Bulletin of the American Physical Society
APS March Meeting 2014
Volume 59, Number 1
Monday–Friday, March 3–7, 2014; Denver, Colorado
Session G17: Focus Session: Strong Correlations in Systems Far from Equilibrium II |
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Sponsoring Units: GSNP Chair: Uwe Tauber, Virginia Polytechnic Institute and State University Room: 402 |
Tuesday, March 4, 2014 11:15AM - 11:27AM |
G17.00001: Multistable phase patterns in finite oscillator networks Daniel Goldstein Recent experiments on spatially extend arrays of droplets containing Belousov-Zhabotinsky reactants have shown a rich variety of spatio-temporal patterns. Motivated by this experimental set up, we study a simple model of chemical oscillators in the highly nonlinear excitable regime in order to gain insight into the mechanism giving rise to the observed multistable attractors. By allowing intrinsic fluctuations to influence a simple activator inhibitor model, switching between stable attractors is observed. When coupled, these two attractors have different preferred phase synchronizations, leading to complex behavior. We study rings of coupled oscillators and observe a rich array of oscillating patterns. We characterize the different modes of oscillation in the mean-field model and compare those to the oscillations observed in stochastic simulations. [Preview Abstract] |
Tuesday, March 4, 2014 11:27AM - 11:39AM |
G17.00002: Synchronization for Systems with Spatially Correlated Coupling Huan-Yu Kuo, Kuo-An Wu Synchronization phenomenon in systems of large populations is of great interest in physical, biological, chemical, and social systems. The Kuramoto model describes elements as coupled oscillators whose natural frequencies are drawn from certain prescribed distribution. For globally coupled oscillators, as the coupling strength exceeds a certain threshold, part of the oscillators spontaneously synchronizes while others remain incoherent. However, the interaction between oscillators in many biological and physical systems depends on the distance between two oscillators. We analyze the Kuramoto model with spatial correlated coupling, and we find the existence of a universal critical coupling strength, beyond which a phase transition occurs for certain spatial correlated coupling. We will discuss the relation between the universality of critical coupling strength and the form of specific spatial couplings. [Preview Abstract] |
Tuesday, March 4, 2014 11:39AM - 11:51AM |
G17.00003: A Subpopulation Approach to the Finite Kuramoto Model David Mertens The Kuramoto model is the canonical model for studying spontaneous collective synchronization, notable because the functional form of the order parameter in its second order transition can be calculated analytically. Since its introduction nearly four decades ago, nearly all of the work on the underlying model has focused on the behavior of the order parameter for very large populations. Surprisingly little interest has been paid to small, discrete populations. In this talk I will introduce a new approach to analyzing the finite Kuramoto model based on a remarkably simple resumation of the interaction terms. This representation of the Kuramoto model is mathematically identical to the original Kuramoto model. However, rather than frame the model as an all-to-all interaction between oscillators or an interaction between oscillators and a mean field, this representation suggests a model of interacting subpopulations. This approach provides a much more intuitive starting point for making meaningful approximations and calculating important transitions for specific finite populations, as I will demonstrate. [Preview Abstract] |
Tuesday, March 4, 2014 11:51AM - 12:03PM |
G17.00004: Contact process on generalized Fibonacci chains: infinite-modulation criticality and double-log periodic oscillations Hatem Barghathi, David Nozadze, Thomas Vojta We study the nonequilibrium phase transition of the contact process with aperiodic transition rates using a real-space renormalization group as well as Monte-Carlo simulations. The transition rates are modulated according to the generalized Fibonacci sequences defined by the inflation rules A $\to$ AB$^k$ and B $\to$ A. For $k=1$ and 2, the aperiodic fluctuations are irrelevant, and the nonequilibrium transition is in the clean directed percolation universality class. For $k\ge 3$, the aperiodic fluctuations are relevant. We develop a complete theory of the resulting unconventional ``infinite-modulation'' critical point which is characterized by activated dynamical scaling. Moreover, observables such as the survival probability and the size of the active cloud display pronounced double-log periodic oscillations in time which reflect the discrete scale invariance of the aperiodic chains. We illustrate our theory by extensive numerical results, and we discuss relations to phase transitions in other quasiperiodic systems. [Preview Abstract] |
Tuesday, March 4, 2014 12:03PM - 12:15PM |
