# 2019 Applied Dynamics Seminar Archives

### 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 Joint Quantum Institute

*Abstract: The dynamo effect is a class of macroscopic phenomena responsible for generation and maintaining magnetic fields in astrophysical bodies. It hinges on hydrodynamic three-dimensional motion of conducting gases and plasmas that achieve high hydrodynamic and/or magnetic Reynolds numbers due to large length scales involved. The existing laboratory experiments modeling dynamos are challenging and involve large apparatuses containing conducting fluids subject to fast helical flows. Here we propose that electronic solid-state materials -- in particular, hydrodynamic metals -- may serve as an alternative platform to observe some aspects of the dynamo effect. In this talk, I will discuss two candidate systems -- Well semimetals and critical fluctuating superconductors, where electronic turbulence and dynamo effect appear within experimental reach.*

*[1] V. Galitski, M. Kargarian, and S. Syzranov, "Dynamo Effect and Turbulence in Hydrodynamic Weyl Metals," Phys. Rev. Lett. 121, 176603 (2018)*

*[2] Y. Liao and V. Galitski, "Two-Fluid Hydrodynamics and Viscosity Suppression in Fluctuating Superconductors,"*

### April 4, 2019

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

Johns Hopkins University | Department of Applied Mathematics

*Abstract: In his famous undergraduate physics lectures, Richard Feynman remarked about the problem of fluid turbulence: "Nobody in physics has really been able to analyze it mathematically satisfactorily in spite of its importance to the sister sciences.” This statement was already false when Feynman made it. Unbeknownst to him, Lars Onsager decades earlier had made an exact mathematical analysis of the high Reynolds-number limit of incompressible fluid turbulence, using a method that would now be described as a non-perturbative renormalization group analysis and discovering the first “conservation-law anomaly” in theoretical physics. Onsager’s results were only cryptically announced in 1949 and he never published any of his detailed calculations. Onsager’s analysis was finally rescued from oblivion and reproduced by the speaker in 1994. The ideas have subsequently been intensively developed in the mathematical PDE community, where deep connections emerged with John Nash’s work on isometric embeddings. Furthermore, the method has more recently been successfully applied to new physics problems, compressible fluid turbulence and relativistic fluid turbulence, yielding many new testable predictions. This talk will briefly review Onsager’s exact analysis of the original incompressible turbulence problem and subsequent developments. Then a new application to kinetic plasma turbulence will be described, with novel predictions for turbulence in nearly colllisionless plasmas such as the solar wind and the terrestrial magnetosheath.*

### April 11, 2019

#### Chaotic Dynamics of Driven Graphene Josephson Junctions

University of Maryland | Department of Physics

*Abstract: Josephson junctions with topological materials as weak links pervade the research of Majorana bound states. Yet these junctions exhibit many complex phenomena, some which are accessible due to new material and fabrication technology. A comprehensive picture is important both for elucidation of the physics of Majorana bound states and fundamental research into Josephson junctions. In this talk I will detail the physics of Josephson junctions and the chaotic behavior we observe in high-quality, graphene-based Josephson junctions under application of RF radiation. We quantify a instability measured in the AC Josephson regime which is analyzed in terms of crisis-induced intermittency. Further, these observations cast doubt over arguments that AC Josephson effect in the low RF drive amplitude region would offer the opportunity to observe 4-π current phase relation in topological Josephson junctions.*

### 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 2, 2019

#### Cluster Synchronization in Multilayered Networks

Naval Research Laboratory

*Abstract: The behavior of dynamical systems (nodes or oscillators) that are coupled together in complex networks are greatly affected by the structure of those networks. Various patterns of synchronization among subsets of nodes are possible when the network has symmetries and input or balanced partitions. Symmetries and partitions will be introduced in this talk along with the dynamical patterns they can support. The basic machinery from group theory will be used to analyze the patterns, especially for their dynamical stability. The main portion of the talk will be about extending these ideas to networks with multiple oscillator types called multilayered networks. This extension while looking straightforward has some interesting structures that govern the behavior of synchronous clusters in the network as a whole as well as the symmetries of the network.*

### 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.*

### May 16, 2019

New methods for fractal and Wada basins

King Juan Carlos University | Applied Physics

*Abstract: In dynamical systems, basins of attraction are defined as the set of initial conditions leading to a particular asymptotic behavior. Nonlinear systems often give rise to fractal boundaries in phase space, hindering predictability. A special case of fractal boundaries appears when a single boundary separates three or more different basins of attraction. Then we say that the set of basins has the Wada property and initial conditions near that boundary become particularly unpredictable. Although it could seem an odd situation, many physical systems showing this topological property appear in the literature. In this talk, I will review some basic aspects on Wada basins, and then I will describe some new recently developed methods to ascertain the Wada property in dynamical systems. These new methods present important advantages with respect to the previously known method, provide new perspectives on the Wada property and broaden the situations where it can be verified. Also, I will show how the novel concept of basin entropy helps us quantify the unpredictability associated to different basins of attraction and its relation with Wada basins.*

2019 Archive | 2018 Archive | 2017 Archive | 2016 Archive | 2015 Archive