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# 2016 Applied Dynamics Seminar Archives

# February 4, 2016

#### Nonlinear Dynamics of a Plucked String

Dan Lathrop and Ed Ott

University of Maryland, IREAP

### February 11, 2016

#### Scattering Theory for the Boltzmann Equation and the Arrow of Time

David Levermore

University of Maryland, Dept of Mathematics

*Abstract: We develop a scattering theory for a class of eternal solutions of the Boltzmann equation posed over all space. In three spatial dimensions, each of these solutions has thirteen conserved qualities. The Boltzmann entropy has a unique minimizer with the same thirteen conserved values. This minimizer is a local Maxwellian that is also a global soution of the Botlzmann equation - a so-called global Maxwellian. We show that each of our external solutions has a streaming asymptotic state as time goes to minus- or plus-infinity. However, it does not converge to the associated gloabl Maxwellian as time goes to infinity unless it is that global Maxwellian. The Blotzmann entropy decreases as time increases, but does not decrease to its minimum as time goes to infinity. Said another way, the final step in the traditional argument for the heat death of the universe is not valid. *

### February 18, 2016

#### Particle laden flows

Andrea Bertozzi

UCLA, Dept of Mathematics

*Abstract: Modeling of particle laden flow, especially in the case of higher particle concentrations, does not readily allow for first principles models. Rather, semi-empirical models of the bulk dynamics require careful comparison with experiments. At UCLA we have developed this theory for the geometry of viscous thin film flow with non-neutrally buoyant particles. We have found that for these slower flows, that diffusive flux models, involving a balance between shear-induced migration and hindered settling, can provide reasonably accurate predictive models. I will discuss the current state of this work including recent extensions to bidensity slurries and the relevant mathematics needed to understand the dynamics. Lubrication theory can be derived for this problem and results in a coupled system of conservation laws including regular shock dynamics and singular shocks. I will also briefly discuss relevant applications such as spiral separators.*

### February 25, 2016

#### Titles Below

Jeffery Demers and Ayoti Patra

University of Maryland, IPST/Dept of Chemistry

#### Jeff Demers

#### Universal energy diffusion in a quivering billiard

*Abstract: In this talk, I will discuss a particular limit of time-dependent billiard motion called "the quivering limit," and the resulting billiard systems called "quivering billiards." I will show that the quivering limit is well-defined and physically interesting, yet allows for analytic calculations of physical quantities such as correlations and time-dependent energy distributions. As time allows, I will share some interesting and surprising features of quivering billiards; namely that time-dependent billiards behave universally in the quivering limit, regardless of billiard shape or dimensionality, and that the insights gained through studying quivering billiards resolve some long standing problems in the time-dependent billiard literature. I will also mention some exciting ongoing projects which employ quivering billiards to address current topics of interest in non-equilibrium thermodynamics and statistical mechanics at the nanoscale.*

#### Ayoti Patra

#### Shortcuts to adiabaticity for a quantum tilted piston

*Abstract: Shortcuts to Adiabaticity are techniques used to control a system evolving under a rapidly changing Hamiltonian. I will start by describing one such technique, known as 'Transitionless Quantum Driving', in which a quantum system is subjected to evolve under a composite Hamiltonian H_0(t) + H_{CD}(t), such that it remains in a given energy eigenstate of H_0(t) throughout the evolution. I will describe a method to obtain the term H_{CD}(t) starting from an analogous problem of 'classical dissipationless driving'. I will illustrate this method using the example of a tilted piston.*

### March 3, 2016

#### Nonlinear Dynamics of SQUID Metamaterials

Steve Anlage

University of Maryland, Depts of Physics and Electrical & Computer Engineering

### March 10, 2016

#### Many body physics of disordered microfluidic droplet ensembles

Itamar Shani

University of Maryland, IREAP

*Abstract: Non-equilibrium systems with long-range interactions that exhibit complex collective dynamics are common in Nature, for example stellar motion, electric conduction, sedimentation, and plasma. However, understanding collective motion from basic principles is challenging because these systems are not governed by global laws such as energy minimization, and since every constituent interacts with many others. I will present experimental observations and theory of the dynamics of microfluidic droplet ensembles driven in a two-dimensional channel and governed by long-range hydrodynamic dipolar interactions. While the ensemble is spatially disordered, the droplet velocities exhibit long-range correlations proportional to 1/r2 with four-fold angular symmetry. Scatterings between three droplets at a time can break the long-range order by creating a large scale motion of contraction-expansion that dominates velocity correlations. We discovered that three-body collisions are also the fundamental element of irreversible dynamics in the reversible Stokes flow regime. The low-dimensionality of the system and the linearity of the flow equations facilitate a microscopic description of the rich collective behavior. *

