Bulletin of the American Physical Society
APS March Meeting 2019
Volume 64, Number 2
Monday–Friday, March 4–8, 2019; Boston, Massachusetts
Session R57: Noise-driven Dynamics in Far-from-equilibrium Systems II |
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Sponsoring Units: GSNP DBIO Chair: Stephen Teitsworth, Duke University Room: BCEC 256 |
Thursday, March 7, 2019 8:00AM - 8:12AM |
R57.00001: Enhancing noise-induced escape in systems with distributed delays Ira Schwartz, Yuliya N. Kyrychko Many real world dynamical systems exhibit complex behavior often induced by intrinsic time delays, as well as influenced by random perturbations. An important problem, therefore, is to understand how random disturbances are organized such that the dynamics escape from a stable |
Thursday, March 7, 2019 8:12AM - 8:24AM |
R57.00002: A study of rare-event extinction phenomena in three species cyclic predation games. Shannon Serrao, Darka Labavic, Hildegard Meyer-Ortmanns In the modified May-Leonard model with cyclically competing three species, we compute the statistics of rare-event two species extinction process from a long lived metastable three-species coexistence state due to large fluctuations. We employ a master equation based eikonal quasi-stationary approximation of the metastable state effectively reducing the problem to the classical dynamics evolution of a Hamiltonian in six degrees of freedom. We then solve the evolution of this system by applying the Iterative Action Minimization Method(IAMM) and compute the action along the optimal path across the transcritical bifurcation. Our results are compared with action computed from the generating function based Hamiltonian of the said (3,1) game. The results obtained are validated for regions across the transcritical bifurcation in the system and investigated for different values of the system size parameter V. |
Thursday, March 7, 2019 8:24AM - 8:36AM |
R57.00003: Scaling laws governing stochastic death of individual cells and the extinction of populations. Srividya Iyer-Biswas, Kunaal Joshi In this talk I will disciss the scaling laws governing stochastic death of individual cells and the extinction of populations, bridge the timescales of single-cell and population dynamics under conditions when there is significant mortality, and make connections to ongoing experiments on C. Crescentus cells. |
Thursday, March 7, 2019 8:36AM - 8:48AM |
R57.00004: Intergenerational dynamics of individual cells reveal rules governing stochastic cell-size homeostasis Kunaal Joshi, Srividya Iyer-Biswas In this talk I will first establish that cell size homeostasis is maintained under appropriate growth conditions, using multigenerational data from our experiments on individual C. Crescentus cells. I will then discuss how our data on intergenerational dynamics of cell size, cell shape and cell division times, obtained under several growth conditions, reveal the rules governing stochastic cell-size homeostasis. |
Thursday, March 7, 2019 8:48AM - 9:00AM |
R57.00005: Kinetic inversion of repressors and activators in gene expression regulation. Zhiyue Lu, Chudong Wu, Aaron Dinner In gene expression regulation, repressors and activators compete to bind with the gene’s regulatory element, and the chance of activators binding with the regulatory element dictates the activation level of the gene. In a thermal equilibrium regime, this chance of binding is well determined by the concentrations of activators and repressors as well as their binding free energies to the regulatory element -- a high level of repressor will result in a low chance of activator binding. However, inspired by the experimental observations of cooperativity between activators and repressors, we propose a non-equilibrium dynamics model to describe the gene regulatory dynamics when the concentration of the repressor changes rapidly over time. We demonstrate a minimal Markov model where a rapidly changing level of repressor significantly increases the level of activation beyond predicted by equilibrium theory and effectively enhance the activator. Our model introduced an internal degree of freedom of the regulatory element, and its kinetic barrier allows the system to harnesses the chemical work done by the rapidly changing concentration of the repressor and use it to boost the level of gene activation beyond the equilibrium prediction. |
Thursday, March 7, 2019 9:00AM - 9:12AM |
R57.00006: A partial differential equation for the mean first-return-time phase of a stochastic oscillator Benjamin Lindner, Alexander Cao, Peter J. Thomas Phase reduction of limit cycle dynamics provides a low-dimensional representation of high-dimensional oscillator dynamics. For a deterministic dynamical system with a stable limit cycle, the change to a phase variable is well established. In contrast, for stochastic limit cycle systems, a phase reduction can be defined in several nonequivalent ways (e.g. Schwabedal and Pikovsky Phys. Rev. Lett. 110, 205102 (2013), Lindner and Thomas Phys. Rev. Lett. 113, 254101 (2014)]. Schwabedal and Pikovsky introduced a phase for stochastic oscillators based on a foliation of the basin of attraction, with the property that the mean transit time around the cycle from each leaf to itself is uniform and developed a numerical procedure to estimate the corresponding isochrons. For robustly oscillating planar systems driven by white Gaussian noise, we establish a partial differential equation with a mixture of reflecting and jump boundary conditions that governs this phase function. We solve this equation numerically for several examples of noisy oscillators. In addition, we obtain an explicit expression for the isochron function, for the rotationally symmetric case, and compare this analytical result with oscillators that have been studied numerically in the literature. |
