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# 2018 Applied Dynamics Seminar Archives

### February 1, 2018

#### Reviewing artificial intelligence and the book Life 3.0

University of Maryland | Department of Mathematics

*Abstract: TBA*

### February 8, 2018

#### Experiments with arbitrary networks in time-multiplexed delay systems

University of Maryland | Department of Physics ; IREAP

*Abstract: Complex networks of coupled oscillators have proven to be systems that can display incredibly rich dynamical behaviors. Despite great theoretical advances in our understanding of coupled oscillator networks, it has proven difficult to design experiments that permit the study of dynamics on large networks with arbitrary topology. Here we present a new experimental approach that allows for the investigation of large networks of truly identical nodes with arbitrary topology. Our approach relies upon the space-time interpretation of systems with time delay in order to construct a network of coupled maps using a single nonlinear, time-delayed feedback loop. This system has many advantages: the network nodes are truly identical, the network is easily reconfigurable, and the network dynamics occur at high speeds. We use this system to study cluster synchronization and chimera states in both small and large networks of different topologies.*

### February 15, 2018

#### The spherical Couette system: simple yet complex

Johns Hopkins University | Department of Earth & Planetary Sciences

*Abstract: The spherical Couette system consists of two concentric spheres rotating differentially about a common axis. The space in between the spheres is filled with a conducting fluid. It is a relatively simple system without any thermal or density stratification and and has potential applications to planetary and stellar interiors. In addition, it is also an extremely interesting fluid dynamical system displaying a host of complex instabilities and other fluid dynamics phenomena. In the first part of the talk, I shall introduce the system and explore the generic regimes of different instabilities. This will be followed by some results using hydrodynamic simulations of this system with two pseudo-spectral codes MagIC and XSHELLS while comparing them with experimental data. Focus will be on the origin of special wave instabilities called 'inertial modes' and the transition to turbulence. In the next part, I will present magnetohydrodynamic simulations exploring the effect of an external magnetic field on inertial modes. In the final part of the talk, I will present simulations of self-consistent dynamo action in this system and the parameter dependence of the same.*

### February 22, 2018

#### Classical-to-quantum correspondence and transitions in chaotic dynamics of out-of-time-ordered correlators

University of Maryland | Department of Physics

*Abstract: One of the most intriguing phenomena in the studies of classical chaos is the butterfly effect, which manifests itself in that small changes in initial conditions lead to drastically different trajectories. It is characterized by a Lyapunov exponent that measures divergence of the classical trajectories. The question how/if this prototypical effect of classical chaos theory generalizes to quantum systems (where the notion of a trajectory is undefined) has been of interest for decades, but became more popular recently, when it was realized that there exist intriguing connections to string theory and general relativity in some quantum chaotic models. At the center of this activity is the so-called out-of-time-ordered correlator (OTOC) - a quantity that in the classical limit seems to approximate the classical Lyapunov correlator. In this talk, I will discuss the connection between the standard Wigner-Dyson approach to "quantum chaos" and that based on the OTOC on the example of a chaotic billiard and a disordered interacting electron system (i.e., a metal). I will also consider the standard model of quantum and classical chaos - kicked rotor - and calculate the correlator and Lyapunov exponents. The focus will be on how classical chaos and Lyapunov divergence develop in the OTOC and cross-over to the quantum regime. We will see that the quantum out-of-time-ordered correlator exhibits a clear singularity at the Ehrenfest time, when quantum interference effects sharply kick in: transitioning from a time-independent value to its monotonous decrease with time. In conclusion, I will discuss many-body generalizations of such quantum chaotic models.*

