Seminars and Colloquia by Series

Linear and nonlinear vibration-based energy harvesting

Series
Applied and Computational Mathematics Seminar
Time
Monday, January 23, 2012 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Alper Erturk – Georgia Tech, School of Mechanical Engineering
The transformation of vibrations into low-power electricity has received growing attention over the last decade. The goal in this research field is to enable self-powered electronic components by harvesting the vibrational energy available in their environment. This talk will be focused on linear and nonlinear vibration-based energy harvesting using piezoelectric materials, including the modeling and experimental validation efforts. Electromechanical modeling discussions will involve both distributed-parameter and lumped-parameter approaches for quantitative prediction and qualitative representation. An important issue in energy harvesters employing linear resonance is that the best performance of the device is limited to a narrow bandwidth around the fundamental resonance frequency. If the excitation frequency slightly deviates from the resonance condition, the power output is drastically reduced. Energy harvesters based on nonlinear configurations (e.g., monostable and bistable Duffing oscillators with electromechanical coupling) offer rich nonlinear dynamic phenomena and outperform resonant energy harvesters under harmonic excitation over a range of frequencies. High-energy limit-cycle oscillations and chaotic vibrations in strongly nonlinear bistable beam and plate configurations are of particular interest. Inherent material nonlinearities and dissipative nonlinearities will also be discussed. Broadband random excitation of energy harvesters will be summarized with an emphasis on stochastic resonance in bistable configurations. Recent efforts on aeroelastic energy harvesting as well as underwater thrust and electricity generation using fiber-based flexible piezoelectric composites will be addressed briefly.

Parallel heat transport in reverse shear magnetic fields

Series
Math Physics Seminar
Time
Monday, January 23, 2012 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Daniel Blazevski – University of Texas
I will discuss local and nonlocal anisotropic heat transport along magnetic field lines in a tokamak, a device used to confine plasma undergoing fusion. I will give computational results that relate certain dynamical features of the magnetic field, e.g. resonance islands, chaotic regions, transport barriers, etc. to the asymptotic temperature profiles for heat transport along the magnetic field lines.

A numerical algorithm for the computation of periodic orbits of the Kuramoto-Sivashinsky equation.

Series
CDSNS Colloquium
Time
Monday, January 23, 2012 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jordi Lluis Figueras – Uppsala University
In this talk we will present a numerical algorithm for the computation of (hyperbolic) periodic orbits of the 1-D K-S equation u_t+v*u_xxxx+u_xx+u*u_x = 0, with v>0. This numerical algorithm consists on apply a suitable Newton scheme for a given approximate solution. In order to do this, we need to rewrite the invariance equation that must satisfy a periodic orbit in a form that its linearization around an approximate solution is a bounded operator. We will show also how this methodology can be used to compute rigorous estimates of the errors of the solutions computed.

Discrete Mathematical Biology Working Seminar

Series
Other Talks
Time
Monday, January 23, 2012 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 114
Speaker
Shel Swenson – Georgia Tech
A discussion of the paper "Beyond energy minimization: approaches to the kinetic folding of RNA'' by Flamm and Hofacker (2008).

Recent advances on the structure of metric measure spaces with Ricci curvature bounded from below

Series
Job Candidate Talk
Time
Thursday, January 19, 2012 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Nicola Gigli – University of Nice
I'll show how on metric measure spaces with Ricci curvature bounded from below in the sense of Lott-Sturm-Villani there is a well defined notion of Heat flow, and how the study of the properties of this flow leads to interesting geometric and analytic properties of the spaces themselves. A particular attention will be given to the class of spaces where the Heat flow is linear. (From a collaboration with Ambrosio and Savare')

Asymptotic behavior for solutions of the random Schrödinger with long-range correlations.

Series
Stochastics Seminar
Time
Thursday, January 19, 2012 - 15:05 for 1 hour (actually 50 minutes)
Location
skyles 006
Speaker
Christophe Gomez – Department of Mathematics, Stanford University
In this talk we will describe the different behaviors of solutions of the random Schrödinger with long-range correlations. While in the case of arandom potential with rapidly decaying correlations nontrivial phenomenaappear on the same scale, different phenomena appear on different scalesfor a random potential with slowly decaying correlations nontrivial .

On the behavior at infinity of solutions to difference equations in Schroedinger form

Series
Analysis Seminar
Time
Wednesday, January 18, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Lillian Wong – Georgia Tech
We offer several perspectives on the behavior at infinity of solutions of discrete Schroedinger equations. First we study pairs of discrete Schroedinger equations whose potential functions differ by a quantity that can be considered small in a suitable sense as the index n \rightarrow \infty. With simple assumptions on the growth rate of the solutions of the original system, we show that the perturbed system has a fundamental set of solutions with the same behavior at infinity, employing a variation-of-constants scheme to produce a convergent iteration for the solutions of the second equation in terms of those of the original one. We use the relations between the solution sets to derive exponential dichotomy of solutions and elucidate the structure of transfer matrices. Later, we present a sharp discrete analogue of the Liouville-Green (WKB) transformation, making it possible to derive exponential behavior at infinity of a single difference equation, by explicitly constructing a comparison equation to which our perturbation results apply. In addition, we point out an exact relationship connecting the diagonal part of the Green matrix to the asymptotic behavior of solutions. With both of these tools it is possible to identify an Agmon metric, in terms of which, in some situations, any decreasing solution must decrease exponentially.This talk is based on joint work with Evans Harrell.

FINITE TIME DYNAMICS: the first steps and outlook.

Series
Research Horizons Seminar
Time
Wednesday, January 18, 2012 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Leonid A. Bunimovich – Georgia Tech
It is well known that typically equations do not have analytic (expressed by formulas) solutions. Therefore a classical approach to the analysis of dynamical systems (from abstract areas of Math, e.g. the Number theory to Applied Math.) is to study their asymptotic (when an independent variable, "time", tends to infinity) behavior. Recently, quite surprisingly, it was demonstrated a possibility to study rigorously (at least some) interesting finite time properties of dynamical systems. Most of already obtained results are surprising, although rigorously proven. Possible PhD topics range from understanding these (already proven!) surprises and finding (and proving) new ones to numerical investigation of some systems/models in various areas of Math and applications, notably for dynamical analysis of dynamical networks. I'll present some visual examples, formulate some results and explain them (when I know how).

Coupling and Upscaling of Particle Models in Multiscale Physics

Series
Job Candidate Talk
Time
Tuesday, January 17, 2012 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Matthew Dobson – NSF Postdoctoral Fellow, Ecole des Ponts ParisTech
Multiscale numerical methods seek to compute approximate solutions to physical problems at a reduced computational cost compared to direct numerical simulations. This talk will cover two methods which have a fine scale atomistic model that couples to a coarse scale continuum approximation. The quasicontinuum method directly couples a continuum approximation to an atomistic model to create a coherent model for computing deformed configurations of crystalline lattices at zero temperature. The details of the interface between these two models greatly affects the model properties, and we will discuss the interface consistency, material stability, and error for energy-based and force-based quasicontinuum variants along with the implications for algorithm selection. In the case of crystalline lattices at zero temperature, the constitutive law between stress and strain is computed using the Cauchy-Born rule (the lattice deformation is locally linear and equal to the gradient). For the case of complex fluids, computing the stress-strain relation using a molecular model is more challenging since imposing a strain requires forcing the fluid out of equilibrium, the subject of nonequilibrium molecular dynamics. I will describe the derivation of a stochastic model for the simulation of a molecular system at a given strain rate and temperature.

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