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At least 973 records · Page 54Linked to original sources

arXiv2013

Dissipation, Generalized Free Energy, and a Self-consistent Nonequilibrium Thermodynamics of Chemically Driven Open Subsystems

Nonequilibrium thermodynamics of a system situated in a sustained environment with influx and efflux is usually treated as a subsystem in a larger, closed "universe". It remains a question what the minimally required description for the surrounding of such an open driven system is, so that its nonequilibrium thermodynamics can be established solely based on the internal stochastic kinetics. We provide a solution to this problem using insights from studies of molecular motors in a chemical nonequilibrium steady state (NESS) with sustained external drive through a regenerating system, or in a quasi-steady state (QSS) with an excess amount of ATP, ADP, and Pi. We introduce the key notion of {\em minimal work} that is needed, $W_{min}$, for the external regenerating system to sustain a NESS ({\em e.g.}, maintaining constant concentrations of ATP, ADP and Pi for a molecular motor). Using a Markov (master-equation) description of a motor protein, we illustrate that the NESS and QSS have identical kinetics as well as the Second Law in terms of a same positive entropy production rate. The difference between the heat dissipation of a NESS and its corresponding QSS is exactly the $W_{min}$. This provides a justification for introducing an {\em ideal external regenerating system} and yields a {\em free energy balance equation} between the net free energy input $F_{in}$ and total dissipation $F_{dis}$ in an NESS: $F_{in}$ consists of chemical input minus mechanical output; $F_{dis}$ consists of dissipative heat; and the amount of useful energy becoming heat is the NESS entropy production. Furthermore, we show that for non-stationary systems, the $F_{dis}$ and $F_{in}$ correspond to the entropy production rate and housekeeping heat in stochastic thermodynamics, and identify a relative entropy $H$ as a generalized free energy.

cond-mat.stat-mech↗

arXiv2013

One-dimensional transport of interacting particles: Currents, density profiles, phase diagrams and symmetries

Driven lattice gases serve as canonical models for investigating collective transport phenomena and properties of non-equilibrium steady states (NESS). Here we study one-dimensional transport with nearest-neighbor interactions both in closed bulk systems and in open channels coupled to two particle reservoirs at the ends of the channel. For the widely employed Glauber rates we derive an exact current-density relation in the bulk for unidirectional hopping. An approach based on time-dependent density functional theory provides a good description of the kinetics. For open systems, the system-reservoir couplings are shown to have a striking influence on boundary-induced phase diagrams. The role of particle-hole symmetry is discussed and its consequence on the topology of the phase diagrams. It is furthermore demonstrated that systems with weak bias can be mapped onto systems with unidirectional hopping.

cond-mat.stat-mech↗

arXiv2013

Contextual analysis framework for bursty dynamics

To understand the origin of bursty dynamics in natural and social processes we provide a general analysis framework, in which the temporal process is decomposed into sub-processes and then the bursts in sub-processes, called contextual bursts, are combined to collective bursts in the original process. For the combination of sub-processes, it is required to consider the distribution of different contexts over the original process. Based on minimal assumptions for inter-event time statistics, we present a theoretical analysis for the relationship between contextual and collective inter-event time distributions. Our analysis framework helps to exploit contextual information available in decomposable bursty dynamics.

physics.soc-ph↗

arXiv2013

Distributional Ergodicity in Stored-Energy-Driven Lévy Flights

We study a class of random walk, the stored-energy-driven Lévy flight (SEDLF), whose jump length is determined by a stored energy during a trapped state. The SEDLF is a continuous-time random walk with jump lengths being coupled with the trapping times. It is analytically shown that the ensemble-averaged mean square displacements exhibit subdiffusion as well as superdiffusion, depending on the coupling parameter. We find that time-averaged mean square displacements increase linearly with time and the diffusion coefficients are intrinsically random, a manifestation of {\it distributional ergodicity}. The diffusion coefficient shows aging in subdiffusive regime, whereas it increases with the measurement time in superdiffusive regime.

