Bulletin of the American Physical Society
APS March Meeting 2022
Volume 67, Number 3
Monday–Friday, March 14–18, 2022; Chicago
Session T09: Noise-Driven Dynamics in Far-From-Equilibrium Systems IIRecordings Available
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Sponsoring Units: GSNP DBIO Chair: Katherine Newhall, University of North Carolina Chapel Hill Room: McCormick Place W-180 |
Thursday, March 17, 2022 11:30AM - 11:42AM |
T09.00001: Non-equilibrium hydrodynamic fluctuations in binary fluids during effusion Ishan Srivastava, Daniel R Ladiges, Andrew J Nonaka, John B Bell, Alejandro L Garcia Microscopic thermal fluctuations introduce noise in mesoscale fluid hydrodynamics at equilibrium, which gets enhanced and correlated over a long range when the fluid is driven out of equilibrium. In the presence of an effusive porous membrane where the mean free path of the molecules is larger than the characteristic pore size, these long-ranged hydrodynamic fluctuations can get significantly modified. We incorporate a Langevin model that satisfies the fluctuation theorem for gas effusion into a fluctuating hydrodynamics framework to simulate the non-equilibrium behavior of binary fluids across an effusive membrane. This talk will describe the structure of hydrodynamic fluctuations that emerges when the fluid is driven out of equilibrium by confinement between reservoirs of varying concentrations in the presence of an effusive membrane. The role of cross-diffusion between species and thermal diffusion on hydrodynamic fluctuations will be discussed. |
Thursday, March 17, 2022 11:42AM - 11:54AM |
T09.00002: Characterizing irreversibility in noise-driven dynamical systems with stream functions Stephen W Teitsworth, John Neu Stochastic line integrals provide a useful means for quantitatively characterizing irreversibility and heat transfer in noise-driven dynamical systems. One realization is the stochastic area, recently studied theoretically and experimentally in coupled noise-driven linear electrical circuits [1,2]. For the case of stationary statistics in two-dimensional systems, we show that the stochastic area can be concisely expressed in terms of a stream function, the sign of which determines the orientation of probability current. We formulate an inhomogeneous boundary value problem for the stream function in which the source term depends on non-equilibrium driving terms (e.g., temperature difference for a system driven by multiple thermal noises.) The stream function allows determination of analytical expressions for the dependence of stochastic area growth rate on parameters of interest such as the system noise strengths and the character of system nonlinearity when present. In this talk we apply the stream function technique to the following systems: two masses moving in one spatial dimension and coupled by a linear or nonlinear spring with each mass driven by a distinct thermal noise source; and a nonlinear tunnel diode circuit model driven by multiple noise sources. |
Thursday, March 17, 2022 11:54AM - 12:06PM |
T09.00003: Dynein-Inspired Multilane Exclusion Process with Open Boundary Conditions Priyanka Priyanka, Uwe C Tauber, Riya Nandi Motivated by the sidewise motions of dynein motors shown in experiments, we use a variant of the exclusion process to model the multistep dynamics of dyneins on a cylinder with open ends. Due to the varied step sizes of the particles in a quasi-two-dimensional topology, we observe the emergence of a novel phase diagram depending on the various load conditions. Under high-load conditions, our numerical findings yield results similar to the TASEP model with the presence of all three standard TASEP phases, namely the low-density (LD), high-density (HD), and maximal-current (MC) phases. However, for medium- to low-load conditions, for all chosen influx and outflux rates, we only observe the LD and HD phases, and the maximal-current phase disappears. Further, we also measure the dynamics for a single dynein particle which is logarithmically slower than a TASEP particle with a shorter waiting time. Our results also confirm experimental observations of the dwell time distribution: The dwell time distribution for dyneins is exponential in less crowded conditions, whereas a double exponential emerges under overcrowded conditions. |
Thursday, March 17, 2022 12:06PM - 12:18PM |
T09.00004: Enhancing associative memory recall in non-equilibrium materials through activity. Agnish K Behera, Madan Rao, Srikanth Sastry, Suriyanarayanan Vaikuntanathan Memory is a key feature in many biological and physical systems. The Hopfield model is a paradigm for explaining associative memory. Under equilibrium conditions, the Hopfield network can store and retrieve upto 0.14N patterns, where N is the number of spins in the system. Recent works have explored how the capacity of the Hopfield model can be increased through various schemes which include changing the form of learning and changing the form of interactions between the different degrees of freedom. Since biological systems work far from equilibrium, we want to address this through the effect of nonequilibrium activity in the system. We introduce activity into the system as AOUP noise which breaks detailed balance and takes the system out of equilibrium. Under such conditions the system can store and retrieve more patterns than the equilibrium case at the same "Effective" temperature. Using a perturbative scheme we probe the change in the free energy landscape of this active system and show the rate of entropy production helps the system to access memory regions which were previously inaccessible. Using the Martin-Siggia-Rose Lagrangian formalism we also derive a set of exact equations which predict conditions of improved memory. |
Thursday, March 17, 2022 12:18PM - 12:30PM |
