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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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### 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

Institution 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 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