Eric Sembrat's Test Bonanza

Fluid membranes (vesicles) are area-preserving interfaces that resist bending. They are  models of cell membranes, intracellular organelles, and viral particles.  We are interested in developing simulation tools for dilute suspensions of deformable vesicles. These tools should be computationally efficient, that is, they should scale well as the number of vesicles increases.  For very low Reynolds numbers, as it is often the case in mesoscopic length scales, the Stokes approximation can be used for the background fluid.  We use a boundary integral formulation for the fluid that results in a set of nonlinear integro-differential equations for the vesicle dynamics. The motion of the vesicles is determined by balancing the nonlocal hydrodynamic forces with the elastic forces due to bending and tension. We report results from numerical experiments that have produced new results regarding the rheology. In particular, we consider various viscoelastic effects: shape equilibria in shear flows, migration on flows with ``curvature'', and pattern formation in confined flows.

Graphene has been known for decades in many forms (exfoliated, epitaxial, isolated) and a number of its properties were measured or inferred from related materials, like graphite and carbon nanotubes. Yet, only recently was its potential as an electronic material recognized.  Epitaxial graphene on silicon carbide (EG) has played a pivotal role in this development: it was the first to be proposed as a platform for graphene-based electronics [1]; the first measurements on graphene monolayers were made on EG; and the graphene-electronic band structure was first measured on EG. The epitaxial graphene program, initiated in 2001 at the Georgia Institute of Technology (GIT), has spearheaded graphene-based electronics and developed methods to produce electronics grade EG. The GIT program demonstrated many of graphene’s fundamental and technologically important properties, including coherence and quantum confinement effects, chemical modification, electrostatic gating and large-scale integration. Currently, EG stands at the forefront of materials that may succeed (not replace!) silicon. In contrast to other candidate graphene-based materials, EG is produced in a simple, high-temperature annealing step on single-crystal silicon carbide, which itself is an important electronic material. Subsequent EG processing is straightforward and compatible with microelectronics procedures.  That is why several research programs have recently adopted the EG electronics paradigm resulting in ultrahigh speed transistors (HRL, IBM) and an EG quantum-Hall-effect resistance standard (NPL). These developments have made it clear that EG is well on its way to become a major player in 21st-century electronics.

[1] C. Berger et al., J. Phys. Chem. B 108, 19912 (2004).

Since the invention of the point contact transistor over 50 years ago, semiconductor technologies have become a ubiquitous mainstay of our Society.  Continued advancements in these technologies rely heavily on materials research spanning many areas including polymer and organic materials which play significant roles as sacrificial, passive and active layers in electronic and photonic devices.   The research outlined in this talk will identify fundamental materials parameters that will allow for the definition of materials architectures leading to sub-nanometer scale dimensional control of features for future semiconductor fabrication technologies.  The understanding of how to control materials architectures at this sub-nanometer level will lead to organic and polymer semiconductor materials technologies enabling the future vision for flexible, printed electronic devices and display technologies.

In the world of moderate Reynolds number, everyday turbulence of fluids flowing across planes and down pipes a velvet revolution is taking place. Experiments are almost as detailed as the numerical simulations, Numerical simulations are yielding exact numerical solutions that one dared not dream about a decade ago, and dynamical systems visualization of turbulent fluid's state space geometry is unexpectedly elegant.

We shall take you on a tour of this newly breached, hitherto inaccessible territory. Mastery of fluid mechanics is no prerequisite, and perhaps a hindrance: the talk is aimed at anyone who had ever wondered why - if no cloud is ever seen twice - we know a cloud when we see one? And how do we turn that into mathematics?          

[colloquium by Shoucheng Zhang is postponed due to a family emergency. If you have attended the  9/28/2010 School of Mathematics PDE Seminar, skip this]

Semiconductor nanowires synthesized in the bottom up approach have shown promising potential for a variety of applications in nanoelectronics, optoelectronics, biosensing and energy conversion. With the small length scale and a variety of material choices, nanowires also offer a versatile playground to explore mesoscopic and quantum physics. I will discuss our recent studies of magneto-transport phenomena in InAs and Bi2Se3 nanowires. In nanowires of InAs, a conventional low band-gap semiconductor, quantum interference and spin-orbit coupling lead to one-dimensional localization or anti-localization of electrons. For nanowires/ribbons of Bi2Se3, a 3D topological insulator, our experiments revealed a novel linear magneto-resistance which is likely due to 2D Dirac electrons on sample surface.

