Bulletin of the American Physical Society
APS March Meeting 2018
Monday–Friday, March 5–9, 2018; Los Angeles, California
Session P47: Nonlinear Dynamics and Chaos 
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Sponsoring Units: GSNP DFD Chair: Alexander Levine, Univ of California  Los Angeles Room: LACC 507 
Wednesday, March 7, 2018 2:30PM  2:42PM 
P47.00001: Nonlinear compact periodic solutions in flat band networks Carlo Danieli , Alexandra Maluckov , Sergej Flach Linear wave equations on translationally invariant flatband (FB) networks exhibit one or more dispersionless bands in their Bloch spectrum. These macroscopically degenerate bands exist due to local symmetries and destructive interference on the lattice. Shortrange hopping FB networks host compact localized (eigen)states (CLS) with nonzero amplitudes restricted to a finite volume. We consider the presence of local nonlinear terms in the wave equations. We study the continuation of CLS into the nonlinear domain while keeping their compactness and renormalizing their frequency. We then study the stability of these nonlinear CLS in terms of resonances with extended and compact localized states. 
Wednesday, March 7, 2018 2:42PM  2:54PM 
P47.00002: Chaos in the Band Structure of a Soft Sinai Lattice Max Porter , Aaron Barr , Ariel Barr , Linda Reichl We study the effect of broken spatial and dynamical symmetries on the band structure of two lattices with unit cells that are soft versions of the classic Sinai billiard. We find significant signatures of chaos in the band structure of these lattices, in energy regimes where the underlying classical unit cell undergoes a transition to chaos. Broken dynamical symmetries and the presence of chaos can diminish the feasibility of changing and controlling band structure in a wide variety of twodimensional latticebased devices, including twodimensional solids, optical lattices, and photonic crystals. 
Wednesday, March 7, 2018 2:54PM  3:06PM 
P47.00003: Transient Fractality as a Mechanism for Emergent Irreversibility in Chaotic Hamiltonian Dynamics Yuto Murashita , Naoto Kura , Masahito Ueda Boltzmann refuted the Loschmidt irreversibility paradox by arguing that the number of events with a positive entropy production should be infinitely more than that with a negative entropy production despite the onetoone correspondence between them. His idea was later verified by numerical simulations of reversible dissipative equations of motion, where it was confirmed that one should sample states exactly on a zerovolume fractal attractor to decrease the entropy. Thus, the probability for a negative entropy production vanishes although it is allowed by the equations of motion. We here address the question of whether this fractal picture applies to chaotic Hamiltonian dynamics. Although the Liouville theorem excludes fractality in the longtime limit, we find that a fractal structure transiently emerges in the Bunimovich billiard. Moreover, this transient fractality can be reformulated in light of the flucutuation theorem. As a result, we give a lower bound for an informationtheoretic irreversibility, which is determined by the transient fractality. 
Wednesday, March 7, 2018 3:06PM  3:18PM 
P47.00004: Investigation of Nonlinearity Effect During Storm Time Disturbance. Oludehinwa Irewola , Olasunkanmi Olusola , Olumide Odeyemi We examine the nonlinearity effect in the Disturbed Storm Time (D_{st} ) Signals during negligible geomagnetic storm and high geomagnetic storm for monthly (JanuaryDecember) D_{st} index time series each year from 20082016 using Recurrence Plot, Recurrence Quantification Analysis and Approximate Entropy. A distinct and noticeable trend between negligible geomagnetic Storm and high geomagnetic storm was observed. It was also observed that during negligible geomagnetic storm, the dynamics of the D_{st} signals behave in stochastic path while the increasing geomagnetic storm (high) tends to behave in deterministic path. As the influence of geomagnetic storm increases, the recurrence plot showed more deterministic structure indicating that that the recurrence plot posseses the potential to detect geomagnetic storm even at infinitesimal influence of geomagnetic storm. Also as the influence of geomagnetic storm varies, the recurrence rate also reflects the dynamical changes and its influence on determinism. From the Observed results, nonlinear dynamics is seen to perform excellently as a diagnostic model to geomagnetic storm disturbance. 
Wednesday, March 7, 2018 3:18PM  3:30PM 
P47.00005: Using a fluctuation analysis of limit cycle oscillations in inner ear hair bundles as a new test of low dimensional dynamical models Janaki Sheth , Alexander Levine , Dolores Bozovic The transduction of sound in the inner ear is an active process involving elastic elements, molecular motors, and ion channels. A manifestation of this process in inner ear hair cells is the presence of spontaneous bundle oscillation, observed in vitro in some species. This limit cycle oscillation has been modelled using both a simple twodimensional Hopf oscillator and more complex variants that explicitly incorporate the physiological variables. The models include stochastic noise in one or more variables representing implicitly the effect of other degrees of freedom. 