### March 17, 2016

#### Spring Break - No Seminar

### March 24, 2016

#### Chimera states/cluster synchronization

Joe Hart and Kanika Bansal

University of Maryland, IREAP

### March 31, 2016

#### Shortcuts to adiabaticity in simple classical systems

Chris Jarzynski

University of Maryland, Department of Chemistry and Biochemistry

*Abstract: Adiabatic invariants are important in classical mechanics, quantum mechanics and thermodynamics. I will consider the following classical problem in one degree of freedom. Given a time dependent Hamiltonian H(q,p,t), we wish to construct an auxiliary potential U(q,t) with the property that all trajectories launched from a specified initial energy shell E_0 of H(q,p,0), and subsequently evolving under H(q,p,t) + U(q,t), will end on a single energy shell E_tau of H(q,p,tau). By Liouville’s theorem these two shells share the same action. In this manner the auxiliary potential U(q,t) steers the trajectories so that the final action is exactly the same as the initial action, for every trajectory and for arbitrarily fast time-dependence of H(q,p,t). I will present a simple solution to this problem and will discuss its relationship to analogous solutions for quantum systems.*

### April 7, 2016

#### Glial Network Regularization of Neuron Learning Dynamics

Juan Restrepo

University of Colorado, Department of Applied Mathematics

### April 14, 2016

#### Measurement inspired modeling of quantum and classical dynamical systems

Denys Bondar

Princeton University, Department of Chemistry

*Abstract: In this talk, I will provide an answer to the question: “What kind of observations and assumptions are minimally needed to formulate a physical theory?” Our answer to this question leads to the new systematic approach of Operational Dynamical Modeling (ODM), which allows to deduce equations of motions from time evolution of observables. Using ODM, we are not only able to re-derive well-known physical theories (such as the Schrodinger and classical Liouville equations), but also infer novel physical dynamics (and solve open problems) in the realm of non-equilibrium quantum statistical mechanics.*

### April 21, 2016

#### Synchronization in Populations of Chemical Oscillators: Quorum Sensing, Phase Clusters, and Chimeras

Ken Showalter

West Virginia University, Department of Chemistry

*Abstract: We have studied large, heterogeneous populations of discrete chemical oscillators (~100,000) to characterize two different types of density-dependent transitions to synchronized behavior, a gradual Kuramoto synchronization and a sudden quorum sensing synchronization. We also describe the formation of phase clusters, where each cluster has the same frequency but is phase shifted with respect to other clusters, giving rise to a global signal that is more complex than that of the individual oscillators. Finally, we describe experimental and modeling studies of chimera states and their relation to other synchronization states in populations of coupled chemical oscillators.*

### April 28, 2016

#### Nonlinear Dynamics and Variational Statistical Data Assimilation

Henry Abarbanel

UC San Diego, Department of Physics

*Abstract: This is about how to do 4DVar, as the meteorologists call it--with some confidence one has found the lowest minimum for the cost function--and, methods for evaluating the corrections to this approximation. Many more subtle details which I would be pleased to get your views about as well.*

