Bulletin of the American Physical Society
APS March Meeting 2017
Volume 62, Number 4
Monday–Friday, March 13–17, 2017; New Orleans, Louisiana
Session V15: General Statistical and Nonlinear Physics |
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Sponsoring Units: GSNP Chair: Jaron Kent-Dobias, Cornell University Room: 274 |
Thursday, March 16, 2017 2:30PM - 2:42PM |
V15.00001: Quantitative characterization of detailed balance breaking in linear noise-driven dynamical systems Akhil Ghanta, John Neu, Stephen Teitsworth In non-equilibrium dynamical systems, the breaking of detailed balance is often manifested by the appearance of \textit{fluctuation loops}, whereby the most probable fluctuation path to a particular state and the relaxation path from it form a loop-like structure in phase space. Such phenomena are present in a diverse array of systems, including noise-driven micromechanical oscillators, coupled electronic circuits, beating cellular flagella, and neuron models. The direct experimental observation of such loops is often challenging, requiring extensive ensemble-averaging of individual stochastic trajectories. Here, we utilize a time-dependent area tensor $A(t)$ - computed from any two independent dynamical variables - to quantitatively characterize the breaking of detailed balance and associated fluctuation loops in linear noise-driven dynamical systems. Analytically, we find that the ratio $A(t)/t$ approaches a constant at long times. This constant can be calculated exactly in terms of system parameters and vanishes precisely when the system satisfies detailed balance. Simulations of model systems are consistent with theoretical results and reveal robust convergence behavior which supports the utility of the area tensor in analyzing experimental data. [Preview Abstract] |
Thursday, March 16, 2017 2:42PM - 2:54PM |
V15.00002: Verification of Landauer's Principle using Optical Fields Saurav Talukdar, Shreyas Bhaban, Murti Salapaka The Landauer's Principle states that information erasure will be accompanied by heat dissipation of at least $k_{b} T\ln 2$per bit, where $k_{b}$ is the Boltzmann constant and $T$ is the temperature. The bound is significant, as it establishes a physical limitation on the improvement modern day electronic switches in terms of size and efficiency. Our analysis adds to the handful of existing studies that have demonstrated an experimental and computational validation of Landauer's Bound. Utilizing optical tweezers, we model a one-bit memory as a Brownian particle in a double well potential and propose a novel method to erase it, based on manipulation of the optical traps. We quantify the heat dissipation in erasing the memory by resorting to 'stochastic thermodynamics' framework for Langevin systems developed by Sekimoto. Using extensive Monte Carlo simulations and experiments we demonstrate that the lower bound for average heat dissipation, per erased bit, is achieved thereby validating Landauer's claim. Thus, we present an independent verification of Landauer's principle, further enforcing the fundamental link between Thermodynamics and Information Theory.~ [Preview Abstract] |
Thursday, March 16, 2017 2:54PM - 3:06PM |
V15.00003: Abstract Withdrawn
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Thursday, March 16, 2017 3:06PM - 3:18PM |
V15.00004: Evidence for a transcritical bifurcation in the 2D Ising model Colin B. Clement, Archishman Raju, Lorien X. Hayden, D. Zeb Rocklin, Cameron Duncan, James P. Sethna We find that the 2D Ising model is at a transcritical bifurcation involving the exchange of stability between two fixed points, similar to the Gaussian and Wilson-Fisher fixed points in 4D. Using perturbative normal-form theory--a method from dynamical systems for analyzing bifurcations--we find the simplest flow equations for the 2D Ising model. From this we predict that the flows of the inverse specific heat undergo a transcritical bifurcation near $D=2$. This is consistent with the conformal bootstrap method, which hints at the existence of two fixed points for $D<2$. We bring Onsager's exact solution to its normal form, which has a logarithmic singularity due to a `resonance' between the temperature and free energy eigenvalues. More broadly, our work seems to imply that such resonances can be understood as bifurcations in measurable quantities. [Preview Abstract] |
Thursday, March 16, 2017 3:18PM - 3:30PM |
