Bulletin of the American Physical Society
APS March Meeting 2018
Volume 63, Number 1
Monday–Friday, March 5–9, 2018; Los Angeles, California
Session X47: Noise-Driven Dynamics in Far-From-Equilibrium SystemsFocus
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Sponsoring Units: GSNP Chair: Thomas Chou, Univ of California - Los Angeles Room: LACC 507 |
Friday, March 9, 2018 8:00AM - 8:36AM |
X47.00001: Stochastic modeling and analysis of tumor-induced blood vessel formation Invited Speaker: Luis Bonilla Imbalance of angiogenesis, the process of blood vessel formation and growth, is behind many diseases, including cancer. Stochastic models of tumor-induced angiogenesis have been proposed since 1990 but most work has been heavily computational. Recently, we have analyzed angiogenesis models that represent cells at the tips of new blood vessels as active particles whose trajectories are the blood vessels. Vessel tips are subject to chemotaxis and haptotaxis forces in Langevin equations and branch stochastically producing new tips. When one active tip meets a preexisting vessel (trajectory of another tip) joins it and ceases to be active, a process called anastomosis. The same occurs when it arrives at the tumor [1,2,3]. Thus anastomosis is a killing point process that depends on the past history of the given realization. For the ensemble averaged density of active tips, we have derived a Fokker-Planck equation that contains source terms with memory characterizing anastomosis [1,2]. For simple geometries, the density of active tips evolves to a soliton-like wave whose shape and velocity follow simple differential equations. Numerical simulations of the stochastic process confirm our findings, which are a step toward controlling angiogenesis [3,4,5]. |
Friday, March 9, 2018 8:36AM - 8:48AM |
X47.00002: Giant Acceleration of DNA Diffusion in an Array of Entropic Barriers Derek Stein, Daniel Kim, Clark Bowman, Jackson Del Bonis-O'Donnell, Anastasios Matzavinos We investigate with experiments and computer simulations the non-equilibrium dynamics of DNA polymers crossing arrays of entropic barriers in nanofluidic devices in a pressure-driven flow. With increasing driving pressure, the effective diffusivity of DNA rises and then peaks at a value that is many times higher than the equilibrium diffusivity. This is an entropic manifestation of "giant acceleration of diffusion", a non-equilibrium dynamical phenomenon for which an analytical solution is available. The phenomenon is sensitive to the effective energy landscape, thus it offers a unique probe of entropic barriers in a system driven away from equilibrium. |
Friday, March 9, 2018 8:48AM - 9:00AM |
X47.00003: Viscophoresis: Motion in a Viscosity Gradient Benjamin Wiener, Derek Stein We report the discovery of a new electrokinetic transport effect driven by viscosity gradients. We call this effect viscophoresis. |
Friday, March 9, 2018 9:00AM - 9:12AM |
X47.00004: Universality of biochemical feedback and its application to immune cells Tommy Byrd, Amir Erez, Robert Vogel, Curtis Peterson, Michael Vennettilli, Grégoire Altan-Bonnet, Andrew Mugler Biochemical feedback can lead to a bifurcation in cellular state space. For well-mixed systems, this transition should exhibit the critical scaling exponents of the Ising universality class in the mean-field limit. Here, we rigorously derive a mapping between a broad class of of biochemical feedback models and the mean-field Ising model, and show that the expected critical scaling exponents emerge. The generality of this mapping allows us to extract the order parameter, effective reduced temperature, magnetic field, and heat capacity from T cell flow cytometry data. We find that T cells obey critical scaling relations and exhibit critical slowing down. We also identify the dynamic critical exponents of the system, and show that our nonequilibrium feedback models exhibit the Kibble-Zurek collapse of critical physical systems. |
Friday, March 9, 2018 9:12AM - 9:24AM |
X47.00005: Emergent Bistable Switching in a Nonequilibrium Crystal Guram Gogia, Justin Burton Multistability is an unifying characteristic of a wide variety of physical, chemical and biological systems which are driven far from equilibrium. In nonequilibrium systems made of bistable elements, global bistability is a common feature, so that the entire system switches behavior. Nevertheless, here we experimentally demonstrate that bistable elements are not required for the global bistability of a collective system. We observe temporal switching between a crystalline, condensed state and a gas-like, excited state in a spatially-extended, quasi-two-dimensional layer of charged microparticles. The switching occurs over a broad range of time scales. Nevertheless, a dominant time scale is set by an external, periodic signal, such as a rotation of the crystal due to an external magnetic field. Increasing the number of particles in the system results into more complex, avalanche-like dynamics - only part of the system switches from crystalline to gaseous phase, and the size of the switching region varies with each avalanche event. We confirm our results using molecular dynamics simulations which show that conservative forces, damping, and stochastic noise are sufficient to induce switching. |