### March 1, 2018

#### Economic inequality from a statistical physics point of view

University of Maryland | Department of Physics

*Abstract: Inequality is an important and seemingly inevitable aspect of the human society. Various manifestations of inequality can be derived from the concept of entropy in statistical physics. In a stylized model of monetary economy, with a constrained money supply implicitly reflecting constrained resources, the probability distribution of money among the agents converges to the exponential Boltzmann-Gibbs law due to entropy maximization. Our empirical data analysis [1] shows that income distributions in the USA, European Union, and other countries exhibit a well-defined two-class structure. The majority of the population (about 97%) belongs to the lower class characterized by the exponential ("thermal") distribution. The upper class (about 3% of the population) is characterized by the Pareto power-law ("superthermal") distribution, and its share of the total income expands and contracts dramatically during booms and busts in financial markets. Interestingly, the same equations can be also applied to heavy-ion collisions [2]. Globally, energy consumption (and CO2 emissions) per capita around the world shows decreasing inequality in the last 30 years and convergence toward the exponential probability distribution, as expected from the maximal entropy principle. In agreement with our prediction [3], a saturation of the global Gini coefficient for energy consumption at 0.5 is observed for the most recent years. All papers are available at http://physics.umd.edu/~yakovenk/econophysics/.*

*[1] Yong Tao et al., "Exponential structure of income inequality: evidence from 67 countries", Journal of Economic Interaction and Coordination (2017) http://doi.org/10.1007/s11403-017-0211-6 http://arxiv.org/abs/1612.01624*

*[2] Xuejiao Yin et al., "A new two-component model for hadron production in heavy-ion collisions", Advances in High Energy Physics (2017) 6708581, http://doi.org/10.1155/2017/6708581*

*[3] S. Lawrence, Q. Liu, and V. M. Yakovenko, "Global inequality in energy consumption from 1980 to 2010", Entropy 15, 5565 (2013), http://dx.doi.org/10.3390/e15125565*

### March 8, 2018

#### APS March Meeting - No seminar

### March 15, 2018

#### Optimal control of networks: energy scaling and open challenges

University of New Mexico | Department of Mechanical Engineering

*Abstract: Recent years have witnessed increased interest from the scientific community regarding the control of complex dynamical networks. Some common types of networks examined throughout the literature are power grids, communication networks, gene regulatory networks, neuronal systems, food webs, and social systems. Optimal control studies strategies to control a system that minimize a cost function, for example the energy that is required by the control action.We show that by controlling the states of a subset of the nodes of a network, rather than the state of every node, the required energy to control a portion of the network can be reduced substantially. The energy requirements exponentially decay with the number of target nodes, suggesting that large networks can be controlled by a relatively small number of inputs, as long as the target set is appropriately sized. An important observation is that the minimum energy solution of the control problem for a linear system produces a control trajectory that is nonlocal. However, when the network dynamics is linearized, the linearization is only valid in a local region of the state space and hence the question arises whether optimal control can be used. We provide a solution to this problem by determining the region of state space where the trajectory does remain local and so minimum energy control can still be applied to linearized approximations of nonlinear systems. We apply our results to develop an algorithm that determines a piecewise open-loop control signal for nonlinear systems. Applications include controlling power grid dynamics and the regulatory dynamics of the intracellular circadian clock. This work is in collaboration with Isaac Klickstein and Afroza Shirin (UNM).*

### March 22, 2018

#### Spring Break - No seminar

### March 29, 2018

#### Magnetic Reconnection and Particle Energization

University of Maryland | IREAP

*Abstract: In many plasmas in nature magnetic reconnection is the primary process whereby energy stored in the magnetic field is transformed into kinetic and thermal energy. It lies at the heart of such phenomena as disruptions in fusion experiments, auroras, and solar flares. In addition, it is strongly suspected that reconnection plays a significant role in generating energetic particles (i.e., non-thermal power laws) in these and other systems. I will discuss the basic physics of magnetic reconnection as well as some of the numerical tools (e.g., particle-in-cell simulations) used to study its complex interplay of scales. Finally, I will discuss recent advances in quantifying how and under what conditions reconnection accelerates particles to non-thermal energies.*

### April 5, 2018

#### Large-scale neural network modeling: from neuronal microcircuits to whole-brain complex network dynamics

Qin Liu

University of Maryland | Department of Physics

*Abstract: Neural networks mediate human cognitive functions, such as sensory processing, memory, attention, etc. Computational modeling has proved to be a powerful tool to test hypotheses of network mechanisms underlying cognitive functions, and to better understand human neuroimaging data. Here we present a large-scale neural network modeling study of human brain visual/auditory processing and how this process interacts with memory and attention. We show how our modeling and simulation can relate phenomena across different scales from the neuronal level to the whole-brain network level. The model can perform a number of cognitive tasks utilizing different cognitive functions by only changing a task-specification parameter. Based on the performance and simulated imaging results of these tasks, we proposed hypothesis for the neural mechanisms underlying several important cognitive phenomena, which could be tested experimentally in the future.*

