Bulletin of the American Physical Society
APS March Meeting 2020
Volume 65, Number 1
Monday–Friday, March 2–6, 2020; Denver, Colorado
Session D24: Control of Noisy Nonlinear Dynamical SystemsFocus
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Sponsoring Units: GSNP Chair: Uwe Tauber, Virginia Tech Room: 401 |
Monday, March 2, 2020 2:30PM - 3:06PM |
D24.00001: Understanding the control process for non-equilibrium systems using
scaling theory Invited Speaker: Priyanka . Control theory is a widely used tool in engineering to |
Monday, March 2, 2020 3:06PM - 3:18PM |
D24.00002: Molecular machinery: quantifying the energetic cost of controlling nanoscale biological systems Steven Large, David Sivak At microscopic scales, biological systems must maintain a high degree of organization in order to properly function. Ultimately, this organization is achieved by the concerted efforts of a collection of nanoscale molecular machines: protein complexes that perform specific functions within the cell. Quantifying the flows of energy, information, and material through such systems is a central challenge in understanding their dynamics and in vivo operation. Currently, a number of important questions related to the function of molecular machines remain unanswered: what design principles produce efficient machines? What fundamental physical limitations are placed on these nonequilibrium systems? In this talk I will discuss our recent efforts to address some of these questions, making use of tools from nonequilibrium thermodynamics to quantify the energetic costs of driving strongly fluctuating systems. In particular, quantifying the dissipation associated with driving a fluctuating system between different states leads to conditions for efficient operation. Among other things, we find that there is an energetically optimal speed for systems to move at. |
Monday, March 2, 2020 3:18PM - 3:30PM |
D24.00003: Effects of structural and cellular heterogeneity on the control of nonlinear biological oscillator networks Narasimhan Balakrishnan, Neda Bagheri Circadian rhythms are biological processes that have a period of roughly 24 hours. In most animals, these rhythms are orchestrated by a specialized network of neurons that possess a regulatory system involving oscillatory genes and proteins. The dynamics of these regulatory networks are highly nonlinear. In this work, we study the functional consequences of structural and cellular heterogeneity (extrinsic noise) on the control of these oscillator networks. Structural heterogeneity refers to variation in size, topology and edge weights within the network of oscillators. We present two optimal control problems, those of modifying the phase of the population of these oscillators in either minimal time, or using minimum effort. We find there is a sweet spot relating heterogeneity and average coupling strength for which the control cost is minimal, and a limit to which heterogeneity enables greater controllability. Insights relating to heterogeneity also suggest evolutionary advantages heterogeneous populations may carry over homogeneous ones. Our findings also may help provide guidelines for the design of synthetic oscillator networks, a field of growing interest. |
Monday, March 2, 2020 3:30PM - 3:42PM |
D24.00004: Corazon espinado: microelectrode closed-loop control in cardiac tissue Conner Herndon, Flavio H Fenton Proper contraction of cardiac muscle relies on the coordinated propagation of transmembrane voltage, and disturbances of this propagation can result in deadly cardiac arrhythmias. One such disturbance strongly associated with the onset of fibrillation is a dynamical instability known as alternans, a beat-to-beat alternation in action potential duration (APD) arising from a period-doubling bifurcation. The restitution hypothesis claims that a return map in APD can describe and predict alternans, and decades of work have shown it can successfully reproduce many experimental observations. The restitution hypothesis likewise predicts a method for suppressing the onset of alternans which has been confirmed by some computational simulations; however, few experiments have addressed these predictions due to its difficult implementation. In this talk, I will discuss our development of a closed-loop control scheme to experimentally address predictions made by the restitution hypothesis via high resolution microelectrode recordings of transmembrane voltages in zebrafish, frog, and rabbit hearts. I will present our results which conclusively show the appearance of alternans in opposition to predictions made by theoretical models and provide an improved model that describes the dynamics. |
Monday, March 2, 2020 3:42PM - 3:54PM |
D24.00005: Induction of spatio-temporal spiral defects in an inhomogeneous stochastic May-Leonard system Shannon Serrao, Uwe Claus Tauber We study the induction of spiral defects in an inhomogeneous two-dimensional Monte Carlo toroidal lattice simulation of the stochastic three-species May-Leonard model with asymmetric predation rates. In an isolated setting, strongly asymmetric predation rates cause fast extinction from coexistence of all three species to a single surviving population. However, when spatially coupled to a fully symmetric May-Leonard patch, the spiral patterns from this stable region induce transient plane wave fronts and ultimately quasi-stationary spiral patterns in the asymmetric region. We quantitatively analyze the initial injection of plane wave fronts from the symmetric region and the subsequent formation of spirals, and explore the conditions for the stabilization of the weaker ecosystem. To this end, we study characteristic correlation lengths and oscillation frequencies, the shape and size of the spirals induced in the asymmetric region in comparison to the isotropic spirals in the symmetric regime, and the effects of varying system size and individuals' mobility. |