Friday, March 9, 2018 9:24AM - 9:36AM |
X47.00006: Effective Potential for Cellular Size Control Stanislav Burov, David Kessler For various species of biological cells, experimental observations indicate the existence of universal distributions of the cellular size, scaling relations between the cell-size moments and simple rules for the cell-size control. In this talk we address a class of models for the control of cell division, and present the steady state distributions. By introducing concepts such as effective force and potential, we are able to address the appearance of scaling collapse of different distributions and the connection between various moments of the cell-size. Our approach allows us to derive strict bounds which a potential cell-size control scenario must meet in order to yield a steady state distribution. Symmetric and a-symteric division are addressed. |
Friday, March 9, 2018 9:36AM - 9:48AM |
X47.00007: Extinction and Survival in Two-Species Annihilation Eli Ben-Naim, Jacques Amar, Sean Davis, Paul Krapivsky We study diffusion-controlled two-species annihilation with a finite number of particles. In this stochastic process, particles move diffusively, and when two particles of opposite type come into contact, the two annihilate. We focus on the behavior in three spatial dimensions and for initial conditions where particles are confined to a compact domain. Generally, one species is in the majority and one is in the minority, and we find that the difference between the number of majority and minority species, which is a conserved quantity, controls the behavior. When the number difference exceeds a critical value, the minority becomes extinct and a finite number of majority particles survive, but below this critical difference, a finite number of particles of both species survive. The critical difference Δc grows algebraically with system size N when the number of particles is very large, Δc ~ N1/3. Furthermore, when the initial concentrations of the two species are equal, the average number of lasting majority and minority particles, M+ and M-, exhibit two distinct scaling behaviors, M- ~ N1/2 and M- ~ N1/6. In contrast, when the initial populations are equal, these two quantities are comparable M+ ~ N1/3. |
Friday, March 9, 2018 9:48AM - 10:00AM |
X47.00008: Characterization of detailed balance violation in noise-driven nonlinear dynamical systems Stephen Teitsworth, Dripto Debroy, John Neu Understanding the spatio-temporal structure of most probable fluctuation pathways to rarely occurring states is a central problem in the study of noise-driven, far-from-equilibrium dynamical systems. When the underlying system does not possess detailed balance, the optimal fluctuation pathway to a particular state and relaxation pathway from that state may combine to form a loop-like structure in the system phase space called a fluctuation loop. Previous work on linear systems has demonstrated the utility of a time-dependent area tensor: at long times, the off-diagonal components grow linearly in time with a coefficient that relates to detailed balance violation [1]. Here, we show that a suitably averaged form of this result applies to general nonlinear systems. Furthermore, for systems with multiple stable fixed points and sufficiently weak noise amplitude, the area tensor exhibits a piecewise linear time dependence as the system rarely makes noise-induced hops from one basin of attraction to another, and is most often found in the neighborhoods of its fixed points. These results are demonstrated using both piecewise linear and continuous nonlinear model systems in two dimensions. |
Friday, March 9, 2018 10:00AM - 10:12AM |
