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Series: Other Talks

We study whether all stationary solutions of 2D Euler equation must be radially symmetric, if the vorticity is compactly supported or has some decay at infinity. Our main results are the following:

(1) On the one hand, we are able to show that for any non-negative smooth stationary vorticity that is compactly supported (or has certain decay as |x|->infty), it must be radially symmetric up to a translation.

(2) On the other hand, if we allow vorticity to change sign, then by applying bifurcation arguments to sign-changing radial patches, we are able to show that there exists a compactly-supported, sign-changing smooth stationary vorticity that is non-radial.

We have also obtained some symmetry results for uniformly-rotating solutions for 2D Euler equation, as well as stationary/rotating solutions for the SQG equation. The symmetry results are mainly obtained by calculus of variations and elliptic equation techniques. This is a joint work with Javier Gomez-Serrano, Jia Shi and Yao Yao.

Series: Other Talks

Chun-Hung will discuss his employment experience as an ACO alummus. The conversations will take place over coffee.

Series: Other Talks

Mathapalooza! is simultaneously a Julia Robinson Mathematics Festival and an event of the Atlanta Science Festival. There will be puzzles and games, a magic show by Matt Baker, mathematically themed courtroom skits by GT Club Math, a presentation about math and dance by Manuela Manetta, a presentation about math and music by David Borthwick, and a gallery of mathematical art curated by Elisabetta Matsumoto. It is free, and we anticipate engaging hundreds of members of the public in the wonders of mathematics. More info at https://mathematics-in-motion.org/about/Be there or B^2 !

Series: Other Talks

Georgia Tech is leading the way in Creating the Next in higher education.In this talk I will present (1) My vision for ACO and (2) how my research relates naturally to ACO both where the A,C,O fields are going, and my own specific interests

Series: Other Talks

Understanding the structure of RNA is a problem of significant interest to biochemists. Thermodynamic energy functions are often key to this pursuit, but it is well-established that these energy functions do not perform well when applied to longer RNA sequences. This work specifically investigates the branching properties of RNA secondary structures, viewed as plane trees. By employing Markov chain Monte Carlo techniques, we sample from the probability distributions determined by these thermodynamic energy functions. We also investigate some of the challenges in employing Markov chain Monte Carlo, in particular the existence of local energy minima in transition graphs. This talk will give background, share preliminary results, and discuss future avenues of investigation.

Series: Other Talks

This is a SCMB MathBioSys Seminar posted on behalf of Melissa Kemp (GT BME)

Constriction of blood vessels in the extremities due to traumatic injury to halt excessive blood loss or resulting from pathologic occlusion can cause considerable damage to the surrounding tissues with significant morbidity and mortality. Optimal healing of damaged tissue relies on the precise balance of pro-inflammatory and pro-healing processes of innate inflammation. In this talk, we will present a discrete multiscale mathematical model that spans the tissue and intracellular scales, and captures the consequences of targeting various regulatory components. We take advantage of the canalization properties of some of the functions, which is a type of hierarchical clustering of the inputs, and use it as control to steer the system away from a faulty attractor and understand better the regulatory relations that govern the system dynamics.EDIT: CANCELLED

Series: Other Talks

Thesis defense:

Advisors: Turgay Uzer and Cristel Chandre

Summary:

Thirty years after the demonstration of

the production of high laser harmonics through nonlinear laser-gas

interaction, high harmonic generation (HHG) is being used to probe

molecular dynamics in real time and is realizing its

technological potential as a tabletop source of attosecond pulses in the

XUV to soft X-ray range. Despite experimental progress, theoretical

efforts have been stymied by the excessive computational cost of

first-principles simulations and the difficulty of

systematically deriving reduced models for the non-perturbative,

multiscale interaction of an intense laser pulse with a macroscopic gas

of atoms. In this thesis, we

investigate first-principles reduced models for HHG using

classical mechanics. On the microscopic level, we examine the

recollision process---the laser-driven collision of an ionized electron

with its parent ion---that drives HHG. Using nonlinear dynamics, we

elucidate the indispensable role played by the ionic

potential during recollisions in the strong-field limit. On the

macroscopic level, we show that the intense laser-gas interaction can be

cast as a classical field theory. Borrowing a technique from plasma

physics, we systematically derive a hierarchy of

reduced Hamiltonian models for the self-consistent interaction between

the laser and the atoms during pulse propagation. The reduced models

can accommodate either classical or quantum electron dynamics, and in

both cases, simulations over experimentally-relevant

propagation distances are feasible. We build a classical model based on

these simulations which agrees quantitatively with the quantum model

for the propagation of the dominant components of the laser field.

Subsequently, we use the classical model to trace

the coherent buildup of harmonic radiation to its origin in phase

space. In a simplified geometry, we show that the anomalously high

frequency radiation seen in simulations results from the delicate

interplay between electron trapping and higher energy recollisions

brought on by propagation effects.

Series: Other Talks

Oral Comprehensive Exam

The purpose of this work is approximation of generic Hamiltonian dynamical systems by those with a finite number of islands. In this work, we will consider a Lemon billiard as our Hamiltonian dynamical system apparently with an infinitely many islands. Then, we try to construct a Hamiltonian dynamical system by deforming the boundary of our lemon billiard to have a finite number of islands which are the same or sub-islands of our original system. Moreover, we want to show elsewhere in the phase space of the constructed billiard is a chaotic sea. In this way, we will have a dynamical system which preserves some properties of our lemon billiards while it has much simpler structure.

Series: Other Talks

Cristobal Guzman will discuss his employment experience as an ACO alummus. The conversations will take place over coffee.

Series: Other Talks

Thermodynamics

provides a robust conceptual framework and set

of laws that govern the exchange of energy and matter. Although these

laws were originally articulated for macroscopic objects, it is hard to

deny that nanoscale systems, as well, often exhibit “thermodynamic-like”

behavior. To what extent can the venerable

laws of thermodynamics be scaled down to apply to individual microscopic

systems, and what new features emerge at the nanoscale? I will review

recent progress toward answering these questions, with a focus on the

second law of thermodynamics. I will argue

that the inequalities ordinarily used to express the second law can be

replaced by stronger equalities, known as fluctuation relations, which

relate equilibrium properties to far-from-equilibrium fluctuations. The

discovery and experimental validation of these

relations has stimulated interest in the feedback control of small

systems, the closely related Maxwell demon paradox, and the

interpretation of the thermodynamic arrow of time. These developments

have led to new tools for the analysis of non-equilibrium experiments

and simulations, and they have refined our understanding of

irreversibility and the second law.

Bio

Chris

Jarzynski received an AB degree in physics from Princeton

University in 1987, and a PhD in physics from the University of

California, Berkeley in 1994. After postdoctoral positions at the

University of Washington in Seattle and at Los Alamos National

Laboratory in New Mexico, he became a staff member in the Theoretical

Division at Los Alamos. In 2006, he moved to the University of Maryland,

College Park, where he is now a Distinguished University Professor in

the Department of Chemistry and Biochemistry, with joint appointments in

the Institute for Physical Science and Technology

and the Department of Physics. His research is primarily in the area of

nonequilibrium statistical physics, where he has contributed to an

understanding of how the laws of thermodynamics apply to nanoscale

systems. He has been the recipient of a Fulbright Fellowship,

the 2005 Sackler Prize in the Physical Sciences, and the 2019 Lars

Onsager Prize in Theoretical Statistical Physics. He is a Fellow of the

American Physical Society and the American Academy of Arts and Sciences.

Contact: Professor Jennifer Curtis Email: jennifer.curtis@physics.gatech.edu