Bulletin of the American Physical Society
APS March Meeting 2022
Volume 67, Number 3
Monday–Friday, March 14–18, 2022; Chicago
Session Y08: Chaos and Nonlinear Dynamics IIRecordings Available
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Sponsoring Units: GSNP Chair: Greg Voth, Wesleyan University Room: McCormick Place W-179B |
Friday, March 18, 2022 8:00AM - 8:12AM |
Y08.00001: Prediction and Suppression of Dragon Kings Nahal S Sharafi, Sarah Hallerberg, Sarah Hallerberg A wide range of dynamical systems exhibit extreme events and critical transitions. The extent of damage and destruction these high-profile events may leave behind indicates the importance of the task of predicting them. We introduce a novel, unifying approach towards prediction of critical transitions. We explore rare events in the form of "Dragon Kings", unique, dramatic events that live beyond the distribution of other event sizes. We employ a network of synchronized |
Friday, March 18, 2022 8:12AM - 8:24AM |
Y08.00002: Creating localized periodic structures with spatially localized perturbations within a defect chaotic state Michel Pleimling, Jason Czak In past attempts to control spatio-temporal chaos, spatially extended systems were subjected to protocols that perturbed them as a whole, often overlooking the potential stabilizing interaction between adjacent regions. We have shown that selectively applying a time-delayed feedback scheme to a specific region of a system can generate periodic patterns that are distinct form those observed when controlling the whole system. Depending on the protocol used, these new patterns can emerge either in the perturbed or the unperturbed region. Specifically, we use spatially localized time-delayed feedback on the one-dimensional complex Ginzburg-Landau equation and demonstrate, through the numerical integration of the resulting real and imaginary equations the stabilization of novel periodic patterns within a defect chaotic regime. The mechanism underlying the observed pattern generation is related to the interplay between diffusion across the interfaces separating the different regions and time delayed feedback. |
Friday, March 18, 2022 8:24AM - 8:36AM |
Y08.00003: Timing of the Fermi-Pasta-Ulam-Tsingou Metastable State Kevin A Reiss, David K Campbell The issue of the long metastable state in the Fermi-Pasta-Ulam-Tsingou (FPUT) lattice has been a core concern in Statistical Mechanics since its discovery. The ergodic hypothesis mandates that even arbitrarily small perturbations to a harmonic lattice should allow enough mixing for the time averaged modal energies to equal the ensemble average. However, the metastable state for specific initial conditions has been observed to have a lifetime longer than computationally achievable, for low enough energy. We use a comparison to the Toda lattice to define the end of the metastable state for the α-FPUT model, and then employ a numerical investigation to find the lifetime of this state. In this way, the end of the metastable state demonstrates a transition from nearly integrable dynamics over to non-integrable dynamics. Using many varying initial conditions, we find a scaling of the lifetime of the metastable state for different energies and system sizes. A similar technique is then applied to the β-FPUT model to determine the lifetime of the metastable state. Results are compared to the 'Echo' method which measures the strength of chaos through perturbed reverse integration. |
Friday, March 18, 2022 8:36AM - 8:48AM |
Y08.00004: Minimizing Losses in Classical Nonlinear Oscillators Nik O Gjonbalaj, Anatoli S Polkovnikov, David K Campbell Shortcuts to adiabaticity (STAs) have been used to make rapid changes to a system while eliminating or minimizing disturbances to the system's state. Especially in quantum systems, these shortcuts allow us to minimize inefficiencies and heating in experiments and quantum computing, but the theory of STAs can also be generalized to classical systems. We focus on one such STA, approximate counter-diabatic (ACD) driving, and numerically compare its performance in two classical systems: a quartic anharmonic oscillator and the β Fermi-Pasta-Ulam-Tsingou (FPUT) lattice. In particular, we modify an existing variational technique to optimize the approximate driving and then develop classical figures of merit to quantify the performance of the driving. We find that relatively simple driving terms can dramatically suppress excitations regardless of system size. ACD driving in classical oscillators could have many applications, from minimizing heating in bosonic gases to investigating other classical nonlinear systems with many degrees of freedom. |
Friday, March 18, 2022 8:48AM - 9:00AM |
Y08.00005: Coalescence of Attractors in Dynamical Systems Cheyne Weis, Michel Fruchart, Ryo Hanai, Kyle Kawagoe, Peter B Littlewood, Vincenzo Vitelli We study a class of bifurcations generically occurring in dynamical systems with Z2 symmetry in which limit cycles, limit tori, or strange attractors coalesce with their mirror image. Mathematically, the bifurcations are characterized by the coalescence of covariant Lyapunov vectors, generalizing the notion of exceptional points to nonlinear dynamical systems. A generic way to construct these bifurcations for arbitrary attractors is presented, and we show that it is a normal form in the case of limit cycles. Breaking the Z2 symmetry explicitly leads to the formation of memory observable through the presence of hysteresis cycles. Our results apply to systems including minimal models of coupled neurons, ecological systems, and open quantum systems. |
Friday, March 18, 2022 9:00AM - 9:12AM |