X47.00009: Measurement of detailed balance violation in noise-driven linear circuits Juan Gonzalez, John Neu, Stephen Teitsworth In the context of noise-driven dynamical systems, detailed balance implies the equality of transition rates between pairs of system states, and also the vanishing of probability current everywhere in the system phase space under steady-state conditions. We report here on the measurement of the violation of detailed balance in coupled, noise-driven linear electronic circuits; in particular, we study two nominally identical RC circuits that are coupled either via variable capacitance or with more general linear coupling. The time-dependent voltages across each of the two primary capacitors serve as our dynamical variables, and the system is driven by two independent noise sources with independently variable amplitudes. Detailed balance violation is quantitatively detected by two methods: 1) explicit construction of the probability current density, and 2) by constructing the time-dependent area tensor as recently introduced in Ref. [1]. In comparing the two methods, we find that the area tensor is relatively simple to implement, computationally inexpensive, and provides a highly accurate means for detecting violations of detailed balance. |
Friday, March 9, 2018 10:12AM - 10:24AM |
X47.00010: Time periodic flocking phenomena Carolina Trenado, Luis Bonilla Animals having a trend to align their velocities to an average of their neighbors' may flock as illustrated by the Vicsek model and its variants. If, in addition, they feel a systematic trend, the result may be a periodic adjustment of the flock. This is demonstrated by analyzing a modified Vicsek model of self-propelled particles and its corresponding Ihle-Enskog kinetic equation valid in the limit of infinitely many particles. We have carried out a stability and bifurcation analysis of the order-disorder transition to a time periodic solution characterized by a new order parameter. Direct numerical simulations confirm the theoretical findings. |
Friday, March 9, 2018 10:24AM - 10:36AM |
X47.00011: Asymmetric Noise-induced Large Fluctuations in Mixed Reality Systems Ira Schwartz, Klimka Szwaykowska, Thomas Carr With the availability more cheap and powerful computing, interest in the use of mixed-reality experiments has grown in the engineering and physical sciences. These experiments consist of a simulated, or virtual model coupled directly to physical experiments. Within the physical experiment, there is a good deal of noise since it is connected to the real world. In contrast, the virtual part of the coupled system represents a somewhat idealized version of reality in which noise can be eliminated entirely, or at least well characterized. Thus, mixed-reality systems have very skewed sources of uncertainty spread through the entire system. |
Friday, March 9, 2018 10:36AM - 10:48AM |
X47.00012: Driving and dissipation stabilizing quantum metastable states Bernardo Spagnolo, Angelo Carollo, Davide Valenti Usually, quantum fluctuations enhance the escape from a quantum dissipative metastable state. A critical issue is whether the dissipation and/or an external driving force can enhance the stability of quantum metastable states. Here, we show that dissipation and driving can enhance the stability of a quantum metastable system strongly interacting with a thermal bath. We find that the escape time from the metastable region, with unstable initial condition, has a nonmonotonic behavior versus the system-bath coupling and the temperature, producing a stabilizing effect. Moreover, the combined effects of strong Ohmic dissipation and monochromatic driving give rise to an additional nonmonotonic behavior as a function of the driving frequency. The quantum noise enhanced stability phenomenon is observed in the system investigated. Moreover, by investigating the resonantly activated escape from a quantum metastable state with strong Ohmic dissipation in the presence of a fluctuating driving field, the quantum stochastic resonant activation phenomenon is observed. These results shed new light on the role of the environmental fluctuations in stabilizing quantum metastable systems, to control the escape dynamics, and exploit dissipation induced steady states for quantum computation. |
Friday, March 9, 2018 10:48AM - 11:00AM |
X47.00013: Seasonal Forcing in Stochastic Epidemic Models Eric Forgoston, Lora Billings We consider two types of stochastic epidemic models, where the internal noise is due to the random interactions of individuals in the population. We provide an overview of the general theoretic framework that allows one to understand noise-induced rare events, such as spontaneous disease extinction. Although there are many paths to extinction, there is one path termed the optimal path that is probabilistically most likely to occur. In this work, we demonstrate how to extend the theory to identify the optimal path to extinction when seasonality in the contact rate is included in the models. |
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