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# Applied Dynamics Seminar Series

# Applied Dynamics Seminar Series

## Thursdays, 12:30 p.m.

## IREAP Large Conference Room (ERF 1207)

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### January 31, 2019

#### No seminar

### February 7, 2019

#### Propagation of Ultrashort, Intense Laser Pulses Through the Atmosphere

Naval Research Laboratory

*Abstract: The propagation of ultra-short (~100 fs), intense (~10–100 TW/cm2) laser pulses in the atmosphere is rich in nonlinear physics and may have a broad range of applications. Experiments using terawatt pulses with durations less than a picosecond demonstrate the formation and long-distance propagation of plasma and optical filaments, white light generation, and the emission of secondary radiation far from the laser frequency. Controlling the propagation of these laser pulses over long atmospheric paths is scientifically and technologically challenging. In this talk, we discuss the various physical mechanisms governing the atmospheric propagation of ultrashort laser pulses and report on several theoretical, computational, and experimental studies carried out by the Naval Research Laboratory (NRL). These studies include recent experiments demonstrating extended channeling through very strong atmospheric turbulence enabled by nonlinear self-focusing of laser pulses in air. In addition, we discuss theoretical considerations for increasing the laser power that can propagated through the atmosphere.*

### February 14, 2019

#### Time-delayed optoelectronic oscillators: theory and applications

University of Maryland | Department of Electrical and Computer Engineering/IREAP

*Abstract: Time-delayed optoelectronic oscillators (OEOs) are at the center of a very large body of scientific literature. The complex behavior of these nonlinear oscillators has been thoroughly explored both theoretically and experimentally, leading to a better understanding of their dynamical properties. Beyond fundamental research, these systems have also inspired a wide and diverse set of applications, such as optical chaos communications, pseudo-random number generation, optoelectronic reservoir computing, ultra-pure microwave synthesis, optical pulse-train generation, and sensing. In this communication, we will provide a comprehensive overview of this field, outline the latest achievements, and discuss the main challenges ahead.*

### February 21, 2019

#### Quantum Lyapunov Spectrum

University of Maryland | Department of Physics

*Abstract: Positive Lyapunov exponents are one of the key characteristics of chaos in classical dynamical systems. Here we discuss the notion of Lyapunov exponents in quantum many-body systems focusing on a recent definition of a whole spectrum of quantum Lyapunov exponents (https://arxiv.org/abs/1809.01671). The talk will not assume prior knowledge of the subject, although some knowledge of quantum mechanics will be helpful.*

### February 28, 2019

#### Lagrangian chaos and passive scalar turbulence

University of Maryland | Department of Mathematics

*Abstract: The purpose of this work is to perform a mathematically rigorous study of Lagrangian chaos and passive scalar turbulence in incompressible fluid mechanics. We study the Lagrangian flow associated to velocity fields arising from various models of fluid mechanics subject to white-in-time, Sobolev-in-space stochastic forcing in a periodic box. We prove that if the forcing satisfies suitable non-degeneracy conditions, then these flows are chaotic in the sense that the top Lyapunov exponent is strictly positive. Our main results are for the 2D Navier-Stokes equations and the hyper-viscous regularized 3D Navier-Stokes equations (at arbitrary Reynolds number and hyper-viscosity parameters). For the passive scalar problem, we study statistically stationary solutions to the advection-diffusion equation driven by these velocities and subjected to random sources. The chaotic Lagrangian dynamics are used to prove a version of anomalous dissipation in the limit of vanishing diffusivity, which in turn, implies that the scalar satisfies Yaglom's 1949 law of passive scalar turbulence in over a suitable inertial range -- the constant flux law analogous to the Kolmogorov 4/5 law. To our knowledge, this work is the first to provide a complete mathematical proof of any such scaling law from fundamental equations of fluid mechanics. The work combines ideas from random dynamical systems (the Multiplicative Ergodic Theorem and an infinite dimensional variation of Furstenberg's Criterion) with elementary approximate control arguments and infinite-dimensional hypoellipticity via Malliavin calculus. Joint work with Alex Blumenthal and Sam Punshon-Smith. *

