arXiv subjects

Yair Shokef

Publications and source records attributed to Yair Shokef.

52 records · Page 3Linked to original sources

arXiv2015

The relation between the structure of blocked clusters and the relaxation dynamics in kinetically-constrained models

We investigate the relation between the cooperative length and the relaxation time, represented respectively by the culling time and the persistence time, in the Fredrickson-Andersen, Kob-Andersen and spiral kinetically-constrained models. By mapping the dynamics to diffusion of defects, we find a relation between the persistence time, $τ_{p}$, which is the time until a particle moves for the first time, and the culling time, $τ_{c}$, which is the minimal number of particles that need to move before a specific particle can move, $τ_{p}=τ^γ_{c}$, where $γ$ is model- and dimension dependent. We also show that the persistence function in the Kob-Andersen and Fredrickson-Andersen models decays subexponentially in time, $P(t)=exp[-(t/τ)^β]$, but unlike previous works we find that the exponent $β$ appears to decay to 0 as the particle density approaches 1.

cond-mat.stat-mech↗

arXiv2014

Finite-density effects in the Fredrickson-Andersen and Kob-Andersen kinetically-constrained models

We calculate the corrections to the thermodynamic limit of the critical density for jamming in the Kob-Andersen and Fredrickson-Andersen kinetically-constrained models, and find them to be finite-density corrections, and not finite-size corrections. We do this by introducing a new numerical algorithm, which requires negligible computer memory since contrary to alternative approaches, it generates at each point only the necessary data. The algorithm starts from a single unfrozen site and at each step randomly generates the neighbors of the unfrozen region and checks whether they are frozen or not. Our results correspond to systems of size greater than 10^7x10^7, much larger than any simulated before, and are consistent with the rigorous bounds on the asymptotic corrections. We also find that the average number of sites that seed a critical droplet is greater than 1.

cond-mat.stat-mech↗

arXiv2014

Jamming Percolation in Three Dimensions

We introduce a three-dimensional model for jamming and glasses, and prove that the fraction of frozen particles is discontinuous at the directed-percolation critical density. In agreement with the accepted scenario for jamming- and glass-transitions, this is a mixed-order transition; the discontinuity is accompanied by diverging length- and time-scales. Because one-dimensional directed-percolation paths comprise the backbone of frozen particles, the unfrozen rattlers may use the third dimension to travel between their cages. Thus the dynamics are diffusive on long-times even above the critical density for jamming.

cond-mat.stat-mech↗

arXiv2014

Jamming by Shape in Kinetically-Constrained Models

We derive expressions for the critical density for jamming in a hyper-rhomboid system of arbitrary shape in any dimension for the Kob-Andersen and Fredrickson-Andersen kinetically-constrained models. We find that changing the system's shape without altering its total volume or particle density may induce jamming. We also find a transition between shapes in which the correlation length between jammed particles is infinite, and shapes that have a finite correlation length.

cond-mat.stat-mech↗

arXiv2012

Jamming transition of kinetically-constrained models in rectangular systems

We theoretically calculate the average fraction of frozen particles in rectangular systems of arbitrary dimensions for the Kob-Andersen and Fredrickson-Andersen kinetically-constrained models. We find the aspect ratio of the rectangle's length to width, which distinguishes short, square-like rectangles from long, tunnel-like rectangles, and show how changing it can effect the jamming transition. We find how the critical vacancy density converges to zero in infinite systems for different aspect ratios: for long and wide channels it decreases algebraically $v_{c}\sim W^{-1/2}$ with the system's width W, while in square systems it decreases logarithmically $v_{c}\sim1/\ln L$ with length L. Although derived for asymptotically wide rectangles, our analytical results agree with numerical data for systems as small as $W\approx10$.

cond-mat.stat-mech↗

arXiv2012

Scaling laws for the response of nonlinear elastic media with implications for cell mechanics

We show how strain stiffening affects the elastic response to internal forces, caused either by material defects and inhomogeneities or by active forces that molecular motors generate in living cells. For a spherical force dipole in a material with a strongly nonlinear strain energy density, strains change sign with distance, indicating that even around a contractile inclusion or molecular motor there is radial compression; it is only at long distance that one recovers the linear response in which the medium is radially stretched. Scaling laws with irrational exponents relate the far-field renormalized strain to the near-field strain applied by the inclusion or active force.

cond-mat.soft↗

arXiv2011

Order-by-disorder in the antiferromagnetic Ising model on an elastic triangular lattice