cond-mat.stat-mech↗

arXiv2013

Frustrated colloidal ordering and fully packed loops in arrays of optical traps

We propose that a system of colloidal particles interacting with a honeycomb array of optical traps that each contain three wells can be used to realize a fully packed loop model. One of the phases in this system can be mapped to Baxter's three-coloring problem, offering an easily accessible physical realization of this problem. As a function of temperature and interaction strength, we find a series of phases, including long range ordered loop or stripe states, stripes with sliding symmetries, random packed loop states, and disordered states in which the loops break apart. Our geometry could be constructed using ion trap arrays, BEC vortices in optical traps, or magnetic vortices in nanostructured superconductors.

cond-mat.soft↗

arXiv2013

Entropic effects in the self-assembly of open lattices from patchy particles

Open lattices are characterized by low volume-fraction arrangements of building blocks, low coordination number, and open spaces between building blocks. The self-assembly of these lattices faces the challenge of mechanical instability due to their open structures. We theoretically investigate the stabilizing effects of entropy in the self-assembly of open lattices from patchy particles. A preliminary account of these findings and their comparison to experiment was presented recently [X. Mao, Q. Chen, S. Granick, \textit{Nat. Mater.}, \textbf{12}, 217 (2013)]. We found that rotational entropy of patchy particles can provide mechanical stability to open lattices, whereas vibrational entropy of patchy particles can lower the free energy of open lattices and thus enables the selection of open lattices verses close-packed lattices which have the same potential energy. These effects open the door to significant simplifications of possible future designs of patchy-particles for open-lattice self-assembly.

cond-mat.soft↗

arXiv2013

Cascades on clique-based graphs

We present an analytical approach to determining the expected cascade size in a broad range of dynamical models on the class of highly-clustered random graphs introduced by Gleeson [J. P. Gleeson, Phys. Rev. E 80, 036107 (2009)]. A condition for the existence of global cascades is also derived. Applications of this approach include analyses of percolation, and Watts's model. We show how our techniques can be used to study the effects of in-group bias in cascades on social networks.

physics.soc-ph↗

arXiv2013

Cross-talk and transitions between multiple spatial maps in an attractor neural network model of the hippocampus: phase diagram (I)

We study the stable phases of an attractor neural network model, with binary units, for hippocampal place cells encoding 1D or 2D spatial maps or environments. Using statistical mechanics tools we show that, below critical values for the noise in the neural response and for the number of environments, the network activity is spatially localized in one environment. We calculate the number of stored environments. For high noise and loads the network activity extends over space, either uniformly or with spatial heterogeneities due to the cross-talk between the maps, and memory of environments is lost. Analytical predictions are corroborated by numerical simulations.

cond-mat.stat-mech↗

arXiv2013

Phase Transitions in the Quadratic Contact Process on Complex Networks

The quadratic contact process (QCP) is a natural extension of the well studied linear contact process where infected (1) individuals infect susceptible (0) neighbors at rate $λ$ and infected individuals recover ($1 \longrightarrow 0$) at rate 1. In the QCP, a combination of two 1's is required to effect a $0 \longrightarrow 1$ change. We extend the study of the QCP, which so far has been limited to lattices, to complex networks. \comment{as a model for the change in a population through sexual reproduction and death.} We define two versions of the QCP -- vertex centered (VQCP) and edge centered (EQCP) with birth events $1-0-1 \longrightarrow 1-1-1$ and $1-1-0 \longrightarrow 1-1-1$ respectively, where `$-$' represents an edge. We investigate the effects of network topology by considering the QCP on random regular, Erdős-Rényi and power law random graphs. We perform mean field calculations as well as simulations to find the steady state fraction of occupied vertices as a function of the birth rate. We find that on the random regular and Erdős-Rényi graphs, there is a discontinuous phase transition with a region of bistability, whereas on the heavy tailed power law graph, the transition is continuous. The critical birth rate is found to be positive in the former but zero in the latter.

physics.soc-ph↗

arXiv2013

Coarsening dynamics in one dimension: The phase diffusion equation and its numerical implementation

