research: finite-length effects in DNA elasticity, the coupling of a biased walker with a fluctuating wall and collective effects that occur when multiple walkers change the length of a track.

Our approach to engineer cellular environments is based on self-organizing spatial positioning of single signaling molecules attached to inorganic or polymeric supports, which offers the highest spatial resolution with respect to the position of single signaling molecules. This approach allows tuning cellular material with respect to its most relevant properties, i.e., viscoelasticity, peptide composition, nanotopography and spatial nanopatterning of signaling molecule. Such materials are defined as “nano-digital materials” since they enable the counting of individual signaling molecules, separated by a biologically inert background. Within these materials, the regulation of cellular responses is based on a biologically inert background which does not trigger any cell activation, which is then patterned with specific signaling molecules such as peptide ligands in well defined nanoscopic geometries. This approach is very powerful, since it enables the testing of cellular responses to individual, specific signaling molecules and their spatial ordering. Detailed consideration is also given to the fact that protein clusters such as those found at focal adhesion sites represent, to a large extent, hierarchically-organized cooperativity among various proteins. Moreover, “nano-digital supports” such as those described herein are clearly capable of involvement in such dynamic cellular processes as protein ordering at the cell’s periphery which in turn leads to programming cell responses.

Chaotic system, characterized by sensitivity to initial conditions, handles abundant dynamics, sometimes leading to unimagined results in reality. In the past two decades, dynamical analysis and control of chaos attracted a lot of interests of scientists. Specifically, since chaos synchronization was found in 1991, generating and synchronizing chaotic systems has become a hot issue and been intensively studied. In this presentation, I would like to introduce some advances in generating new chaotic attractors and synchronizing chaos. Initially, starting from designing new chaotic systems, I demonstrate three types of systematic approaches to generate multi-scroll attractors and hyper-chaotic attractors, which possess more than one positive Lyapunov exponent. Next, to deal with two serious challenges in chaos synchronization process, communication delay and channel interference, a synchronization scheme based on impulsive control is presented to achieve robust chaos synchronization. As an extended result, chaotic network synchronization is also demonstrated together with adaptive control. In the end, a novel synchronization scheme, intermittent impulsive synchronization scheme (IISS), is designed to break through the limit of general impulsive synchronization scheme when the control window is restricted.

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For how to join a CNS webinar, click here:
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Flagellated bacteria swim by rotating thin helical filaments, each driven at its base by a reversible rotary motor, powered by an ion flux. Studies of the physiology of the bacterial flagellar rotary motor have been limited to the regime of relatively high load due to technical limitations. Here, we developed a new technique that allows systematic study of the motor near zero load. Sixty-nanometer-diameter gold spheres were attached to motors lacking flagellar filaments, and a novel laser darkfield setup was used to monitor the sphere rotation. Resurrection experiments were carried out near zero load: paralyzed motors without torque generating units were resurrected by adding torque generating units to the motor one at a time. In contrast to the incremental increase in rotation rate during resurrection at high load, the rotation rate for motors near zero load jumped to the maximum value upon addition of the first torque-generating unit. Switching properties of the flagellar motor near zero load also were investigated, and the switching rates showed a linear dependence on motor torque. Rotation in either direction (clockwise: CW or counterclockwise: CCW) has been thought to be symmetric, exhibiting the same torques and speeds. Here, we measured the torque-speed relationship across all load regimes for CW rotation, and found that the torque decreases linearly with speed, a result remarkably different from that for CCW rotation. This work provides further insights into the torque-generating mechanism, helps to better understand the motor switching mechanism, and places tighter constraints on possible motor models.

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 magnetic flux inside perfect conductors.

Video recording of lecture:  http://smartech.gatech.edu/handle/1853/38409

The classical picture of the transition to turbulence in fluid flows is that of successive instabilities where starting from a stationary basic state complexity arises via a sequence of bifurcations. In contrast, shear flows undergo a sudden and direct transition from laminar to turbulent motion as the driving velocity increases. In this talk we examine the richness of this transition in pipe flow. We show that turbulence, which is transient at low Reynolds numbers, becomes sustained at a distinct critical point. The turbulent state emerging through this phase transition is a large-scale pattern consisting of localized chaotic clusters that may relaminarize, merge, nucleate new ones or annihilate each other. By further increasing the Reynolds number, we investigate the onset of fully turbulent flow. Our data show that surprisingly even at relatively high Reynolds numbers laminar islands continue to appear in an otherwise turbulent flow. The observed scaling behavior infers that a state of fully turbulent flow is only reached in the asymptotic Reynolds number limit.

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Steady fluid solutions can play a special role in characterizing the dynamics of a flow: stable states might be realized in practice, while unstable ones may act as attractors in the unsteady evolution. Unfortunately, determining stability is often a process substantially more laborious than computing steady flows; this is highlighted by the fact that, for several comparatively simple flows, stability properties have been the subject of protracted disagreement (see e.g. Dritschel et al. 2005, and references therein).

In this talk, we build on some ideas of Lord Kelvin, who, over a century ago, proposed an energy-based stability argument for steady flows. In essence, Kelvin’s approach involves using the second variation of the energy to establish bounds on the growth of a perturbation. However, for numerically obtained fluid equilibria, computing the second variation of the energy explicitly is often not feasible. Whether Kelvin’s ideas could be implemented for general flows has been debated extensively (Saffman & Szeto, 1980; Dritschel, 1985; Saffman, 1992; Dritschel, 1995).

We recently developed a stability approach, for families of steady flows, which constitutes a rigorous implementation of Kelvin’s argument. We build on ideas from bifurcation theory, and link turning points in a velocity-impulse diagram to exchanges of stability. We further introduce concepts from imperfection theory into these problems, enabling us to reveal hidden solution branches. Our approach detects exchanges of stability directly from families of steady flows, without resorting to more involved stability calculations. We consider several examples involving fundamental vortex and wave flows. For all flows studied, we obtain stability results in agreement with linear analysis, while additionally discovering new steady solutions, which exhibit lower symmetry.

Paolo is a candidate for J Ford Fellowship at CNS

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It has recently become possible to compute precise equilibrium, traveling wave, and periodic orbit solutions to pipe and plane Couette flow at Reynolds numbers above the onset of turbulence. These invariant solutions capture the complex dynamics of unstable coherent structures in wall-bounded flows and provide a framework for understanding turbulent flows as dynamical systems. We present a number of weakly unstable equilibria, traveling waves, and periodic orbits of plane Couette flow and visualizations of their physical and state-space dynamics. What emerges is a picture of low-Reynolds turbulence as a walk among a set of weakly unstable invariant solutions.

(Joint work with J. F. Gibson and J. Halcrow)

[If you had attended the 11/17/2010 Physics Colloquium, 9/28/2010 School of Mathematics PDE Seminar, or 9/17/2010 Physics Grad Seminar, skip this]

Yves Couder and coworkers have recently reported the results of a startling series of experiments in which droplets bouncing on a fluid surface exhibit wave-particle duality and, as a consequence, several dynamical features previously thought to be peculiar to the microscopic realm, including single-particle diffraction, interference, tunneling and quantized orbits. We explore this fluid system in light of the Madelung transformation, whereby Schrodinger's equation is recast in a hydrodynamic form. Doing so reveals a remarkable correspondence between bouncing droplets and subatomic particles, and provides rationale for the observed macroscopic quantum behaviour. New experiments are presented, and indicate the potential value of this hydrodynamic approach to both visualizing and understanding quantum mechanics.