Thursday, March 7, 2019 9:12AM - 9:24AM |
R57.00007: Fitness landscapes as predictor of noise-driven self-organized pattern formation on surfaces �zg�n Yavuz, Onur Tokel, Fatih Ilday, Serim Ilday Pattern formation far from equilibrium often exhibits a richness that is quite distinct from near-equilibrium dynamics. Perhaps the most visible consequence is the formation of different patterns in addition to the one favored at or near equilibrium. Can these, then, be controlled, and selected, externally? Here, we adopt the concept of "fitness landscapes" from evolutionary biology to show how nonlocal feedback gain of tailored defects controls and steers the evolution of nanopatterns using Nonlinear Laser Lithography (Ilday, Nat. Photon., 2013), an optical method that forms feedback-regulated patterns with nanometer uniformity. Through numerical simulations and experimental demonstration, we show that stimulated symmetry breaking can direct these nanopatterns to all possible 2D Bravais lattices. |
Thursday, March 7, 2019 9:24AM - 9:36AM |
R57.00008: Wavenumber Selection in Pattern Forming Systems Saloni Saxena, John Michael Kosterlitz Pattern forming systems are characterized by the emergence of a band of stable spatially periodic states as a control parameter is varied. Wavenumber selection refers to the evolution of such systems to one of these states at long times, irrespective of initial conditions. Numerical studies of pattern forming phenomena indicate that the presence of noise is a mechanism for wavenumber selection at long times. We investigate this for the noisy Stabilized Kuramoto Sivashinsky (SKS) equation. Computational difficulties restricted earlier numerical simulations of this equation to small system sizes and a narrow range of control parameters^{[1]}. Our aim now is two-fold: to determine whether wavenumber selection occurs for larger system sizes and to do so for a broader range of control parameter values. With the use of spectral methods of integration, we have been able to simulate larger system sizes and obtain a crude probability distribution of final states. We present our results for various system sizes and demonstrate a possible connection to large deviation theory^{[2]}. The drawbacks of our approach and possible improvements are also discussed. |
Thursday, March 7, 2019 9:36AM - 9:48AM |
R57.00009: Crossover between parabolic and hyperbolic scaling, oscillatory modes and resonances near flocking Carolina Trenado, Luis Bonilla A stability and bifurcation analysis of a kinetic equation indicates that the flocking bifurcation of the two-dimensional Vicsek model exhibits an interplay between parabolic and hyperbolic behavior. For box sizes under a certain large value, flocking appears continuously from a uniform disordered state at a critical value of the noise. Bifurcation equations contain two time scales and, due to mass conservation, comprise a scalar equation for the density disturbance from the homogeneous state and a vector equation for a current density. At the shorter scale, they are a hyperbolic system in which time and space scale in the same way. The equations are diffusive at the longer time scale. The bifurcating solution depends on the angle and is uniform in space as in the normal form of the usual pitchfork bifurcation. We show that linearization about the latter solution is described by a Klein-Gordon equation in the hyperbolic time scale. Then there are persistent oscillations with many incommensurate frequencies about the bifurcating solution that may resonate with a periodic forcing of the alignment rule. These predictions are confirmed by direct numerical simulations of the Vicsek model. |
Thursday, March 7, 2019 9:48AM - 10:00AM |
R57.00010: Spin lattices of walking droplets Pedro Saenz, Giuseppe Pucci, Sam E Turton, Alexis Goujon, Rodolfo R Rosales, Jorn Dunkel, John Bush In this talk, we will introduce a hydrodynamic analog system that allows us to investigate simultaneously the wave-mediated self-propulsion and interactions of effective spin degrees of freedom in inertial and rotating frames. Millimetric liquid droplets can walk across the surface of a vibrating fluid bath, self-propelled through a resonant interaction with their own guiding wave fields. A walking droplet, or `walker’, may be trapped by a submerged circular well at the bottom of the fluid bath, leading to a clockwise or counter-clockwise angular motion centered at the well. When a collection of such wells is arranged in a 1D or 2D lattice geometry, a thin fluid layer between wells enables wave-mediated interactions between neighboring walkers. Through experiments and mathematical modeling, we demonstrate the spontaneous emergence of coherent droplet rotation dynamics for different types of lattices. For sufficiently strong pair-coupling, wave interactions between neighboring droplets may induce local spin flips leading to ferromagnetic or antiferromagnetic order. Transitions between these two forms of order can be controlled by tuning the lattice parameters or by imposing a Coriolis force mimicking an external magnetic field. |
Thursday, March 7, 2019 10:00AM - 10:12AM |
R57.00011: Observation of Stochastic Resonance Induced by Dichotomous Noise in a Liquid Crystal Light Valve with Optical Feedback Yoshitomo Goto, Tomoyuki Nagaya, Hiroshi Orihara Noise-induced phenomena are widely observed in nature and are of great interest in the field of nonlinear dynamics. Stochastic resonance (SR), which is one of the most well-known noise-induced phenomena, has been discussed intensively [1], [2]. SR is a phenomenon in which the response of a nonlinear bistable system to a weak signal is enhanced by the addition of noise. In the present study, we focus on a liquid crystal light valve (LCLV) with optical feedback as one of the bistable systems. In the LCLV with optical feedback, the average orientation of the LC molecules, so-called director, shows bistability in some conditions [3], [4]. In this report, we discuss SR in LCLV with optical feedback system induced by the dichotomous noise (DN), characterized by an autocorrelation time. |