### April 12, 2018

#### Macroscopic Behavior of Systems of Many Interacting Orientable units: The Strong Influence of Dimensionality on the Dynamics

University of Maryland | Department of Physics and IREAP

*Abstract: The Kuramoto model, originally motivated by the dynamics of many interacting oscillators, has been used and generalized for a wide range of applications involving the collective behavior of large heterogenous groups of dynamical units whose states are characterized by a scalar angle variable. One such application in which we are interested is the alignment of velocity vectors among members of a swarm. Despite being commonly used for this purpose, the Kuramoto model can only describe swarms in 2 dimensions, and hence the results obtained do not apply to the often relevant situation of swarms in 3 dimensions. Partly based on this motivation, we study the Kuramoto model generalized to D dimensions, focusing on the 3-dimensional case. We show that in 3 dimensions, as well as for all odd dimensionality, the generalized Kuramoto model for heterogenous units has dynamics that are remarkably different from the dynamics in 2 dimensions. In particular, for odd D the transition of the time asymptotic equilibrium state to coherence occurs discontinuously as the coupling constant K is increased through zero, as opposed to the D=2 case (and, as we will show, also the case of even D) for which the transition to coherence occurs as K increases through a *postitive* critical value K _{c}. We observe that the odd-dimensional Kuramoto models with a large number of swarm elements is not low dimensional in the sense of Ott & Antonsen (2008). However, application of our generalized form of the Ott-Antonsen ansatz does reduce the complexity of the problem when compared with the full system of equations. We generalize our results beyond the Kuramoto model to a wider class of swarm dynamics in high dimensions, and we show that the Ott-Antonsen ansatz can be appropriately generalized for this class of systems. We expect that our results will hence be useful for solving questions involving coupled systems on a sphere in high dimensions, beyond just the Kuramoto model.*

### April 19, 2018

#### Turbulence closure ideas from plasma physics

University of Maryland | Department of Physics

*Abstract: First-principles turbulence simulations are expensive but very useful in many contexts. One approach to improving one's ability to predict experimental or observational data is to design algorithms for ever more processors, allowing ever higher (and more realistic) resolution. But one can also try to work in the opposite direction, developing closures to reduce the resource demands of computations. In a typical high-resolution turbulence simulation that I undertake, there are O(10**9) spectral amplitudes. Only a tiny percentage of these modes are excited to any appreciable level. I will discuss (and seek advice from the audience!) approaches we are pursuing to develop algorithms that solve a closed (or somewhat reduced) first-principles system with as little resolution as should be required. *

### April 26, 2018

#### High-speed prediction of a chaotic system using reservoir computers

Ohio State University | Department of Physics

*Abstract: A reservoir computer is an approach to machine learning that appears to be ideally suited for classifying time varying signals or as a black-box system for forecasting the behavior of a dynamical system. It consists of a recurrent artificial neural network that serves as a “universal” dynamical system into which data are input, where the connections on the input layer and recurrent links within the network are chosen randomly and held fixed. Only the weights of network output layer are adjusted during the training period, which greatly reduces the training time. I will discuss our recent progress on realizing high-speed prediction of the Mackey-Glass chaotic system (>10^8 predictions per second) using a reservoir computer based on a time-delay autonomous Boolean network realized on a field programmable gate array. I will also touch on our efforts to control a dynamical system with a reservoir computer and some recent results on methods to identify the optimum size of the reservoir computer network for a given task.*

### May 3, 2018

#### Heterogenous chaotic attractors

University of Maryland | Department of Mathematics

*Abstract: There is a saying: "there are two kinds of people in the world—the simple-minded and the muddle-headed." I prefer the former. But much of the investigation of chaotic attractors uses models that are sometimes overly simplistic at least for studying high dimensional chaotic attractors. Our goal is to produce more models that are still simplistic but better reflect typical high dimensional chaotic attractors and permit a better but still simple-minded understanding of chaos in high dimensions. This is a report on joint work with Miguel Sanjuan and Yoshi Saiki.*