Wednesday, March 7, 2018 3:30PM  3:42PM 
P47.00006: Sensitive detection schemes for small variations in the damping coefficient based on the DuffingHolmes oscillator Khaled Aledealat In this work we proposed two detection schemes based on the nonlinear properties of the DuffingHolmes oscillator for the detection of small variations in the damping coefficient. Theoretically, a variation in the damping coefficient up to 0.001% with the possibility to be pushed further can be detected based on our model. A potential onoff magnetic sensor suitable for biomedical applications is suggested by implementing these two schemes with the Giant magnetoresistance based magnetic sensors. 
Wednesday, March 7, 2018 3:42PM  3:54PM 
P47.00007: Dynamical Derivation of Heat Transport Sahar Behpour , David Lambert , Paolo Grigolini The theoretical derivation of the empirical Fourier law is still an open subject of investigation. We plan to contribute to the solution of this problem moving along the lines of the earlier work of [1]. A set of nonlinearly interacting classical oscillators with energy E large enough generates chaos turning classical dynamics into thermodynamics. Following [1] we adopt the popular model proposed by Fermi, Pasta and Ulam (FPU), with a chain of N oscillators, in the condition where the Boltzmann principle S = k ln W applies, and we define temperature T according to the thermodynamic prescription 1/T = dS/dE. We add two additional oscillators, with vanishing kinetic energy, to the right and left end of the FPU chain and we study theoretically and numerically the equilibration process. The kinetic energy of the two additional oscillators is used as an indicator of the local temperature at the border of the FPU chain. We plan to apply iteratively this process to establish, with the help of the central limit theorem, the emergence of Fourier law. 
Wednesday, March 7, 2018 3:54PM  4:06PM 
P47.00008: Phononic Frequency Combs Adarsh Ganesan , Ashwin Seshia Optical frequency combs, by its manifestation as a frequency ruler, has revolutionized optical frequency metrology and spectroscopy. Only very recently, the phononic analogue of such frequency combs was experimentally demonstrated1 in a microelectromechanical resonator confirming predictions made by numerical simulations of a FermiPastaUlam system2. This initial experimental demonstration was followed up in further studies35 where variants of phononic frequency combs have been systematically studied using similar device testbeds over a range of drive conditions. The generation of phononic frequency combs in each case is inherently related to nonlinear modal coupling in such structures with exquisite control of geometry, material properties and conditions required for engineering application. In addition to the general scientific interest, phononic frequency combs also enable a unique approach to tracking the resonant frequency of a micromechanical resonator without an external feedback loop with the potential for improvements in frequency stability compared to conventional feedback oscillators6. 
Wednesday, March 7, 2018 4:06PM  4:18PM 
P47.00009: Seeded localized nonlinear excitations in the FermiPastaUlamTsingou system – Stability, delocalization and journey to equilibrium Rahul Kashyap , Matthew Westley , Surajit Sen It is well known that the FermiPastaUlamTsingou system admits localized nonlinear excitations. We show that these excitations exhibit nearly periodic behavior at early times but delocalize by leaking energy in the form of solitary waves and other metastable excitations in the absence of phonons. Further, we show that the excitations share qualitative features with the strongly nonlinear Duffing oscillator. After the delocalization is complete, the system enters a quasiequilibrium phase characterized by a Gaussian velocity distribution, high kinetic energy fluctuations and no equipartitioning of energy. Finally, at late times, we calculate the specific heat capacity of the system and compare it to analytical results to show that the system transitions past the quasiequilibrium phase to equilibrium. 
Wednesday, March 7, 2018 4:18PM  4:30PM 
P47.00010: Amplitude Death in a Ring of Nonlinear Oscillators with Unidirectional Coupling JungWan Ryu , JongHo Kim , WooSik Son , DongUk Hwang It has been widely studied that the interaction among subsystems can lead to the collective behavior such as synchronization and amplitude death. Among these collective behaviors in coupled oscillators, the amplitude death refers to a situation where individual oscillators cease to oscillate when they are coupled, which is a useful control mechanism for stabilizing systems to steady states. Most of the previous studies on amplitude death have dealt with bidirectional coupling cases. Here, we studied the amplitude death in a ring of coupled nonlinear oscillators with unidirectional couplings and discuss the differences between amplitude death behavior in unidirectional and bidirectional coupling cases. 