Y08.00006: Developable cones in annular rings Lucia Stein-Montalvo, Arman Guerra, Kanani Almeida, Ousmane Kodio, Douglas P Holmes Thin, confined sheets may distribute strain energy smoothly (e.g. the wrinkled edges of the lotus leaf), or focus it into small, sharp, sacrificial regions (e.g. the ridges and vertices, or d-cones, in discarded wrapping paper). The d-cone emerges when a circular sheet is forced, via indentation, through a ring of smaller radius. Its radial directors are unstrained, and the bulk shape follows that of an elastic ring. |
Friday, March 18, 2022 9:12AM - 9:24AM |
Y08.00007: From Shallow to Deep: Buckling Behavior of Clamped Spherical Caps Kanghyun Ki, Jeongrak Lee, Anna Lee We revisit the buckling of clamped spherical caps under uniform pressure, focusing on the effect of the shallowness and geometric imperfection. For decades, studies on the relationship between shallowness and buckling pressure have flourished. However, a large discrepancy between the analytic solution and experiments has been reported, mainly on the shallow spherical caps. We first experimentally investigate the buckling of clamped spherical caps over the broad shallowness range. We also conduct finite element simulations by varying shallowness and the defect geometry. The buckling pressure of the shells shows the decaying sinusoidal form with increasing shallowness, in excellent agreement between experimental and FEM results. Moreover, we find the shell with a small defect and specific shallowness non-axisymmetrically buckles at multiple snap-through regions on the side of the shell (between the pole and the clamped boundary). On the other hand, the shell with a larger defect axisymmetrically buckles at the pole regardless of its shallowness. With the parametric studies, we provide the buckling strength and behavior criteria varying the defect geometry. |
Friday, March 18, 2022 9:24AM - 9:36AM |
Y08.00008: Probing the hidden equilibrium states of a buckled beam Sagy Lachmann, Shmuel M Rubinstein Buckling is a phenomenon that sees designs both utilizing it positively or trying to avoid its catastrophic consequences. Understanding what sets the critical threshold for buckling (i.e. the buckling load) is therefore of great importance. However, thin-walled structures are very defect-sensitive and are therefore hard to control and model. The often- irreversible outcome of a buckle makes experimental evaluation of the critical load challenging. Recently, it has been shown that finite-amplitude perturbations of such systems can produce a stability landscape which predicts the buckling load for a system with a dominant imperfection. Here, we show that the stability landscape can also identify new stable and unstable equilibrium modes of a real systems, and reveal the correlation structure of its defects and its true resting shape. |
Friday, March 18, 2022 9:36AM - 9:48AM |
Y08.00009: Measuring dynamical interaction from data Akira Kawano, Greg J Stephens Dynamical interactions, such as between brain and behavior, are ubiquitous in nature. However, measuring such coupling from data is challenging because the underlying interaction can be dynamic, i.e., depend on the states of the systems, and the observation may be incomplete, e.g., only a subset of variables are observable. A key idea to overcome such problems is to evaluate the mutual predictability of individually reconstructed phase spaces - cross-embedding. When applied to real data however, the quantification of coupling through cross-embedding is complicated by the multiple ways to implement and evaluate the mutual prediction. Here, we introduce a new approach, the mutual information between individually partitioned state spaces, with which we can describe the state-dependent coupling by the phase space density of one system conditioned by the state of the other. We apply this approach to coupled Rössler systems, where the underlying interaction process is successfully detected from incomplete observation. |
Friday, March 18, 2022 9:48AM - 10:00AM |
Y08.00010: Nonlinear Dynamics of US Inflation, Money Supply, and Growth Time Series Tai Young-Taft, Harold M Hastings Recently attention has been paid to significant though incipient inflationary effects in core economies, e.g. the Euro Zone and US. ‘Supply chain bottlenecks’ have been cited as a causative factor, as well as inflation in energy prices. |
Friday, March 18, 2022 10:00AM - 10:12AM |
Y08.00011: Phase transitions, critical behavior, and emergent order in systems of musical harmony Huay Din, Jesse A Berezovsky The emergence of order in a thermodynamic system can be understood as a temperature dependent trade-off between minimizing energy and maximizing entropy of the system. We posit that the ordered arrangement of musical pitches that constitute a system of musical harmony arises analogously from a trade-off between minimizing the perception of dissonance and maximizing the variety of compositions possible within the system. We show that by quantifying these factors, a system of harmony can be formulated as an XY model governed by an effective free energy. Methods from statistical mechanics can then be applied that serve to minimize free energy, reproducing familiar structures of Western and non-Western harmony. In the mean field approximation, phase transitions occur from disordered sound to ordered distributions of pitches, including 12-fold octave divisions used in modern and historical Western music, as well as those used in several other musical traditions [1]. Numerical simulation of quenched tones on a 3D lattice shows a transition from disordered sound to the 12-fold octave division with frozen vortex strings as predicted by the Kibble-Zurek mechanism. These topological defects can be interpreted as musical chords, and the branching network of strings as chord progressions. These results provide a new approach for understanding, appreciating, and composing music from first principles. |
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