V15.00005: Universal scaling and the essential singularity at the Ising first-order transition Jaron Kent-Dobias, James Sethna The Ising model is perhaps the most-studied problem in physics. Near
its continuous phase transition the model's thermodynamic quantities
diverge or vanish with power laws and logarithms. The renormalization
group connects the exponents in these functions to those of an {\sc rg}
fixed point because, as an analytic transformation, it preserves all
nonanalytic behavior. These power laws and logarithms are not the only
nonanalytic feature near the critical point, however---as one approaches
the line of first order transitions as $H\to0$ for $T |
Thursday, March 16, 2017 3:30PM - 3:42PM |
V15.00006: Abstract Withdrawn
|
Thursday, March 16, 2017 3:42PM - 3:54PM |
V15.00007: Generating Localized Nonlinear Excitations in the Fermi-Pasta-Ulam-Tsingou chains. Alexandra Westley, Surajit Sen Here, we will discuss properties of energy trapping in the decorated Fermi-Pasta-Ulam-Tsingou (FPUT) mass-spring chains with quadratic and quartic coupling terms. It is well-known that the FPUT system admits highly localized nonlinear excitations (LNE) which are stable for long periods of time. We seek to generate these LNEs at will by creating regions in the chain of stiffer or softer springs, or by placing mass impurities throughout. We will show that NLEs tend to coalesce in regions of stiff springs from random perturbations throughout the system. These locations may serve as extremely powerful energy traps or heat sinks in certain materials. Furthermore, we will demonstrate that this process occurs by means of trapping solitary (or anti-solitary) waves into tight spaces. [Preview Abstract] |
Thursday, March 16, 2017 3:54PM - 4:06PM |
V15.00008: Experimental Realization Of Periodically Driven PT-Symmetric Systems. Mahboobeh Chitsazi, Huanan Li, Fred Ellis, Tsampikos Kottos We provide the first experimental realization of a periodically driven PT-Symmetric system. Our set-up consists of two coupled 240 MHz LC resonators with balanced gain and loss controlled using a combination of photocells and a MOSFET transistors. The capacitance that couples the two resonators is parametrically driven at 4.6 MHz with a suitable network of varactor diodes. We find that driven PT-System supports a sequence of spontaneous PT-Symmetric phase transitions which lead to a cascade of PT-Symmetric broken domains bounded by exceptional point degeneracies. The latter are analyzed and are understood using an equivalent floquet frequency lattice with local PT-Symmetry. The position and size of these instability islands can be controlled through the gain/loss parameter as well as the amplitude and frequency of the coupling modulation. [Preview Abstract] |
Thursday, March 16, 2017 4:06PM - 4:18PM |
V15.00009: Wavepacket dynamics in a family of nonlinear Fibonacci lattices Mohit Pandey, David Campbell We examine the dynamics of a quantum particle in a variety of one-dimensional Fibonacci lattices (which are shifted from each other) in the presence of interaction. To describe the nonlinear interactions we employ the discrete nonlinear Schrödinger (DNLS) equation. Using a single-site localized state in the lattice as our initial condition, we evolve the wavepacket numerically using DNLS equation. We compute the root-mean-square width of the wavepacket as it evolves in time and show how the ``global location" of initial wavepacket affects the dynamics. We compare and contrast our results with earlier studies of related but distinct models. [Preview Abstract] |
Thursday, March 16, 2017 4:18PM - 4:30PM |
V15.00010: Avalanche processes in the star KIC 8462852 (Tabby's star) Mohammed Sheikh, Richard Weaver, Karin Dahmen Tabby's star (KIC 8462852) has shown unexpected drops in light flux of more than one fifth of its median value. From the light curve (flux vs. time), we relate the drops in light flux to avalanches studied in condensed matter systems such as ferromagnetism and plastic flow. Similar to other studies of avalanches, we define a threshold below which we consider an event to be an avalanche. These avalanches are characterized by a size, defined as the net radiant energy per unit area lost, and a duration, defined as the time the avalanche remains under the threshold. Near criticality, avalanche sizes and durations are expected to follow power law distributions with cutoffs. We identify the exponents of these power law distributions using the small avalanches in the light curve, and show that they roughly conform to a mean field theory. In addition, we also look at the the large events that have caused interest in Tabby's star. The large events are not within the scaling regime, and are possibly limited by system size. However, a model allowing for dynamic weakening as avalanches are nucleated can be used to explain these events in the context of mean field theory. [Preview Abstract] |
