Bulletin of the American Physical Society
APS March Meeting 2018
Volume 63, Number 1
Monday–Friday, March 5–9, 2018; Los Angeles, California
Session F47: Nonlinear Dynamics and Hamiltonian Systems 
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Sponsoring Units: GSNP Chair: Michael Wilkinson, Open Univ Room: LACC 507 
Tuesday, March 6, 2018 11:15AM  11:27AM 
F47.00001: Horizontal stability of a bouncing ball Daniel Harris, Brendan McBennett, Avishai Halev When a ball is released onto a vibrating flat surface, it will ultimately bounce periodically on the surface if the forcing amplitude is sufficiently small. In this work, we explore the dramatic effect that the inclusion of underlying surface topography can have on the observed motion of the ball. Particular focus is given to detailing the surprising manner in which a concave surface can actually destabilize purely vertical bouncing, such that horizontal motion naturally ensues. We show that the resulting motion can be periodic, quasiperiodic, or even chaotic and depends sensitively on the shape of the underlying surface. 
Tuesday, March 6, 2018 11:27AM  11:39AM 
F47.00002: The rolling suitcase instability Sylvain Courrech du Pont, Giulio Facchini, Ken Sekimoto

Tuesday, March 6, 2018 11:39AM  11:51AM 
F47.00003: Redundant variables: iterated maps and the 2d Ising model Archishman Raju, James Sethna The period doubling route to chaos in iterated maps has a beautiful renormalization group description first extensively studied by Feigenbaum. The fixed point of the renormalization group can be moved by making a coordinate change, leading to a redundancy in the description. We examine the existence and effect of redundant variables in the renormalization group description of such maps. We relate our analysis to redundant variables in the 2d Ising model, and conjecture that it may explain some scaling features of the exact solution. 
Tuesday, March 6, 2018 11:51AM  12:03PM 
F47.00004: Estimation of surrogate measure for the largest Lyapunov exponent from the information entropy of symbolic dynamics Takaya Miyano, Hiroshi Gotoda A positive Lyapunov exponent is the most convincing signature of chaos. However, existing methods for estimating the Lyapunov exponent from a time series often give unreliable estimates because they trace the time evolution of the distance between a pair of initially neighboring trajectories in phase space. Here, we propose a mathematical method for estimating a surrogate measure for the Lyapunov exponent from the information entropy of a symbolic time series without tracing initially neighboring trajectories. We apply the proposed method to numerical and experimental time series to verify its validity. 
Tuesday, March 6, 2018 12:03PM  12:15PM 
F47.00005: Testing for Partially Predictable Chaos in Delayed Dynamical Systems Hendrik Wernecke, Bulcsu Sandor, Claudius Gros For deterministic chaos initially close trajectories diverge exponentially leading to a loss of correlation followed by a diffusive decorrelation. If the decorrelation of trajectories is dominated by the diffusive process happening on a much longer time scale than the Lyapunov prediction time, the chaotic attractor is partially predictable for long time [1]. However, due to the high level of correlation, the standard tests for chaos either yield ambiguous results or misclassify partially predictable chaos as laminar flow. 
Tuesday, March 6, 2018 12:15PM  12:27PM 
F47.00006: Laminar chaos David Müller, Andreas Otto, Guenter Radons Dynamical systems with timedelay arise in many fields such as life science, climate dynamics, synchronization of networks and engineering. In nature the delay is typically not constant but rather timevarying, e.g. due to environmental fluctuations. Recently we found that in such systems there exists a dichotomy, which results in drastic differences in the Lyapunov characterisics of the two classes [1, 2]. 
(Author Not Attending)

