arXiv subjects

Dov Levine

Publications and source records attributed to Dov Levine.

At least 37 records · Page 2Linked to original sources

arXiv2014

Self Organization and Self Avoiding Limit Cycles

A simple periodically driven system displaying rich behavior is introduced and studied. The system self-organizes into a mosaic of static ordered regions with three possible patterns, which are threaded by one-dimensional paths on which a small number of mobile particles travel. These trajectories are self-avoiding and non-intersecting, and their relationship to self-avoiding random walks is explored. Near $ρ=0.5$ the distribution of path lengths becomes power-law like up to some cutoff length, suggesting a possible critical state.

cond-mat.stat-mech↗

arXiv2013

Entropic commensurate-incommensurate transition

The equilibrium properties of a minimal tiling model are investigated. The model has extensive ground state entropy, with each ground state having a quasiperiodic sequence of rows. It is found that the transition from the quasiperiodic ground state to the high temperature disordered phase proceeds through a sequence of periodic arrangements of rows, in analogy with the Frenkel-Kontorova model, but with temperature playing the role of the strength of the substrate potential.

cond-mat.stat-mech↗

arXiv2011

Characterizing order in amorphous systems

We measure and compare three correlation lengths proposed to describe the extent of structural order in amorphous systems. In particular, the recently proposed "patch correlation length" is measured as a function of temperature and fragility and shown to be comparable with other measures. In addition, we demonstrate that the patch method also allows us to characterize the symmetries of the local order without any a priori knowledge of it.

cond-mat.stat-mech↗

arXiv2010

Order in glassy systems

A directly measurable correlation length may be defined for systems having a two-step relaxation, based on the geometric properties of density profile that remains after averaging out the fast motion. We argue that the length diverges if and when the slow timescale diverges, whatever the microscopic mechanism at the origin of the slowing down. Measuring the length amounts to determining explicitly the complexity from the observed particle configurations. One may compute in the same way the Renyi complexities K_q, their relative behavior for different q characterizes the mechanism underlying the transition. In particular, the 'Random First Order' scenario predicts that in the glass phase K_q=0 for q>x, and K_q>0 for q<x, with x the Parisi parameter. The hypothesis of a nonequilibrium effective temperature may also be directly tested directly from configurations.

cond-mat.stat-mech↗

arXiv2009

Ion transport through confined ion channels in the presence of immobile charges

We study charge transport in an ionic solution in a confined nanoscale geometry in the presence of an externally applied electric field and immobile background charges. For a range of parameters, the ion current shows non-monotonic behavior as a function of the external ion concentration. For small applied electric field, the ion transport can be understood from simple analytic arguments, which are supported by Monte Carlo simulation. The results qualitatively explain measurements of ion current seen in a recent experiment on ion transport through a DNA-threaded nanopore (D. J. Bonthuis et. al., Phys. Rev. Lett, vol. 97, 128104 (2006)).

cond-mat.stat-mech↗

arXiv2009

Order in extremal trajectories

Given a chaotic dynamical system and a time interval in which some quantity takes an unusually large average value, what can we say of the trajectory that yields this deviation? As an example, we study the trajectories of the archetypical chaotic system, the baker's map. We show that, out of all irregular trajectories, a large-deviation requirement selects (isolated) orbits that are periodic or quasiperiodic. We discuss what the relevance of this calculation may be for dynamical systems and for glasses.

cond-mat.stat-mech↗

arXiv2009

Correlation length for amorphous systems

Crystals and quasicrystals can be characterized by an order that is a purely geometric property of an instantaneous configuration, independent of particle dynamics or interactions. Glasses, on the other hand, are ostensibly amorphous arrangements of particles. A natural and long-standing question has been whether they too have, albeit in a hidden way, some form of geometric order. Here we define a coherence length that applies to systems which are typically characterized as amorphous, as well as to those that are conventionally ordered. We argue that the divergence of such a length is consistent with current theories of the `ideal' glass transition.

cond-mat.dis-nn↗

arXiv2008

Frequency-dependent fluctuation-dissipation relations in granular gases

The Green-Kubo relation for two models of granular gases is discussed. In the Maxwell model in any dimension, the effective temperature obtained from the Green-Kubo relation is shown to be frequency independent, and equal to the average kinetic energy, known as the granular temperature. In the second model analyzed, a mean-field granular gas, the collision rate of a particle is taken to be proportional to its velocity. The Green-Kubo relation in the high frequency limit is calculated for this model, and the effective temperature in this limit is shown to be equal to the granular temperature. This result, taken together with previous results, showing a difference between the effective temperature at zero frequency (the Einstein relation) and the granular temperature, shows that the Green-Kubo relation for granular gases is violated.

cond-mat.soft↗

arXiv2008

Non-equilibrium fluctuation theorems in the presence of local heating

We study two non-equilibrium work fluctuation theorems, the Crooks' theorem and the Jarzynski equality, for a test system coupled to a spatially extended heat reservoir whose degrees of freedom are explicitly modeled. The sufficient conditions for the validity of the theorems are discussed in detail and compared to the case of classical Hamiltonian dynamics. When the conditions are met the fluctuation theorems are shown to hold despite the fact that the immediate vicinity of the test system goes out of equilibrium during an irreversible process. We also study the effect of the coupling to the heat reservoir on the convergence of $<\exp(-βW)>$ to its theoretical mean value, where $W$ is the work done on the test system and $β$ is the inverse temperature. It is shown that the larger the local heating, the slower the convergence.