### March 7, 2019

#### APS March Meeting - No seminar

### March 14, 2019

#### Reaction fronts and swimming organisms in laminar flows: manifolds and barriers

Bucknell University | Department of Physics

*Abstract: We present experiments on the effects of laminar flows on the spreading of the excitable Belousov-Zhabotinsky chemical reaction and on the motion of swimming bacteria. The results of these experiments have applications for a wide range of systems including microfluidic chemical reactors, cellular-scale processes in biological systems, and blooms of phytoplankton in the oceans. To predict the behavior of reaction fronts, we adapt tools used to describe chaotic fluid mixing in laminar flows. In particular, we propose "burning invariant manifolds" (BIMs) that act as one-way barriers that locally block the motion of reaction fronts. These barriers are measured experimentally in a range of vortex-dominated 2- and 3-dimensional fluid flows. A similar theoretical approach predicts "swimming invariant manifolds" (SwIMs) that are one-way barriers the impede the motion of microbes in a flow. We are conducting experiments to test the existence of SwIMs for both wild-type and smooth swimming *Bacillus subtilis* in hyperbolic and vortex-dominated fluid flows.*

### March 21, 2019

#### Spring Break - No seminar

### March 28, 2019

#### Turbulence and dynamo effect in electronic materials

University of Maryland | Department of Physics

*Abstract: TBA*

### April 4, 2019

#### 'We have no good fundamental theory (of turbulence) at all': Was Feynman right?

Johns Hopkins University | Department of Applied Mathematics

*Abstract: TBA*

### April 11, 2019

#### Chaotic Dynamics of Driven Graphene Josephson Junctions

University of Maryland | Department of Physics

*Abstract: TBA*

### April 18, 2019

#### The physical processes of brain waste removal

University of Rochester | Department of Mechanical Engineering

*Abstract: The human brain accounts for just 2% of the body's mass but metabolizes 25% of its calories, producing significant metabolic waste. However, waste buildup links to neurodegenerative diseases like Alzheimer's and Parkinson's. The brain removes waste via the recently-discovered glymphatic system, a combination of spaces and channels through which cerebrospinal fluid flows to sweep away toxins like amyloid-beta. With an interdisciplinary group of neuroscientists and physical scientists, I study the physical processes of the glymphatic system: Where does fluid flow, and how fast? What drives flow? Does flow shear cause waste accumulation? What characteristics of the system enable essential functions? How can we improve waste removal? Can we use glymphatic flow to deliver drugs? The team combines physics tools like particle tracking and newly-invented front tracking with biological tools like two-photon imaging through cranial windows in order to address these questions with in vivo flow measurements. I will talk about recent results showing that glymphatic flow proceeds along vessels with near-optimal shapes, pulses with the heart, is driven by artery walls, and can be manipulated by changing the wall motion.*

### April 25, 2019

#### Controlling dynamical systems using a deep reservoir computer

Ohio State University | Department of Physics

*Abstract: I will describe the design of a smart controller for dynamical systems based on reservoir computers. I use this approach to control fixed points, unstable period orbits, and arbitrary orbits for the Lorenz chaotic system. We have also applied the controller to other systems, such as a mathematical model of a drone (quadcopter). The controller to easily adopt to a partial degradation of the system allowing the drone to maintain stable flight. I will discuss our progress on using this approach to controlling the dynamics of a chaotic electronic circuit.*

### May 9, 2019

Identifying and Harnessing Attractor Dynamics in Neural Systems with Applications to Chaotic Time-Series Prediction and Turing-Complete Program Learning

Syracuse University | Department of Computer Science

*Abstract: In this talk, we will describe two branches of research related to neural attractor dynamics: the first focuses on *identifying* attractors, in order to understand what a trained network has learned; and the second focuses on *harnessing* attractors, in order to teach a network useful computations. More specifically, the first part of this talk presents "directional fibers," which are mathematical objects that can be used to systematically enumerate fixed points in many dynamical systems. Directional fibers are curves in high-dimensional state space that contain the fixed points of a system and can be numerically traversed. We will define directional fibers, derive their important theoretical properties, and describe empirical results of applying directional fibers to locate fixed points in recurrent neural networks. For example, directional fibers revealed that a network trained on the Lorenz system will have fixed points in correspondence with the Lorenz system fixed points, even though the Lorenz fixed points were not included in the training data. The second part of this talk presents a "Neural Virtual Machine" (NVM), which is a purely neural system that can emulate a Turing-complete computer architecture. The NVM uses local learning rules and itinerant neural attractor dynamics to represent, learn, and execute symbolic computer programs written in an assembly-like language. We will present the dynamical equations of the NVM, explain how it can be used to carry out algorithmic tasks, and present results of computer experiments that quantify its performance and scaling requirements. In particular, we demonstrate that the number of neurons required is only linear in the size of the programs being emulated.*