Bulletin of the American Physical Society
APS March Meeting 2023
Volume 68, Number 3
Las Vegas, Nevada (March 5-10)
Virtual (March 20-22); Time Zone: Pacific Time
Session YY01: V: Chaotic and Driven Systems |
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Sponsoring Units: GSNP Chair: Christopher Griffin, Applied Research Laboratory Room: Virtual Room 1 |
Wednesday, March 22, 2023 10:00AM - 10:12AM |
YY01.00001: Chaotic Dynamics of an Elastically Bouncing Dumbbell Scott V Franklin The dynamics of an elastically bouncing dumbbell are analogous to those of a ball bouncing on a sinusoidally oscillating surface with one important exception: the dumbbell's angular velocity, analogous to the surface's oscillation frequency, changes with each bounce, making the subsequent motion significantly more complicated. We investigate this dynamical system over a range of aspect ratios and initial energy, finding periodic, quasi-periodic and chaotic motions. As the initial energy is increased, the dumbbell can flip over and tumble. We find that, for large particle aspect ratios, narrow bands of energies well above this minimum where tumbling suddenly ceases. Because energy is conserved, the dynamics of a bounce are uniquely determined by the angle and angular velocity. The Lyapunov exponents of paths in this two dimensional phase space can be calculated, identifying periodic islands within the chaotic sea. Finally, for certain parameters, the angle at each collision moves from its initial value in a subdiffusive manner, and we determine the characteristic exponents. |
Wednesday, March 22, 2023 10:12AM - 10:24AM |
YY01.00002: Exploring the Role of Spatial Coupling in Spatiotemporal Chaos using Covariant Lyapunov Vectors Aditya Raj, Mark Paul One aspect of spatiotemporal chaos that often presents a formidable challenge is the difficulty in building a physical understanding of the role of the spatial couplings on the complex dynamics. In many systems of interest, such as fluid systems, the spatial couplings can be quite complex with both local and long-range contributions resulting from diffusive and nonlinear convective physical phenomena. We use the covariant Lyapunov vectors (CLVs) to provide new insights into the role of the spatial couplings for the chaotic dynamics of large 1D and 2D coupled map lattices (CMLs). By using CMLs we are able to explore a large parameter space and a broad variation of spatial couplings. We explore spatiotemporal chaos when there is local diffusive coupling, a weak long-range coupling, and a nonlinear convective coupling. We investigate how these spatial couplings affect the spatiotemporal features of the CLVs, we quantify the dimension and degree of hyperbolicity of the dynamics using the CLVs and lastly, we probe how the decomposition of the dynamics into physical and transient modes is affected by the spatial couplings. |
Wednesday, March 22, 2023 10:24AM - 10:36AM |
YY01.00003: Harmonic dispersion relation for strongly nonlinear elastic waves Mahmoud Hussein, Romik Khajehtourian Wave motion lies at the heart of many disciplines in the physical sciences and engineering. For example, problems and applications involving light, sound, heat, or fluid flow are all likely to involve wave dynamics at some level. We present a theory for the dispersion of generated harmonics in a traveling nonlinear wave. The harmonics dispersion relation, derived by the theory, provides direct and exact prediction of the collective harmonics spectrum in the frequency-wavenumber domain, and does so without prior knowledge of the spatial-temporal solution. It is valid throughout the evolution of a distorting unbalanced wave or the steady-steady propagation of a balanced wave with waveform invariance. The new relation is applicable to a family of initial wave functions characterized by an initial amplitude and wavenumber. We demonstrate the theory on nonlinear elastic waves traveling in a homogeneous rod with and without linear dispersion, showing that the theory is not limited by the strength of the nonlinearity or wave amplitude. Finally, we use the underlying formulation to present an analysis on the condition required for synthesis of solitary waves. |
Wednesday, March 22, 2023 10:36AM - 10:48AM |
YY01.00004: Phonon rogue waves in materials William Perry, Andrew V Brooks, Xiaoliang Zhang, Xiaoguang Zhang The effect of phonons on a material’s properties is usually considered in the regime where their influence on the atomic structure is to generate small displacements from equilibrium as these configurations dominate the available phase space. However, rare events in which phonons combine to generate larger deviations from equilibrium may have more impact on material properties than their share of the phase space would suggest. We calculate the rate at which these phonon rogue waves are expected to arise under the model that individual phonons are independent and uncorrelated. We apply these statistics to both phonon based transient defects and phonon generated Ampere field fluctuations. The rate of transient defect generation provides a correction to electron mobility calculations in graphene[1], while we use the Ampere field fluctuations to treat the spin-phonon interaction in Ge quantum dots, GaAs, InAs, and InSb more directly than in the previously utilized Redfield theory[2]. |
Wednesday, March 22, 2023 10:48AM - 11:00AM |