cond-mat.stat-mech↗

arXiv2007

Isolated Non-Equilibrium Systems in Contact

We investigate a solvable model for energy conserving non-equilibrium steady states. The time-reversal asymmetry of the dynamics leads to the violation of detailed balance and to ergodicity breaking, as manifested by the presence of dynamically inaccessible states. Two such systems in contact do not reach the same effective temperature if standard definitions are used. However, we identify the effective temperature that controls energy flow. Although this operational temperature does reach a common value upon contact, the total entropy of the joint system can decrease.

cond-mat.stat-mech↗

arXiv2006

Energy distribution and effective temperatures in a driven dissipative model

We investigate non-equilibrium behavior of driven dissipative systems, using the model presented in [Phys. Rev. Lett. 93, 240601 (2004)]. We solve the non-Boltzmann steady state energy distribution and the temporal evolution to it, and find its high energy tail to behave exponentially. We demonstrate that various measures of effective temperatures generally differ. We discuss infinite hierarchies of effective temperatures defined from moments of the non-exponential energy distribution, and relate them to the "configurational temperature", measured directly from instantaneous particle locations without any kinetic information. We calculate the "granular temperature", characterizing the average energy in the system, two different "fluctuation temperatures", scaling fluctuation-dissipation relations, and the "entropic temperature", defined from differentiating the entropy with respect to energy.

cond-mat.stat-mech↗

arXiv2006

Fluctuation-dissipation relations in driven dissipative systems

Exact theoretical results for the violation of time dependent fluctuation-dissipation relations in driven dissipative systems are presented. The ratio of correlation to delayed response in the stochastic model introduced in [Phys. Rev. Lett. 93, 240601 (2004)] is shown to depend on measurement time. The fluctuation temperature defined by this ratio differs both from the temperature of the environment performing the driving, and from other effective temperatures of the system, such as the average energy (or "granular temperature"). General explanations are given for the time independence of fluctuation temperature for simple measurements or long measurement times.

cond-mat.stat-mech↗

arXiv2006

Correlation and response in a driven dissipative model

We consider a simple dissipative system with spatial structure in contact with a heat bath. The system always exhibits correlations except in the cases of zero and maximal dissipation. We explicitly calculate the correlation function and the nonlocal response function of the system and show that they have the same spatial dependence. Finally, we examine heat transfer in the model, which agrees qualitatively with simulations of vibrated granular gases.

cond-mat.stat-mech↗

arXiv2004

An exactly solvable model for driven dissipative systems

We introduce a solvable stochastic model inspired by granular gases for driven dissipative systems. We characterize far from equilibrium steady states of such systems through the non-Boltzmann energy distribution and compare different measures of effective temperatures. As an example we demonstrate that fluctuation-dissipation relations hold, however with an effective temperature differing from the effective temperature defined from the average energy.

cond-mat.stat-mech↗

arXiv2004

Propagation of interacting force chains in the continuum limit

We study the effect of mergers in the force chain model describing the stress profile in static granular materials. Combining numerical and analytical calculations we show that granular materials do not generally behave in an elastic-like manner, however they may under specific conditions, which are elaborated. Non-elastic behavior resulting from the non-linearity of the full force chain model is discussed.

cond-mat.soft↗

arXiv2003

The Role of Friction in Compaction and Segregation of Granular Materials

We investigate the role of friction in compaction and segregation of granular materials by combining Edwards' thermodynamic hypothesis with a simple mechanical model and mean-field based geometrical calculations. Systems of single species with large friction coefficients are found to compact less. Binary mixtures of grains differing in frictional properties are found to segregate at high compactivities, in contrary to granular mixtures differing in size, which segregate at low compactivities. A phase diagram for segregation vs. friction coefficients of the two species is generated. Finally, the characteristics of segregation are related directly to the volume fraction without the explicit use of the yet unclear notion of compactivity.

cond-mat.stat-mech↗

arXiv2001

Geometry of Frictionless and Frictional Sphere Packings

We study static packings of frictionless and frictional spheres in three dimensions, obtained via molecular dynamics simulations, in which we vary particle hardness, friction coefficient, and coefficient of restitution. Although frictionless packings of hard-spheres are always isostatic (with six contacts) regardless of construction history and restitution coefficient, frictional packings achieve a multitude of hyperstatic packings that depend on system parameters and construction history. Instead of immediately dropping to four, the coordination number reduces smoothly from $z=6$ as the friction coefficient $μ$ between two particles is increased.

cond-mat.soft↗

arXiv2000

Electrostatic Attraction of Coupled Wigner Crystals: Finite Temperature Effects

In this paper, we present a unified physical picture for the electrostatic attraction between two coupled planar Wigner crystals at finite (but below their melting) temperature. At very low temperatures, we find a new regime where the attraction, arising from the long-wavelength excitation of the plasmon mode, scales with the interplanar distance $d$ as $d^{-2}$. At higher temperatures, our calculation agrees with known results. Furthermore, we analyze the temperature dependence of the short-ranged attraction arising from ``structural'' correlations and argue that thermal fluctuations drastically reduce the strength of this attraction.

cond-mat.soft↗