Thursday, March 16, 2017 4:30PM - 4:42PM |
V15.00011: Entropy Driven Solid—Solid Transitions in Colloids Chrisy Xiyu Du, Greg van Anders, Richmond Newman, Sharon Glotzer In classical, equilibrium statistical mechanics, entropy-driven order remains one of the most enigmatic phenomena. Although there is considerable work on entropy-driven fluid-solid transitions, the multiplicity of crystals that form in systems of hard, anisotropically shaped colloids suggests the possibility of studying entropy-driven solid-solid phase transitions. Here, we introduce a family of minimal model systems that exhibit solid—solid phase transitions that are driven by changes in the shape of colloidal particles. We carry out a detailed investigation of the thermodynamics of a series of isochoric, diffusionless solid—solid phase transitions within a single shape family, and find transitions that require thermal activation, or are “discontinuous”, and transitions that occur without thermal activation, or are “continuous”. Our results have direct implications for designing reconfiguration in soft materials, and our approach opens new avenues for the detailed study of the basic physics of solid-solid transitions, with potential applications in other areas of physics. [Preview Abstract] |
Thursday, March 16, 2017 4:42PM - 4:54PM |
V15.00012: Pattern formation in mass conserving reaction-diffusion systems Fridtjof Brauns, Jacob Halatek, Erwin Frey We present a rigorous theoretical framework able to generalize and unify pattern formation for quantitative mass conserving reaction-diffusion models. Mass redistribution controls chemical equilibria locally. Separation of diffusive mass redistribution on the level of conserved species provides a general mathematical procedure to decompose complex reaction-diffusion systems into effectively independent functional units, and to reveal the general underlying bifurcation scenarios. We apply this framework to Min protein pattern formation and identify the mechanistic roles of both involved protein species. MinD generates polarity through phase separation, whereas MinE takes the role of a control variable regulating the existence of MinD phases. Hence, polarization and not oscillations is the generic core dynamics of Min proteins in vivo. This establishes an intrinsic mechanistic link between the Min system and a broad class of intracellular pattern forming systems based on bistability and phase separation (wave-pinning). Oscillations are facilitated by MinE redistribution and can be understood mechanistically as relaxation oscillations of the polarization direction. [Preview Abstract] |
Thursday, March 16, 2017 4:54PM - 5:06PM |
V15.00013: Wave propagation in spatially modulated domains Steffen Martens, Alexander Ziepke, Harald Engel Propagation of traveling wave patterns, including traveling fronts and solitary excitation pulses, in a $3$D domain with spatially varying cross-section is reduced to an equivalent $1$D reaction-diffusion-advection equation [S. Martens et al., PRE \textbf{91}, 022902]. Treating the boundary-induced advection term as a weak perturbation, in a second step, an equation of motion for traveling waves within confined media can be derived. Both methods predict properly the nonlinear dependence of the propagation velocity on the ratio of the modulation period of the geometry to the intrinsic width of the front, or pulse. As a main feature, we observe finite intervals of propagation failure of waves induced by the domain's modulation and derive an analytically tractable condition for their occurrence [A. Ziepke, JCP \textbf{145}, 094108]. For the highly diffusive limit, using homogenization techniques, we show that wave velocities are governed by an effective diffusion coefficient [S. Martens, JCP \textbf{145}, 016101]. Furthermore, we discuss the effects of a single bottleneck on the period of pulse trains and observe period changes by integer fractions dependent on the bottleneck width and the period of the entering pulse train; being in accordance with experimental results. [Preview Abstract] |
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