YY01.00005: Giant concentration fluctuations far-from-equilibrium and reduction to a soluble model of turbulent advection Amir Jafari Giant concentration fluctuations are a manifestation of nonequilibrium long-range correlations in diffusive mixing of a solute in a quiescent fluid. Donev et al. in 2014 pointed out unexpected links of liquid diffusion with turbulent advection of a passive scalar, showing that power-law structure functions arise by a cascade process. In the asymptotic limit of high Schmidt number, typical of liquid mixtures, they found that the Landau-Lifschitz fluctuating hydrodynamic equations for a binary fluid reduce to a version of the soluble Kraichnan model of turbulent advection. However, their numerical simulations of the model did not obviously reproduce the experimentally observed k^{-4} structure function. We resolve this discrepancy by solving the model analytically. Surprisingly, although the theory accounts for nonlinear advection, it yields precisely the same static and dynamic structure functions predicted by linearized fluctuating hydrodynamics. We argue that this is a simple example of anomaly non-renormalization. In addition, however, the model predicts non-Gaussian higher-order statistics of concentration fluctuations and applies also to difficult problems with large concentration gradients, high concentrations, and transient processes beyond the scope of linearized theory. |
Wednesday, March 22, 2023 11:00AM - 11:12AM |
YY01.00006: Stochastic analysis of reactive processes in interacting particle systems Reda Tiani, Uwe C. Täuber Most of the literature on deterministic and stochastic models of reacting mixtures focuses on point-like particles reacting in the absence of any interaction energy between them. However, many realizations in biological and soft-matter systems, naturally deviate from such an idealized picture by involving strongly interacting species. In such systems new collective phenomena can emerge as exemplified by the occurrence of chemically-driven phase separation. Therefore, we investigate the effects of particle interactions by means of a general formalism based on the chemical master equation. By using a local detailed balance condition, transition rates are generalized in order to account for interaction energies between the reacting species in a thermodynamically consistent way. As a first step, such interactions are assumed to be of mean-field type and spatial degrees of freedom are neglected. The formalism is then applied to the Schlögl model, a generic model for far-from-equilibrium bistability. Statistical averages, such as the mean and variance of the number of particles, can be analyzed both analytically and numerically through a singular perturbation analysis and the Gillespie's simulation algorithm, respectively. In particular, we address the effects of mean-field interactions on the resulting stochastic dynamics, both away from and in the non-equilibrium steady state. |
Wednesday, March 22, 2023 11:12AM - 11:24AM Author not Attending |
YY01.00007: A Generalized Coarse-Graining Procedure from Diffusive Master Equations to PDEs Andrew B Li, Andrew B Li, Leonid Miroshnik, Sang M Han, Ganesh Balakrishnan, Talid Sinno A key challenge in developing continuum models is to relate parameters to the underlying microscopic processes. Previous work [1] has shown that it is possible to relate phase field model parameters to the underlying hopping mechanisms of a microscopic master equation. However, one of the limitations is that established procedures for accomplishing this place restrictions on the admissible types of physics and/or dynamical processes. In this talk we will discuss how to use a symmetric and antisymmetric decomposition to extend this approach to a completely general diffusive microscopic process. |
Wednesday, March 22, 2023 11:24AM - 11:36AM |
YY01.00008: Noise effects in outbreak statistics: large and small fluctuations Jason M Hindes Motivated by recent epidemic outbreaks, including those of COVID-19, we solve the canonical problem of calculating the dynamics and likelihood of extensive outbreaks in a population within a large class of stochastic epidemic models, including the susceptible-infected-recovered (SIR) model and its general extensions. In the limit of large populations, we compute the probability distribution for all extensive outbreaks including those that entail unusually large or small proportions of a population infected, given both demographic and parameter noise. Our approach reveals that, unlike other well-known examples of large fluctuations occurring in stochastic systems, the statistics of extreme outbreaks emanate from a full continuum of Hamiltonian paths satisfying unique boundary conditions. Moreover, we find that both the outbreak variance and the probabilities for extreme outbreaks depend sensitively on the source of noise. |
Wednesday, March 22, 2023 11:36AM - 11:48AM |
YY01.00009: Signal transmission in chains of coupled nonlinear oscillators Paul Woafo In this presentation, we will present how periodic and noisy inputs are propagated along chains of coupled nonlinear oscillators with stochastic variation of their natural frequencies. It will be demonstrated that the phenomena of double amplification, chaos generation along the chains and filtering phenomenon under certain conditions. Some biological and industrial implications will be discussed considering calcium waves dynamics and micro electromechanical systems. |
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