Many nonlinear partial differential equations (PDEs) display a coarsening dynamics, i.e., an emerging pattern whose typical length scale $L$ increases with time. The so-called coarsening exponent $n$ characterizes the time dependence of the scale of the pattern, $L(t)\approx t^n$, and coarsening dynamics can be described by a diffusion equation for the phase of the pattern. By means of a multiscale analysis we are able to find the analytical expression of such diffusion equations. Here, we propose a recipe to implement numerically the determination of $D(λ)$, the phase diffusion coefficient, as a function of the wavelength $λ$ of the base steady state $u_0(x)$. $D$ carries all information about coarsening dynamics and, through the relation $|D(L)| \simeq L^2 /t$, it allows us to determine the coarsening exponent. The main conceptual message is that the coarsening exponent is determined without solving a time-dependent equation, but only by inspecting the periodic steady-state solutions. This provides a much faster strategy than a forward time-dependent calculation. We discuss our method for several different PDEs, both conserved and not conserved.

nlin.PS↗

arXiv2013

An Efficient Linear Programming Algorithm to Generate the Densest Lattice Sphere Packings

Finding the densest sphere packing in $d$-dimensional Euclidean space $\mathbb{R}^d$ is an outstanding fundamental problem with relevance in many fields, including the ground states of molecular systems, colloidal crystal structures, coding theory, discrete geometry, number theory, and biological systems. Numerically generating the densest sphere packings becomes very challenging in high dimensions due to an exponentially increasing number of possible sphere contacts and sphere configurations, even for the restricted problem of finding the densest lattice sphere packings. In this paper, we apply the Torquato-Jiao packing algorithm, which is a method based on solving a sequence of linear programs, to robustly reproduce the densest known lattice sphere packings for dimensions 2 through 19. We show that the TJ algorithm is appreciably more efficient at solving these problems than previously published methods. Indeed, in some dimensions, the former procedure can be as much as three orders of magnitude faster at finding the optimal solutions than earlier ones. We also study the suboptimal local density-maxima solutions (inherent structures or "extreme" lattices) to gain insight about the nature of the topography of the "density" landscape.

cond-mat.stat-mech↗

arXiv2013

Oscillations in turbulence-condensate system

We consider developed turbulence in the Gross-Pitaevsky model where condensate appears due to an inverse cascade. Despite being fully turbulent, the system demonstrates non-decaying periodic oscillations around a steady state, when turbulence and condensate periodically exchange a small fraction of waves. We show that these collective oscillations are not of a predator-prey type, as was suggested earlier; they are due to phase coherence and anomalous correlations imposed by the condensate.

nlin.CD↗

arXiv2013

Stiff directed lines in random media

We investigate the localization of stiff directed lines with bending energy by a short-range random potential. We apply perturbative arguments, Flory scaling arguments, a variational replica calculation, and functional renormalization to show that a stiff directed line in 1+d dimensions undergoes a localization transition with increasing disorder for d > 2=3. We demonstrate that this transition is accessible by numerical transfer matrix calculations in 1+1 dimensions and analyze the properties of the disorder dominated phase in detail. On the basis of the two-replica problem, we propose a relation between the localization of stiff directed lines in 1+d dimensions and of directed lines under tension in 1+3d dimensions, which is strongly supported by identical free energy distributions. This shows that pair interactions in the replicated Hamiltonian determine the nature of directed line localization transitions with consequences for the critical behavior of the Kardar-Parisi-Zhang (KPZ) equation. We support the proposed relation to directed lines via multifractal analysis revealing an analogous Anderson transition-like scenario and a matching correlation length exponent. Furthermore, we quantify how the persistence length of the stiff directed line is reduced by disorder.