T09.00005: Simulation Studies of a Particle-Based Molecular Motor Toy Model Alex Albaugh, Geyao Gu, Ray Fu, Todd Gingrich Molecular motors are at the heart of life. These diminutive engines drive muscle contraction, molecular transport, cellular motion, and other important life processes by transducing energy stored in chemical fuel into mechanical work. I will introduce a particle-based toy model for an "information ratchet", a motor that rectifies thermal noise into directed motion. I will discuss simulation methodology to sample that model's steady-state behavior and show how those simulations reveal the tradeoffs between motor accuracy, velocity, and efficiency and demonstrate the motor's response to a range of operating conditions. I will further show how modest design changes can reverse the motor's direction. Finally, I will present how this approach creates a bridge between experimental studies and theoretical frameworks like stochastic thermodynamics and thermodynamic uncertainty relationships. Going forward, these computational methods should prove to be valuable tools for creating better artificial molecular motors. |
Thursday, March 17, 2022 12:30PM - 12:42PM |
T09.00006: Optimizing a Chemically-Fueled Molecular Motor Geyao Gu, Alex Albaugh, Ray Fu, Todd Gingrich Synthetic chemists routinely design molecular structures based on simple heuristics. They tune steric repulsion or intermolecular attractions in order to coax molecules to prefer favored equilibrium structures. More formally, these designs can be viewed as the optimization of equilibrium free energies. The situation is far more complicated when the molecules are designed to achieve a dynamic rather than structural goal. By working with a recently introduced particle-based toy model for a molecular motor [arXiv:2102.06298], we have sought to engineer attractions and repulsions between particles so as to induce a chemically-driven current. We will discuss strategies for that dynamical optimization. |
Thursday, March 17, 2022 12:42PM - 12:54PM |
T09.00007: Anomalous Fluctuations of Extremes in Many-Particle Diffusion Jacob Hass, Eric I Corwin, Ivan Corwin, Aileen Carroll-Godfrey Over one hundred years ago Einstein created a remarkably simple and powerful theory describing the behavior of a single diffusing particle. That theory has since been applied countless times to successfully model widely disparate systems. However, this theory neglects the effects a shared environment has on the particles. As a consequence, the Einstein theory dramatically fails to predict the behavior of extreme diffusion, i.e. outlier particles which have moved the farthest from their starting points. We study particles undergoing a random walk in a beta distributed environment and provide theoretical predictions, which we confirm numerically, of the behavior of the maximally displaced particle. By introducing a shared environment, we find three scaling regimes relating to the KPZ equation for the variance of the maximally displaced particle, contrary to the Einstein diffusion model which predicts a single scaling regime. Understanding the behavior of outliers will have wide ranging applicability to physical, biological, epidemiological, economic, and social systems where outliers often determine behavior. |
Thursday, March 17, 2022 12:54PM - 1:06PM |
T09.00008: Transport Regimes of Underdamped Brownian Particles in aTilted Washboard Potential Jarrod E Schiffbauer, Marygrace M Prinster, Trey Jiron In this work, a Runge-Kutta numerical solution to the Langevin equation is computed for a tilted washboard potential. The parameter-space of temperature, tilt, and well-depth is analyzed for underdamped Brownian diffusion through the potential. In addition to the known non-monotonic temperature response of the diffusivity, we observe a negative differential mobility due to an overall decrease in jump rate and corresponding to a regime of anomalous diffusion. A new phase diagram is obtained, corresponding to a transition between sub-diffusion and normal diffusion as temperature approaches the intermediate barrier height, . Lifson-Jackson calculations of diffusivity’s monotonic temperature response for overdamped particles are contrasted with the nonmonotonic response of the underdamped system, highlighting the importance of inertia in the system dynamics. The zero-temperature dynamics are then analyzed through a bifurcation diagram, mimicking the dynamics of a damped, driven pendulum. Velocity power spectra reveal second harmonic generation corresponding to multistable particle dynamics and the dynamics converges to the zero-temperature limit for the instantaneous velocity, complementing the results for average velocity as shown by Cheng and Yip. |
Thursday, March 17, 2022 1:06PM - 1:18PM |
T09.00009: Modeling and analysis of systems with nonlinear functional dependence on random quantities David Sabin-Miller, Daniel M Abrams Many real-world physical systems exhibit noisy evolution; interpreting their finite-time behavior as arising from continuous-time processes (in the Ito or Stratonovich sense) has led to significant success in modeling and analyzing them. In this talk we explore a class of differential equations where evolution depends nonlinearly on a random or effectively-random quantity, and we argue that these equations may exhibit finite-time stochastic behavior in line with an equivalent Ito process, which is of great utility for their numerical simulation and theoretical analysis. We put forward a method for this conversion, develop an equilibrium-moment relation for Ito attractors, and show that this relation holds for our example nonlinear-converted Ito system. This work enables the theoretical and numerical examination of a wider class of mathematical models which might otherwise be oversimplified due to lack of appropriate tools. |