G17.00005: Dynamic Phase Transitions in Driven Cyclic Kinetic Networks Todd Gingrich, Suriyanarayanan Vaikuntanathan, Phillip Geissler Many physical processes can be modeled by Markovian rate processes. When detailed balance is broken, as is generically the case in biological processes, the dynamics exhibits nonvanishing fluxes around cycles and produces entropy. We demonstrate that a particular class of kinetic networks, those with a nearly periodic, pseudo-one-dimensional cyclical character, yield a nontrivial statistics of the large deviations in the observed fluxes. This behavior can be understood analytically in the limit of large networks, where we demonstrate the existence of a dynamic phase transition. The observation suggests that interesting, and potentially useful, large dynamical fluctuations are common even in rate processes with a single degree of freedom. As the analysis holds for networks driven out of equilibrium, potential application to biologically relevant networks is especially intriguing. [Preview Abstract] |
Tuesday, March 4, 2014 12:15PM - 12:27PM |
G17.00006: Non-equilibrium transitions and critical points in a two-temperature Ising model Nick Borchers, R.K.P. Zia, Michel Pleimling From complex biological systems to a simple simmering pot, thermodynamic systems held out of equilibrium are exceedingly common in nature. Despite this, a general theory to describe these types of phenomena remains elusive. In this talk, we further explore a simple two-temperature modification of the venerable Ising model in hopes of shedding some light on these issues. Of particular interest is the ``freezing by heating'' transition, and a range of larger system sizes are considered in the hopes of determining the transitions critical temperature and exponents. While this transition initially appeared as second-order, evidence suggesting a possible weak first-order nature obscured by finite size effects will also be explored. [Preview Abstract] |
Tuesday, March 4, 2014 12:27PM - 1:03PM |
G17.00007: Exploring universal scaling laws far from equilibrium with turbulent liquid crystal Invited Speaker: Kazumasa A. Takeuchi Recent theoretical progress has revealed a variety of universal scaling laws describing various scale-invariant phenomena out of equilibrium, but even the most basic and important of these developments had largely remained without complete experimental verification [1,2]. Here, I show that chaotic convection of electrically driven nematic liquid crystal is an ideal system to overcome past difficulties, which allows thorough experimental tests of theoretical predictions and beyond. First I present the route to turbulence in the electroconvection, focusing in particular on the transition between two regimes of spatiotemporal chaos, called the dynamic scattering modes (DSM) 1 and 2. This transition is characterized by spatiotemporal intermittency, where DSM2 patches randomly migrate, coalesce, and sometimes disappear. Measuring both static and dynamic critical behavior, we identified the directed percolation universality class [3], which is theoretically known as the most fundamental class for absorbing-state phase transitions [1]. We also studied the DSM2 regime under higher applied voltage, where DSM2 domains grow with fluctuating interfaces. Measuring how the interfaces roughen in the course of time, we found evidence for the scaling laws of the Kardar-Parisi-Zhang class [4], the prototypical class for stochastic growing interfaces [2]. Remarkably, fluctuations in the interface positions are found to exhibit the largest-eigenvalue distribution of Gaussian random matrices [4], indicating universality of recent rigorous results for solvable models [5]. The distribution is classified into a few universality subclasses according to the global shape of the interface, or to the initial condition. I also discuss some open problems raised by the experiment [4] on this universality beyond the scaling exponents.\\[4pt] [1] H. Hinrichsen, Adv. Phys. \textbf{49}, 815-958 (2000).\\[0pt] [2] A.-L. Barab\'asi and H. E. Stanley, \textit{Fractal Concepts in Surface Growth}, Cambridge Univ. Press (Cambridge, 1995).\\[0pt] [3] K. A. Takeuchi \textit{et al.}, Phys. Rev. Lett. \textbf{99}, 234503 (2007); Phys. Rev. E \textbf{80}, 051116 (2009).\\[0pt] [4] K. A. Takeuchi and M. Sano, Phys. Rev. Lett. \textbf{104}, 230601 (2010); K. A. Takeuchi \textit{et al.}, Sci. Rep. \textbf{1}, 34 (2011); K. A. Takeuchi and M. Sano, J. Stat. Phys. \textbf{147}, 853-890 (2012).\\[0pt] [5] For reviews, see, T. Kriecherbauer and J. Krug, J. Phys. A \textbf{43}, 403001 (2010); T. Sasamoto and H. Spohn, J. Stat. Mech. (\textbf{2010}), P11013; I. Corwin, Random Matrices: Theory and Applications \textbf{1}, 1130001 (2012). [Preview Abstract] |
Tuesday, March 4, 2014 1:03PM - 1:15PM |
G17.00008: A friction driven Brownian ratchet Alberto Petri, Andrea Gnoli, Fergal Dalton, Giacomo Gradenigo, Giorgio Pontuale, Alessandro Sarracino, Andrea Puglisi Exploiting thermal fluctuations to produce mechanical work requires statistical non-equilibrium conditions. We propose a new mechanism where an asymmetric wheel in a thermal bath exhibits a preferential direction of rotation because of the Coulomb friction at solid-on-solid contacts. The presence of a net drift induced by friction is demonstrated by numerical simulations and analytical calculations. If the thermal bath is replaced by a granular gas, the well-known granular ratchet effect also occurs, and becomes dominant at high collision rates. Depending on the wheel shape, the granular medium can act in opposite direction with respect to the friction-induced torque, resulting in the inversion of the ratchet motion as the collision rate increases. Both these ratchet effects and the predicted inversion are observed in the novel granular ratchet that we have realized experimentally (A.Gnoli et al., Phys.Rev. Lett. 110, 120601 (2013)). This also suggests the possibility of micro and sub-micrometer Brownian motors in equilibrium fluids, based purely upon nano-friction. [Preview Abstract] |