Geometrically frustrated materials have a ground-state degeneracy that may be lifted by subtle effects, such as higher order interactions causing small energetic preferences for ordered structures. Alternatively, ordering may result from entropic differences between configurations in an effect termed order-by-disorder. Motivated by recent experiments in a frustrated colloidal system in which ordering is suspected to result from entropy, we consider in this paper, the antiferromagnetic Ising model on a deformable triangular lattice. We calculate the displacements exactly at the microscopic level, and contrary to previous studies, find a partially disordered ground state of randomly zigzagging stripes. Each such configuration is deformed differently and thus has a unique phonon spectrum with distinct entropy, thus lifting the degeneracy at finite temperature. Nonetheless, due to the free-energy barriers between the ground-state configurations, the system falls into a disordered glassy state.

cond-mat.stat-mech↗

arXiv2011

Effective Temperature of Red Blood Cell Membrane Fluctuations

Biologically driven non-equilibrium fluctuations are often characterized by their non-Gaussianity or by an "effective temperature", which is frequency dependent and higher than the ambient temperature. We address these two measures theoretically by examining a randomly kicked "particle", with a variable number of kicking "motors", and show how these two indicators of non-equilibrium behavior can contradict. Our results are compared with new experiments on shape fluctuations of red-blood cell membranes, and demonstrate how the physical nature of the motors in this system can be revealed using these global measures of non-equilibrium.

physics.bio-ph↗

arXiv2010

Jamming Mechanisms and Density Dependence in a Kinetically-Constrained Model

We add relaxation mechanisms that mimic the effect of temperature and non-equilibrium driving to the recently-proposed spiral model which jams at a critical density rho_c < 1. This enables us to explore unjamming by temperature or driving at rho_c < rho < 1. We numerically calculate the relaxation time of the persistence function and its spatial heterogeneity. We disentangle the three different relaxation mechanisms responsible for unjamming when varying density, temperature, and driving strength, respectively. We show that the spatial scale of dynamic heterogeneity depends on density much more strongly than on temperature and driving.

cond-mat.soft↗

arXiv2009

Randomness-Induced Redistribution of Vibrational Frequencies in Amorphous Solids

Much of the discussion in the literature of the low frequency part of the density of states of amorphous solids was dominated for years by comparing measured or simulated density of states to the classical Debye model. Since this model is hardly appropriate for the materials at hand, this created some amount of confusion regarding the existence and universality of the so- called ``Boson Peak'' which results from such comparisons. We propose that one should pay attention to the different roles played by different aspects of disorder, the first being disorder in the interaction strengths, the second positional disorder, and the third coordination disorder. These have different effects on the low-frequency part of the density of states. We examine the density of states of a number of tractable models in one and two dimensions, and reach a clearer picture of the softening and redistribution of frequencies in such materials. We discuss the effects of disorder on the elastic moduli and the relation of the latter to frequency softening, reaching the final conclusion that the Boson peak is not universal at all.

cond-mat.mtrl-sci↗

arXiv2008

Stripes, Zigzags, and Slow Dynamics in Buckled Hard Spheres

We study the analogy between buckled colloidal monolayers and the triangular-lattice Ising antiferromagnet. We calculate free volume-induced Ising interactions, show how lattice deformations favor zigzag stripes that partially remove the Ising model ground-state degeneracy, and identify the Martensitic mechanism prohibiting perfect stripes. Slowly inflating the spheres yields jamming as well as logarithmically slow relaxation reminiscent of the glassy dynamics observed experimentally.

cond-mat.soft↗

arXiv2008

Geometric Frustration in Buckled Colloidal Monolayers

Geometric frustration arises when lattice structure prevents simultaneous minimization of local interactions. It leads to highly degenerate ground states and, subsequently, complex phases of matter such as water ice, spin ice and frustrated magnetic materials. Here we report a simple geometrically frustrated system composed of closely packed colloidal spheres confined between parallel walls. Diameter-tunable microgel spheres are self-assembled into a buckled triangular lattice with either up or down displacements analogous to an antiferromagnetic Ising model on a triangular lattice. Experiment and theory reveal single-particle dynamics governed by in-plane lattice distortions that partially relieve frustration and produce ground-states with zigzagging stripes and subextensive entropy, rather than the more random configurations and extensive entropy of the antiferromagnetic Ising model. This tunable soft matter system provides an uncharted arena in which the dynamics of frustration, thermal excitations and defects can be directly visualized.

cond-mat.soft↗

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↗

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↗