Thursday, March 17, 2022 1:18PM - 1:30PM |
T09.00010: Scaling study of diffusion in dynamic crowded spaces David Yllanes, Harry Bendekgey, Greg Huber Brownian motion in disordered media is now well understood in the case of immobile hard obstacles. In many practical applications, however, the space itself can be dynamic. An important example is transport inside the cell, a very crowded environment with obstacles of varying sizes and complicated shapes that are constantly being rearranged. This situation has received comparatively little attention. With the ever-increasing quality of microscopy techniques, allowing for the tracking of particles inside living cells, the need for a quantitative model is clear. |
Thursday, March 17, 2022 1:30PM - 1:42PM |
T09.00011: Using tensor network states to describe periodically driven multiparticle Brownian ratchets Nils Strand Single-particle Brownian ratchets have been thoroughly studied, but ratcheting phenomena in interacting many-body systems offer new challenges. Even with interactions as simple as volume exclusion, the mean steady-state current tends to respond dramatically to changes in carrier density. We present a novel approach for computing these currents for a time-periodic 1D ratchet discretized on a periodic-boundary-condition lattice. The approach leverages the time-dependent variational principle (TDVP) method of evolving binary tree tensor network states to compute the response of steady-state currents to particle density, the frequency of the ratchet drive, and the diffusion constant governing thermal motion. The TDVP approximation is controllable, and provided the tensor network's maximal bond dimension is sufficiently large, we demonstrate agreement with brute force Gillespie sampling. The method shows promise for studying classical many-body stochastic systems subject to time-dependent external forces, particularly when rare fluctuations play a crucial role. |
Thursday, March 17, 2022 1:42PM - 1:54PM |
T09.00012: Characterizing noise-induced lifetime of a phase state in a Kerr nonlinear resonator Deividas Sabonis, Alexander Eichler, Gabriel Margiani, Sebastián Guerrero, Toni L Heugel, Christian Marty, Thomas Gisler, Raphael Pachlatko, Nicholas E Bousse, Thomas W Kenny, Oded Zilberberg, Gabrielle D Vukasin, Hyun-Keun Kwon, James Miller, Suchita Agrawal, Christian L Degen, Ramasubramanian Chitra We compare the suitability of several mathematical methods to characterize the lifetime of two-level systems. The methods deal in different ways with random-walk fluctuations during a switch. Such fluctuations are not captured by a simple telegraph-noise picture and can lead to a significant overestimation of the switching rate. We show that this problem can be avoided by choosing the correct counting method. In addition to known methods relying on thresholds and the power spectral density of fluctuations, we establish that a peak in the Allan variance of fluctuations can be used to determine the lifetime. As a simple, classical test system, we utilize a nonlinear Kerr resonator driven into parametric oscillations regime, whose stable solutions mimic the physics of a single spin. We also provide an outlook of how our methods can be used to study Kramer's turnover in the synthetic quasi-potential of a parametric oscillator. |
Thursday, March 17, 2022 1:54PM - 2:06PM |
T09.00013: Universal corrections to reaction-diffusion dynamics above the upper critical dimension Johannes Hofmann Reaction-diffusion models are common in many areas of statistical physics, where they describe the universal late-time dynamics of chemical reactions. In this talk, I will discuss how a Bose gas representation, which maps the real-time dynamics of the reactants to the imaginary-time evolution of an interacting Bose gas, can be used to determine corrections to the late-time scaling above the upper critical dimension, where mean-field theory sets the leading order. I will show that the leading corrections are not given by a small renormalization of the reaction rate due to memory effects, but instead set by higher-order correlation functions that capture memory effects of sub-clusters of reactants. Drawing on methods developed for ultracold quantum gases and nuclear physics, these corrections can be computed exactly for various $k$-particle annihilation processes $k A \to \emptyset$ with $k>2$. |
Thursday, March 17, 2022 2:06PM - 2:18PM |
T09.00014: Synchronization and enhanced catalysis of mechanically coupled enzymes Jaime Agudo-Canalejo, Tunrayo Adeleke-Larodo, Pierre Illien, Ramin Golestanian We examine the stochastic dynamics of two enzymes that are mechanically coupled to each other, e.g. through an elastic substrate or a fluid medium. The enzymes undergo conformational changes during their catalytic cycle, which itself is driven by stochastic steps along a biased chemical free energy landscape. We find conditions under which the enzymes can synchronize their catalytic steps, and discover that the coupling can lead to a significant enhancement in their overall catalytic rate. Both effects can be understood as arising from a global bifurcation in the underlying dynamical system at sufficiently strong coupling. Our findings suggest that, despite their molecular scale, enzymes can be cooperative and improve their performance in metabolic clusters. Moreover, the effective enzyme-enzyme phase coupling we obtain is interesting from a theoretical perspective, as it arises from off-diagonal terms in the mobility matrix that connects forces to velocities, and thus leaves the equilibrium probability distribution of the system intact while introducing non-trivial effects in an out-of-equilibrium setting (in contrast to ad-hoc couplings, e.g. Kuramoto-like). |
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