### May 5, 2016

#### Irregular spiking of pyramidal neurons organizes as scale-invariant neuronal avalanches in the awake state

Dietmar Plenz

NIH, National Institute of Mental Health

### May 12, 2016

#### X-ray Binary Light Curves: Can Data Analysis Lead to a Dynamical Model of Long Term Variability?

Padi Boyd

NASA, Goddard Space Flight Center

*Abstract: The Time Domain Astronomy (TDA) renaissance is already well underway. The K2 mission is amassing an impressive collection of high precision, evenly sampled, long time baseline optical observations on par with those from the original Kepler mission, and high-energy space-based all-sky monitors continue to watch virtually every bright X-ray source in the sky. These facilities monitor accreting compact binaries: some show high-amplitude “superorbital” variability, on timescales longer than the orbital timescale, sometimes ascribed to the motion of a warped, precessing accretion disk. Warped accretion disks appear to be important in many astrophysical environments, from planet formation to accreting supermassive black holes at the hearts of active galaxies. But even the most well-behaved X-ray binary sources show surprising deviations from strictly periodic variability. This talk will explore the variety of non-periodic variations seen in these systems, and some of the analysis tools used beyond traditional power spectral analysis, which is often insufficient. Such tools include phase-space embedding and topological analysis used by some in the nonlinear dynamics community. As the time baseline grows, these tools become more powerful, giving us hints about what drives such variability. I hope to get you thinking and commenting about whether a recently proposed accretion disk dynamo model might be able to explain the double-well-potential-like behavior seen in some systems; thus taking the next steps in understanding the dynamics of accretion disks.*

### September 8, 2016

#### Perception and Memory in Animal Movement

University of Maryland | Department of Biology

*Abstract: Individual animals acquire information from their surroundings, gain and store knowledge from experience, and use what they have learned to navigate through dynamic landscapes. I will first discuss a mathematical model of animal perception in dynamic landscapes (this is formulated as a partial integro-differential equation featuring non-local advection) and then present some biological results that frame challenges in the modeling of spatial memory.*

### September 15, 2016

#### On the Generation of Gravity-Capillary Solitary Waves in Deep Water

Naeem Masnadi

University of Maryland | Department of Mechanical Engineering

*Abstract: Nonlinear solitary waves are known to bifurcate from linear sinusoidal waves in deep water at the minimum phase speed of linear gravity-capillary waves (c_min=23 cm/s). This minimum happens at a finite wavenumber and the solitary waves can be viewed as modulated wavepackets with the wave envelope moving at the same speed as the wave crests. The minimum phase speed is also associated with a resonant condition; the linear response to a surface pressure distribution moving at this speed becomes unbounded. The nonlinear response offers rich and complicated dynamics and several solution regimes are found due to a delicate interplay between the effects of nonlinearity, dispersion and viscous dissipation. I will first review some theoretical background and modeling approaches to the problem of the response of a water surface to a pressure source moving at speeds close to c_min and then present our recent experimental and numerical findings..*

### September 22, 2016

#### The Markovian Mpemba Effect

Oren Raz

University of Maryland | Department of Chemistry and Biochemistry

*Abstract: Under certain conditions, it takes less time to cool a hot system than to cool the same system initiated at a lower temperature. This phenomenon – the “Mpemba Effect”, has been observed in a variety of systems, including water, magnetic alloys and carbon nano-tube resonators. So far, no single generic mechanism to explain this counter-intuitive behavior was suggested. Using the theoretical framework of nonequilibrium thermodynamics, we construct a minimal model that describes this behavior and illustrates the fundamental principles behind it. We derive a sufficient condition for this effect in Markovian systems, and predict an inverse effect: it might take less time to heat a cold system than a warmer one. *

### September 29, 2016

#### Practical Kalman Filtering with and Without a Model

George Mason University | Department of Mathematical Sciences

### October 6, 2016

#### The Force of Fluctuations: Analysis and Control of Extinctions on Networks

Naval Research Laboratory

*Abstract: Noise in various forms is known to cause switching between states, create new meta-stable states, and form global dynamical structures. In this talk, I will review some previous work on the effects of noise in static and adaptive networks, and show how to extend the theory to heterogeneous networks with a specified degree distribution. Applications will be to epidemic spread and novel optimal network control in large populations.** Specifically, we have developed new mathematical and computational techniques demonstrating that both highly connected individuals and those with a few connections should be targeted in specific proportions, using vaccination or treatment, in order to minimize mean extinction times. The optimal approach gives orders of magnitude improvement over known strategies.*

### October 13, 2016

#### Noise-Influenced Dynamics

University of Maryland | Department of Mechanical Engineering* *

### October 20, 2016

#### Chaos, Noise and Random Numbers

Joe Hart and Rajarshi Roy

University of Maryland | Department of Physics, IREAP, IPST

### October 27, 2016

#### European Neolithic societies (8000-4000 BP) exhibited early warning signs in advance of dramatic social collapse: New evidence from modeling and computational statistics