cond-mat.stat-mech↗

arXiv2013

Synchronisation of stochastic oscillators in biochemical systems

A formalism is developed which describes the extent to which stochastic oscillations in biochemical models are synchronised. It is based on the calculation of the complex coherence function within the linear noise approximation. The method is illustrated on a simple example and then applied to study the synchronisation of chemical concentrations in social amoeba. The degree to which variation of rate constants in different cells and the volume of the cells affects synchronisation of the oscillations is explored, and the phase lag calculated. In all cases the analytical results are shown to be in good agreement with those obtained through numerical simulations.

cond-mat.stat-mech↗

arXiv2013

Fluctuation Effects in the Pair-Annihilation Process with Lévy Dynamics

We investigate the density decay in the pair-annihilation process A+A->0 in the case when the particles perform anomalous diffusion on a cubic lattice. The anomalous diffusion is realized via Lévy flights, which are characterized by long-range jumps and lead to superdiffusive behavior. As a consequence, the critical dimension depends continuously on the control parameter of the Lévy flight distribution. This instance is used to study the system close to the critical dimension by means of the nonperturbative renormalization group theory. Close to the critical dimension, the assumption of well-stirred reactants is violated by anticorrelations between the particles, and the law of mass action breaks down. The breakdown of the law of mass action is known to be caused by long-range fluctuations. We identify three interrelated consequences of these fluctuations. First, despite being a nonuniversal quantity and thus depending on the microscopic details, the renormalized reaction rate can be approximated by a universal law close to the critical dimension. The emergence of universality relies on the fact that long-range fluctuations suppress the influence of the underlying microscopic details. Second, as criticality is approached, the macroscopic reaction rate decreases such that the law of mass action loses its significance. And third, additional nonanalytic power law corrections complement the analytic law of mass action term. An increasing number of those corrections accumulate and give an essential contribution as the critical dimension is approached. We test our findings for two implementations of Lévy flights that differ in the way they cross over to the normal diffusion.

cond-mat.stat-mech↗

arXiv2013

Maximum power operation of interacting molecular motors

We study the mechanical and thermodynamic properties of different traffic models for kinesin which are relevant in biological and experimental contexts. We find that motor-motor interactions play a fundamental role by enhancing the thermodynamic efficiency at maximum power of the motors, as compared to the non-interacting system, in a wide range of biologically compatible scenarios. We furthermore consider the case where the motor-motor interaction directly affects the internal chemical cycle and investigate the effect on the system dynamics and thermodynamics.

cond-mat.stat-mech↗

arXiv2013

Trajectory phase transitions and dynamical Lee-Yang zeros of the Glauber-Ising chain

We examine the generating function of the time-integrated energy for the one-dimensional Glauber-Ising model. At long times, the generating function takes on a large-deviation form and the associated cumulant generating function has singularities corresponding to continuous trajec- tory (or "space-time") phase transitions between paramagnetic trajectories and ferromagnetically or anti-ferromagnetically ordered trajectories. In the thermodynamic limit, the singularities make up a whole curve of critical points in the complex plane of the counting field. We evaluate analyti- cally the generating function by mapping the generator of the biased dynamics to a non-Hermitian Hamiltonian of an associated quantum spin chain. We relate the trajectory phase transitions to the high-order cumulants of the time-integrated energy which we use to extract the dynamical Lee-Yang zeros of the generating function. This approach offers the possibility to detect continuous trajectory phase transitions from the finite-time behaviour of measurable quantities.

cond-mat.stat-mech↗

arXiv2013

Some properties of the one-dimensional Lévy crystal

We introduce and discuss the one-dimensional Lévy crystal as a probable candidate for an experimentally accessible realization of space fractional quantum mechanics (SFQM) in a condensed matter environment. The discretization of the space fractional Schrödinger equation with the help of shifted Grünwald-Letnikov derivatives delivers a straight-forward route to define the Lévy crystal of order $α\in (1,2]$. As key ingredients for its experimental identification we study the dispersion relation as well as the density of states for arbitrary $α\in (1,2]$. It is demonstrated that in the limit of small wavenumbers all interesting properties of continuous space SFQM are recovered, while for $α\to 2$ the well-established nearest neighbor one-dimensional tight binding chain arises.

cond-mat.stat-mech↗