Tuesday, March 4, 2014 1:15PM - 1:27PM |
G17.00009: Magnetic friction between a Potts wedge and a Potts block in three dimensions Linjun Li, Michel Pleimling Magnetic systems, whose surfaces are coupled by boundary spins, experience magnetic friction if one system is moving with a relative velocity along the coupled surface. In our current research, we focus on systems consisting of one three-dimensional (3D) magnetic Potts wedge and one 3D magnetic Potts block. For cases where the total number of Potts states is equal to 2 or 9, we systematically study the effects of different interface coupling strengths, relative velocities, and wedge sizes, using numerical simulations. We find that the magnetic friction between the wedge tip and the block surface can change the local magnetic fluctuations on the surface of the block as well as at the tip of the wedge. [Preview Abstract] |
Tuesday, March 4, 2014 1:27PM - 1:39PM |
G17.00010: Equilibrium-like phase transition of a dynamic system Ming Han, Jing Yan, Steve Granick, Erik Luijten Dynamic systems are considered to be intrinsically different from systems in thermal equilibrium. Despite this fundamental dichotomy, here we demonstrate that a non-equilibrium, fully dynamical system can display behavior that constitutes a complete analogy to thermal equilibrium phase behavior. This dynamical system, consisting of Janus colloids strongly controlled by external fields and over-damped by a viscous solvent, phase separates like a binary fluid mixture, with a coexistence curve separating mixed and demixed regimes and a critical point that we demonstrate to belong to the 2D Ising universality class. Within the coexistence curve, we locate the spinodal curve that separates spinodal decomposition from nucleation and growth. [Preview Abstract] |
Tuesday, March 4, 2014 1:39PM - 1:51PM |
G17.00011: Functional Representation and Response Behavior of Aging Anomalous Diffusion Processes Stephan Eule The functional representation of stochastic processes provides a powerful method to calculate average values of path dependent observables. Here, the functional representation of Continuous Time Random Walks (CTRWs) and Fractional Fokker-Planck Equations is presented. This formulation, which is based on an alternative formulation of CTRWs, is then used to tackle the delicate and open problem of calculating the response of a CTRW to an external time-dependent perturbation. For the fractional Ornstein-Uhlenbeck process, the response function is calculated explicitly. It is proven that the fluctuation-dissipation theorem holds when the process is perturbed away from equilibrium. [Preview Abstract] |
Tuesday, March 4, 2014 1:51PM - 2:03PM |
G17.00012: Comparing Record Dynamics Predictions with Simulations and Experiments of Aging Colloids Stefan Boettcher, Nikolaj Becker, Paolo Sibani We describe the spontaneous off-equilibrium relaxation process known as aging in a simple, real-space model: Kinetic constraints bind on-lattice particles together in ``clusters,'' where a phenomenological function of size controls their lifetime. But once a cluster breaks down, its particles can move independently in space, a process akin to ``cage breaking,'' to join other clusters.\footnote{S. Boettcher and P. Sibani, JPCM, \textbf{23}, 065103 (2011);} Known properties of glassy systems \emph{emerge}, such as spatial heterogeneity and record dynamics. Here we compare our simple model with recent molecular dynamics studies of hard-sphere colloids.\footnote{D. El Masri, L. Berthier, and L. Cipelletti, PRE, \textbf{82}, 031503 (2010).} We find agreement with the scaling properties of the particles mean square displacement, and the aging properties of the interface energy, of the intermediate scattering function, and of the probability density function of the particle displacements occurring within different time windows. These properties are related to an underlying Poisson process which describes the salient events or quakes which correspond to the break up of clusters and give a coarse-grained description of the model dynamics, confirmed by re-analysis of experimental data. [Preview Abstract] |
Tuesday, March 4, 2014 2:03PM - 2:15PM |
G17.00013: Dynamics of 2D Ising Model in linearly varying magnetic field Na Xu, Cheng-Wei Liu, Anatoli Polkovnikov, Anders Sandvik We consider non-equilibrium dynamics of systems driven out of equilibrium at some finite rate near phase transitions. In previous work [1] on systems with varying temperature, scaling behaviors have been tested in great detail. Here with Monte Carlo simulations, we investigate the 2D Ising Model with linearly varying magnetic field and demonstrate the applicability of similar scaling functions when approaching the critical point. Moreover, we have found an interesting power-law scaling behavior in this system also below the critical temperature (even close to T$=$0). [1]Cheng-Wei Liu, Anatoli Polkovnikov, Anders W. Sandvik, arXiv:1310.6327 (2013) [Preview Abstract] |
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