University of Maryland | Anthropology Department

*Abstract: This study uses statistical tests known as "early warning signals" (EWS) to determine whether declining socio-ecological resilience presaged a pattern of collapse during the Early Neolithic Period in Europe. Our earlier research has shown with a high degree of certainty that radiocarbon-inferred human demography during the Neolithic exhibits a boom-and-bust pattern. In this new study we analyze our meta-database of radiocarbon dates in order to determine whether societies on the verge of major reorganization—regime shift— may exhibit declining resilience, and if it can be detected using statistical methods. In seven of nine regional datasets we find increasing autocorrelation and variance leading up to collapse, suggesting that these societies began to recover from perturbation more slowly as resilience declined. We use simulation to validate our methods and show that sampling biases, atmospheric effects, radiocarbon calibration error, and taphonomic processes are unlikely to explain the observed EWS patterns. While EWS have been detected in biology and ecology, to our knowledge, this study is the first to find early warning signals of demographic regime shift among human populations.*

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### November 3, 2016

#### Reservoir Computing Using Autonomous Boolean Networks

Ohio State University | Department of Physics

*Abstract: Reservoir computing is a new approach to machine learning that uses a dynamical system for processing information. The dynamical system is a recurrent network where the weights of the network links are randomly assigned, as well as the weights for feeding information into the network. Only the output weights are adjusted to optimize the performance of the reservoir computer for a particular task, which is a linearly optimization problem and hence can be done quickly. I will describe the basic properties of reservoir computers, how they can be realized efficiently in hardware on a field-programmable gate array, and their application to a written-digit classification task and the forecasting of a chaotic dynamical system. *

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### November 10, 2016

#### Spatio-Temporal Optical Vortices

University of Maryland | IPST, Department of Electrical and Computer Engineering, Department of Physics

*Abstract: When an optical pulse propagating through a nonlinear medium exceeds a certain threshold power, it can focus itself and collapse, in theory, to a singularity. In practice, several physical mechanisms mitigate or arrest the catastrophic collapse and the pulse continues propagation as a filamentary structure. This scenario has played out in many nonlinear optics systems over decades: among them are air filamentation, relativistic self-focusing in plasmas, nonlinear generation of broadband light, laser-material processing, and unintentional (and expensive) laser damage. Recently, we showed that self-focusing collapse and collapse arrest is universally accompanied by the generation of robust topological structures: spatio-temporal optical vortices (STOVs). In contrast to the conventional orbital angular momentum vortices in, for example, Laguerre-Gaussian beams, which can be described purely by spatial coordinates, STOVs have electromagnetic phase circulation in a spatio-temporal plane that propagates with the pulse and directs the global pulse energy flow. I will describe our experiments, simulations and calculations leading to our discovery of STOVs , and discuss future possible applications. *

### November 17, 2016

#### ECHO, ECHo, Echo, echo... When Echoes Overwhelm Landau Damping

University of Maryland | Department of Physics, IREAP

*Abstract: The Liouville equation describing a collection of charged particles is time-reversible. In the weakly coupled limit, one can reduce this equation to a Fokker-Planck equation, which is irreversible. The problem of the fate of electromagnetic field fluctuations in a plasma in the limit of very weak irreversibility was addressed by Landau, who demonstrated that as long as there are some collisions (even if rare), and in the absence of sources, gradients, etc, typical field fluctuations are damped with an easily calculated "collisionless" damping rate -- this is Landau damping. The energy of the field fluctuations is converted to particle energy; there is irreversible heating. Landau's calculation is fine in the limit of small amplitude fluctuations, but what happens when the plasma is turbulent? I will show that in a typical nonlinear system (relevant to many physical observations), Landau damping is overwhelmed and ultimately arrested by turbulent "echoes". This finding has important implications for detailed predictions of the heating (and in some cases, for the luminosity) of some interesting astrophysical plasmas. *

### November 24, 2016

#### Thanksgiving Break - No Seminar

### December 1, 2016

#### A book report: How complex cells evolved from bacteria, a story of energy

University of Maryland | Department of Mathematics

### December 8, 2016

#### Fermi Acceleration in Discontinuous Systems

University of Maryland, Department of Mathematics