Monday, March 2, 2020 3:54PM - 4:06PM |
D24.00006: Extracting important parameters from dynamical systems models through coarse-graining Pranav Kantroo, Benjamin B Machta Known microscopic details often motivate models with large numbers of parameters. However, not all parameter combinations are relevant at large length-scales of observation. Some may affect coarse-grained system behavior sensitively, while others may have no discernible effect. Here we utilize the Fisher Information Metric formalism to identify which parameter combinations influence observables even for coarse-grained data. We first derive a general method for calculating this metric from a model whose data has been coarse-grained, and apply this to models coarse-grained by sparse-sampling observables in time. We make the resulting Fisher Information reparameterization invariant by transforming to a basis that measures how coarse-graining reduces observability. We then use this procedure to explicitly calculate the temporally coarse-grained Fisher Information Metric for several stochastic differential equation models. The expansion of the reparameterization invariant Fisher spectrum after coarse-graining separates relevant parameter combinations from irrelevant ones. We then draw concrete parallels between our formalism which uses coarse-graining of the Fisher Information, and the Renormalization Group framework. |
Monday, March 2, 2020 4:06PM - 4:18PM |
D24.00007: NUMERICAL INVESTIGATION OF SIGNAL AMPLIFICATION VIA VIBRATIONAL RESONANCE IN A CHUA’S CIRCUIT. John Laoye, Taiwo Olakunle Roy-Layinde, Kehinde Adam Omoteso, Rasaki Kolawole Odunaike In this paper, we numerically investigated the occurrence of Vibrational Resonance in a modified Chua’s oscillator with a smooth nonlinearity, described by a cubic polynomial. Response curves generated from the numerical simulation at the low frequency reveal that the system’s response amplitude could be controlled by modulating the conductance parameter of the Chua’s circuit, rather modulating the parameters of the fast periodic force. Modulating the frequency of the fast periodic force slightly reduces the response amplitude; shifts the peak point to a higher value of the amplitude of the fast periodic force by widening the resonance curves. Within certain parameter regime of the high frequency (Ω≥ 100 ω), the system’s response gets saturated, and further increase does not affect its amplitude. |
Monday, March 2, 2020 4:18PM - 4:30PM |
D24.00008: Resonance Coherence Optimization of Structure Formation in Nanofilms Undergoing Thermocapillary Instability Yi Hua Chang, Sandra Troian External temporal modulation of time periodic phenomena is a well-known method for inducing resonant behavior in mechanical or electrical systems. While temporal modulation has been used as an effective control mechanism for decades, there have been far fewer studies of external spatial modulation to enforce pattern uniformity and growth in the presence of noise. One such example involves a liquid film undergoing a spinodal instability subject to an externally imposed wavenumber close to the stability threshold of the unforced homogeneous system, which has been shown to induce resonance leading to a bifurcation in equilibrium film shapes. In this talk, we examine a linear instability in molten nanofilms undergoing thermocapillary growth leading to structure formation resembling 3D microlens arrays. Noisy initial conditions, however, are found to generate non-uniform peak heights which accelerate at different rates and significantly compromise pattern fidelity. Using a combination of weakly nonlinear analysis and numerical simulations, we demonstrate the existence of a resonant regime with high spatial coherence leading to microarrays with uniform pitch and height. This regime should provide optimal conditions for fabrication of micro-optical arrays. |
Monday, March 2, 2020 4:30PM - 4:42PM |
D24.00009: An elementary renormalization-group approach to the Generalized Central Limit Theorem and Extreme Value Distributions Ariel Amir The Generalized Central Limit Theorem is a remarkable generalization of the Central Limit Theorem, showing that the sum of a large number of independent, identically-distributed (i.i.d) random variables with infinite variance may converge under appropriate scaling to a distribution belonging to a special family known as Levy stable distributions. Similarly, the maximum of i.i.d. variables may converge to a distribution belonging to one of three universality classes (Gumbel, Weibull and Frechet). I rederive these known results following a mathematically non-rigorous yet highly transparent renormalization-group-like approach that captures both of these universal results following a nearly identical procedure. |
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