Wednesday, March 7, 2018 4:30PM  4:42PM 
P47.00011: Instantons in SelfOrganizing Logic Gates Sean Bearden , Haik Manukian , Fabio Traversa , Massimiliano Di Ventra Selforganizing logic [1] is a recentlysuggested framework that allows the solution of Boolean truth tables “in reverse,” i.e., it is able to satisfy the logical proposition of gates regardless to which terminal(s) the truth value is assigned. It can be realized if time nonlocality (memory) is present. By employing a practical realization of such gates using electronic circuits with memory, we show, numerically, that SOLGs exploit elementary instantons to reach equilibrium points [2]. Instantons are classical trajectories of the nonlinear equations of motion describing SOLGs that connect topologically distinct critical points in the phase space. Our work provides a physical understanding of, and can serve as an inspiration for, new models of bidirectional logic gates that are emerging as important tools in physicsinspired, unconventional computing. 
Wednesday, March 7, 2018 4:42PM  4:54PM 
P47.00012: The minimal “hidden” computer needed to implement a computation David Wolpert , Jeremy Owen , Artemy Kolchinsky

Wednesday, March 7, 2018 4:54PM  5:06PM 
P47.00013: Exploiting Nonlinear Dynamics for Programmable Behavior in Microfluidic Networks Daniel Case , JeanRégis Angilella , Adilson Motter The development of microfluidic systems that do not rely on abundant external hardware, yet retain controllable, complex behavior has been a primary research goal for the past decade. Microfluidic systems are composed of a network of flow channels and are generally considered to be linear systems; however, by creating nonlinearities in the network we are able to produce a diverse range of flow dynamics. Here, I present a simple microfluidic network that exhibits spontaneous oscillations in the flow rate. It is possible to switch between an oscillating and steady flow state by only changing the driving pressure. This functionality does not rely on external hardware and may even serve as an onchip memory or timing mechanism. Further, I demonstrate the ability to control the direction of flow though intermediate channels not directly connected to the controlled terminal. I use analytic models and rigorous fluid dynamics simulations to show these results. We expect this work to advance builtin control mechanisms in microfluidic systems towards the goal of designing portable systems that are as controllable as microelectronic circuits. 
Wednesday, March 7, 2018 5:06PM  5:18PM 
P47.00014: Surface temperatures in New York City: Geospatial
data enables the accurate prediction of radiative heat transfer Thorsten Emig , Masoud Ghandehari Three decades into the research seeking to derive the urban energy budget, the dynamics of the thermal exchange between the densely built infrastructure and the environment are still not well understood. We present a novel hybrid experimentalnumerical approach for the analysis of the radiative heat transfer in New York City. The aim of this work is to contribute to the calculation of the urban energy budget, in particular the stored energy. Improved understanding of urban thermodynamics incorporating the interaction of the various bodies will have implications on energy conservation at the building scale, as well as human health and comfort at the urban scale. The platform presented is based on longwave hyperspectral imaging of nearly 100 blocks of Manhattan, and a geospatial radiosity model that describes the collective radiative heat exchange between multiple buildings. The close comparison of temperature values derived from measurements and the computed surface temperatures (including streets and roads) implies that this geospatial, thermodynamic numerical model applied to urban structures, is promising for accurate and high resolution analysis of urban surface temperatures. 
Wednesday, March 7, 2018 5:18PM  5:30PM 
P47.00015: Chaotic Dynamics of Inner Ear Hair Cells Justin Faber , Dolores Bozovic Hair cells of the auditory and vestibular systems are capable of detecting sounds that induce subnanometer vibrations of the hair bundle, far below the stochastic noise levels of the surrounding fluid. Hair cells of certain species are also known to oscillate without external stimulation. The role of these spontaneous oscillations is not yet understood, but they are believed to be a manifestation of an underlying active mechanism. A deeper understanding of spontaneous motility could impact our understanding of the extreme sensitivity of hearing. Our experiments suggest that chaos exists in the dynamical system of the active hair cell. We observe a transition from chaos to order as increasingly stronger stimulus is applied to the hair bundle. This transition is accompanied by an increase in information transmission from the stimulus to the hair bundle, indicative of signal detection. Further, we use a simple theoretical model to describe the observed chaotic dynamics. The model exhibits an enhancement of sensitivity to weak stimuli when the system is poised in the chaotic regime. We propose that chaos may play a role in the hair cell's ability to detect lowamplitude sounds. 
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