In school, we learned that fluid flow becomes simple in two limits.  Over long lengthscales and at high speeds, inertia dominates and the motion can approach that of a perfect fluid with zero viscosity.  On short lengthscales and at slow speeds, viscous dissipation is important.  Fluid flows that correspond to the formation of a finite-time singularity in the continuum description involve both a vanishing characteristic lengthscale and a diverging velocity scale.  These flows can therefore evolve into final limits that defy expectations derived from properties of their initial states.  This talk focuses on 3 familiar processes that belong in this category: the formation of a splash after a liquid drop collides with a dry solid surface, the emergence of a highly-collimated sheet from the impact of a jet of densely-packed, dry grains, and the pinch-off of an underwater bubble.  In all three cases, the motion is dominated by inertia but a small amount of dissipation is also present.  Our works show that dissipation is important for the onset of splash, plays a minor role in the ejecta sheet formation after jet impact, but becomes irrelevant in the break-up of an underwater bubble.  An important consequence of this evolution towards perfect-fluid flow is that deviations from cylindrical symmetry in the initial stages of pinch-off are not erased by the dynamics.  Theory, simulation and experiment show detailed memories of initial imperfections remain encoded, eventually controlling the mode of break-up.  In short, the final outcome is not controlled by a single universal singularity but instead displays an infinite variety.

(Nonlinear Science Webinar)

Dynamical systems with multiple time scales have invariant geometric objects that organize the dynamics in phase space. The slow-fast structure of the dynamical system leads to phenomena such as canards, mixed-mode oscillations, and bifurcation delay. We'll discuss two projects involving chemical oscillators. The first is the analysis of a simple chemical model that exhibits complex oscillations. Its bifurcations are studied using a geometric reduction  of the system to a one-dimensional induced map. The second investigates the slow-fast mechanisms generating mixed-mode oscillations in a model of the Belousov-Zhabotinsky (BZ) reaction. A mechanism called dynamic Hopf bifurcation is responsible for shaping the dynamics of the system.

If you are not in Howey 501: this webminar is broadcast on evo.caltech.edu (register, start EVO, webinar link is evo.caltech.edu/evoNext/koala.jnlp?meeting=MMMeMn2e2sDDDD9v9nD29M)

The discovery of neutrino oscillations has been one of the major advances in our understanding of particle physics in recent times, and we are still trying to fully understand them and the insights they may give to physics at very high energies and perhaps even into the matter-anti-matter asymmetry of the universe.  Long Baseline Neutrino Oscillation Experiments are becoming one of the main tools for the study of neutrinos.  The talk will briefly outline the history and physics of neutrino oscillations and long baseline experiments, and then discuss results from the current round of experiments - OPERA, MINOS, and now T2K.  I will then discuss what is coming in the near future from existing and under construction experiments, and the exciting new possibilities being opened up by new proposals in the US (and elsewhere).

Two dimensional turbulence is an idealization of real 3D systems with anisotropy caused by geometric confinement or body forcing.  I will review the current state of understanding of 2D turbulent flows including specific theoretical predictions, numerical simulation results and experimental realizations of quasi-2D turbulent systems.  Relevance to geophysical systems will be discussed.

Directed Migration of cells is vital to a wide array of biological processes: from the coordinated migration of cells during embryo development to the uncontrollable migration of a metastatic cancer.  We investigate directed cell migration in the model organism Dictyostelium aiming to understand the underlying biophysics of their motion, their direction, and the coordination among cell groups.   The problem of directed cell migration is often broken into three independent modules: a compass, propulsion, and cell-to-cell signaling.    Applying principles from nonlinear dynamics, we explore the cross coordination of these modules by perturbing one and finding impact on the others.  Our results indicate that the modules are closely linked:  Changes in signal relay can lead to a dramatic increase in cell speed, and cell-surface adhesion affects group behavior.  Considering all modules together allows us to utilize more information and move toward quantitative descriptions of key aspects of the cell-cell signaling and propulsion modules.