F47.00007: Statistical Description of Mixed Systems (Chaotic and Regular) Or Alus, Shmuel Fishman, James Meiss, Mark Srednicki We discuss a statistical theory for Hamiltonian dynamics with a mixed 
Tuesday, March 6, 2018 12:39PM  12:51PM 
F47.00008: Features and Statistics of Sparameters in Nonlinear Wave Chaotic Systems Min Zhou, Edward Ott, Thomas Antonsen, Steven Anlage The Random Coupling Model (RCM) has been shown to successfully predict the statistical properties of linear wave chaotic cavities in the highly overmoded regime. It is of interest to extend the RCM to strongly nonlinear systems. Besides the statistics of harmonics we recently studied, in this talk, we discuss measurements of the nonlinear Sparameters in two nonlinear systems. One system is a diodeloaded ¼bowtie quasi2D microwave cavity where the diodes act as point nonlinearities in a wave chaotic system. Another is a cutcircle quasi2D microwave cavity which is made of Pb plated copper. In the superconducting state, the cavity is very nonlinear. By taking advantage of the high power (up to +35 dBm) vector network analyzer (VNA), we observe that the Sparameters are power dependent. Some features, such as time reversal symmetry breaking, hot spot statistics, nonlinear impedance etc. are observed in these nonlinear systems. The goal is to study how RCM needs to be modified to quantitatively explain these features. 
Tuesday, March 6, 2018 12:51PM  1:03PM 
F47.00009: Wave Chaotic Properties of Cascaded Complex Enclosures Shukai Ma, Bo Xiao, Steven Anlage Predicting the power transmission of interconnected enclosures like a chain of cabins in a ship, is of keen interest to various communities. Here we utilize Random Coupling Model (RCM) to explain the wave chaotic properties of the cavity cascade system. Experiments utilizing a full scale single cavity, and three cavity cascade systems at NRL. We determine loss parameters and find agreement between the statistical properties of experimental normalized impedance with the RCM predictions. We use the scaling properties of Maxwell’s equations to create a scaleddown cavity which preserves the loss parameter of full scale cavity. Experiments show that the statistics of the single cavity impedance matrix elements for full scale and scaled enclosures match. We next study the transmission of the multicavity cascade system with cavities connected by apertures. By describing the coupling between cavities through apertures, we are able to produce predictions for the statistics of the impedance for cascaded cavities. We present results on estimates of the radiation admittance for apertures both experimentally and theoretically, which permits us to complete a quantitative theoretic model for the cavity cascade systems’ statistic properties. 
Tuesday, March 6, 2018 1:03PM  1:15PM 
F47.00010: Interference in Chaotic Metamaterial Billiards with a Variable Number of Interference Slit Configurations Jorge Jose, Natalia Litchinitser The 2slit gedanken experiment played in important role in the foundational understanding of the unintuitive properties of quantum mechanics (QM). This configuration was shown to be correct in early experiments, illustrating the essential nature of the quantum mechanical waveparticle duality. This type of slit configurations has witnessed a recent renaissance due to advances in precision measurement techniques addressing deeper conceptual questions by varying the type of slit scattering configurations. Most slit experiments have been analyzed without considering classically chaotic solutions. Here, we report wave simulation results combining integrable and nonintegrable billiards, having a different number of slit configurations, with embedded combinations of positive and negative index of refraction materials. Specifically, we compared the interference patterns when varying the number of slits in planar rectangular cavities as well as chaotic Dshaped billiards. We studied closed and open billiards. These results may have important conceptual consequences as well as practical device applications. 
Tuesday, March 6, 2018 1:15PM  1:27PM 
F47.00011: Heating Phase Transition in a PeriodicallyDriven Classical Spin System Owen Howell, Phillip Weinberg, Dries Sels, Anatoli Polkovnikov, Pankaj Mehta, Marin Bukov Periodicallydriven systems are currently experiencing an unprecedented revival of interest through theoretical and experimental work on engineering novel states of matter by dressing static systems with carefully designed periodic modulations. However, the usefulness and applicability of this socalled Floquet engineering requires the stability of the periodically driven system to detrimental heating processes. We study a periodicallydriven classical spin chain and show evidence that the mechanism underlying highfrequency prethermal Floquet steady states has a classical nature, and is closely related to Nekhroshev and KAM theory. We thus demonstrate that energy absorption is exponentially suppressed up to trillions (!) of driving periods, offering a stable window for Floquet engineering. Analysing the dependence of heating on the drive frequency, we find a sharp phase transition between a stable zerotemperature and a chaotic infinitetemperature states, with time playing the role of the system size. We discuss heating in twodimensional systems, with potential interesting implications for the currently intractable higherdimensional quantum analogue of this problem. 
Tuesday, March 6, 2018 1:27PM  1:39PM 
F47.00012: Light Propagation and Mode Mixing in Concatenated Multimode Fibers Yujie Cai, Eleana Makri, Tsampikos Kottos We analyze light propagation in concatenated multimode fibers (MMF) using an Random Matrix Theory (RMT) modeling that takes into consideration the polarization mixing and spatial modal mixing between different modes. The latter is a result of fiber imperfections (twisting, defects etc.) and typically is characterized by the strength δ of the coupling between modes and the range of coupling b of different modes. Our analysis lead us to a generalized fluctuationdissipation relation which describes the decay of an initial excited mode to the other modes of the system. We found that this decay is characterized by three regimes: an initial exponential decay, with a rate which is proportional to δ^{2}b; a slower, power law decay which reflects a diffusion process with a step b; and finally a saturation to an ergodic value which is inverse proportional to the number of available modes. 
Tuesday, March 6, 2018 1:39PM  1:51PM 
F47.00013: Breaking of time translation invariance in a deterministic system of Kuramoto oscillators Shadisadat Esmaeili, Darka Labavic, Hildegard MeyerOrtmanns, Michel Pleimling Physical aging has been observed in systems with stochastic thermal fluctuations like spin glasses and colloids. This phenomenon has also been detected in a system of repulsively coupled Kuramoto oscillators under the effect of an external noise, where the noise played the role of the thermal fluctuations in spin glasses. In this study we consider fully deterministic systems of repulsively coupled Kuramoto oscillators on hexagonal lattices of different sizes with different characteristics of the rich attractor space. A disorder is introduced in the system trough a random and regular distribution of natural frequencies of individual oscillators. We find the breaking of timetranslation invariance in the system caused by long transient times. This feature disappears in the regime with weaker negative coupling between the oscillators in the vicinity of the transition point to the monostable state (positive coupling), where we do not find any stable periodic orbits but only irregular phase trajectories. 
Tuesday, March 6, 2018 1:51PM  2:03PM 
F47.00014: Ergodicitybreaking in Discrete Nonlinear Schrödinger Equation MITHUN THUDIYANGAL, Yagmur Kati, Carlo Danieli, Sergej Flach

Tuesday, March 6, 2018 2:03PM  2:15PM 
F47.00015: Kinkoscillon collisions in phi^6 (triplewell) scalar field theory Aliaksei Halavanau Topological and nontopological defects in one dimensional scalar field theories are often mentioned as toy models for more complex cosmic strings and domain wall problems. A classic example is a KleinGordon equation with a nonlinear phi^4 (double well) or phi^6 (triple well) potential. In such a model, kinks/oscillons represent topological/nontopological solitary solutions. Kinks are known to have a fractal collision structure; kinkoscillon collisions remain largely uninvestigated. We present a numerical study of kinkoscillon collisions in a generalized phi^6 (triple well) model. We also point out some similarities of the solutions inherited from the integrable sineGordon model. 
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