Thursday, March 7, 2019 10:12AM - 10:24AM |
R57.00012: Boundary Effects in Stochastic Cyclic Competition Models on a Two-Dimensional Lattice M. Lazarus Arnau, Shannon Serrao, Uwe Claus Tauber We study noise-induced and -stabilized spatial patterns in two distinct stochastic population model variants for cyclic competition of three species, namely the Rock-Paper-Scissors (RPS) and the May-Leonard (ML) models. In two dimensions, it is well established that the ML model can display (quasi-)stable spiral structures, in contrast to simple species clustering in the RPS system. Our ultimate goal is to develop local control schemes which allow us to affect the formation of these spatio-temporal patterns. To this end, we have employed MC simulations to investigate how changing the microscopic rules in a subsection of a two-dimensional lattice influences the macroscopic behavior in the rest of the lattice. Specifically, we implement the ML reaction scheme on a torus, except on a ring-shaped patch, which is set to follow the cyclic Lotka-Volterra predation rules of the RPS model. At the RPS-ML interface we observe a marked disruption of the usual spiral patterns in the form of plane waves emanating from the RPS region. Also, we report a distinct decrease in local population density near the interface in comparison to the bulk of the ML region. |
Thursday, March 7, 2019 10:24AM - 10:36AM |
R57.00013: Thermodynamics of Feedback with application to Landauer's Principle Harish Doddi, Saurav Talukdar, James Melbourne, Murti Salapaka Measurement and feedback are integral components for efficient functioning of physical systems in the microscopic as well as macroscopic world. We will analyze and quantify the thermodynamic costs of performing bit level measurements and energetics of feedback action. The thermodynamic system of interest studied is a Brownian particle in a bi-stable well, which is often used as a model for a single bit memory in the study of erasure of information. Landauer states that the minimum amount of heat dissipation for erasing a memory bit is k_{B}Tln2, which provides the Landauer limit. Recent experiments demonstrate that the erasure can be achieved with energetics close to the Landauer's bound. The protocols in prior art are open-loop, where the information on the state of the memory is not employed in the erasure protocol. Here, we quantify the energetics of erasure protocols with feedback; experimentally as well as via Monte Carlo simulations. Results indicate that the deficit between the heat dissipation in the feedback based erasure protocol and the k_{B}Tln 2 can be accounted for quantitatively by the measurement and feedback mechanisms. Non-conservative bounds are obtained on the deficit. |
Thursday, March 7, 2019 10:36AM - 10:48AM |
R57.00014: Brownian asymmetric simple exclusion process Dominik Lips, Artem Ryabov, Philipp Maass We present a model of a Brownian asymmetric simple exclusion process (BASEP) with overdamped Brownian dynamics that resembles properties of the asymmetric simple exclusion process (ASEP) on a lattice [1]. In this BASEP, particles of size σ with hardcore interaction are driven by a constant drag force through a one-dimensional cosine potential with period λ. The character of the non-equilibrium steady states in the BASEP is strikingly different from that in the ASEP. Compared to the particle current in a system of non-interacting particles, we observe an enhancement for small σ/λ ratios, caused by a barrier reduction effect arising from multi-occupation of potential wells. Larger σ/λ ratios lead to a suppression of the current because of blocking effects. Surprisingly, an exchange-symmetry effect causes the current-density relation to be identical to that of non-interacting particles for commensurable lengths σ=λ. A current-density relation similar to the ASEP is obtained only for a limited parameter regime. The rich behavior of the current-density relation leads to phase diagrams of NESS in open systems with up to five different phases. The topology of these phase diagrams changes with varying σ/λ ratio. |
Thursday, March 7, 2019 10:48AM - 11:00AM |
R57.00015: Entropy dissipation rates in thermodynamically realizable systems Samuel Bryant, Benjamin Machta In biological systems, a key concept of interest is the energy required to induce changes in the state of a system. The modern approach to this problem is to identify the energy cost of such control with entropy dissipation. For systems with deterministic control, the lower bounds on entropy dissipation are well known. However such analyses tend to ignore the cost associated with the method of control which becomes crucial at the biological scale. Here we extend such analyses to take into account the entropy cost of exerting control on a system when the control itself is stochastic in nature and subject to fluctuations. Using the formalism of stochastic thermodynamics, we find an intriguing non-trivial unification of previous results for a realizably controlled non-equilibrium steady state system driven at a finite rate around a loop in thermodynamic space. In particular we show that for a model system, the lower dissipation bound is almost the sum of two previously found bounds. Despite this, our result suggests that even for an infinitely long control protocol, it is still impossible to reach the adiabatic limit for stochastic systems. |
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