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arXiv2009

Non-Affine Shear Modulus in Entangled Networks of Semiflexible Polymers

We investigate the viscoelastic properties of entangled networks of semiflexible polymers. At intermediate time scales the elastic response of these networks to shear deformation is described by the plateau modulus $G$. Different scaling laws with polymer concentration $c$ have been proposed based on the assumption that the deformation field is affine on all length scales. We develop a numerical approach that allows to calculate the modulus via free energy changes for both affine and non-affine deformations. The non-affine deformation field is obtained by a free energy minimization. Our findings allow for a confirmation of a power law $G \propto c^{7/5} l_p^{-1/5}$ with polymer concentration $c$ and persistence length $l_p$ and furthermore quantify the systematic deviations due to the affinity assumption.

cond-mat.soft↗
arXiv2009

Modeling self-organizing traffic lights with elementary cellular automata

There have been several highway traffic models proposed based on cellular automata. The simplest one is elementary cellular automaton rule 184. We extend this model to city traffic with cellular automata coupled at intersections using only rules 184, 252, and 136. The simplicity of the model offers a clear understanding of the main properties of city traffic and its phase transitions. We use the proposed model to compare two methods for coordinating traffic lights: a green-wave method that tries to optimize phases according to expected flows and a self-organizing method that adapts to the current traffic conditions. The self-organizing method delivers considerable improvements over the green-wave method. For low densities, the self-organizing method promotes the formation and coordination of platoons that flow freely in four directions, i.e. with a maximum velocity and no stops. For medium densities, the method allows a constant usage of the intersections, exploiting their maximum flux capacity. For high densities, the method prevents gridlocks and promotes the formation and coordination of "free-spaces" that flow in the opposite direction of traffic.

nlin.CG↗
arXiv2009

Time Irreversibility Problem and Functional Formulation of Classical Mechanics

The time irreversibility problem is the dichotomy of the reversible microscopic dynamics and the irreversible macroscopic physics. This problem was considered by Boltzmann, Poincaré, Bogolyubov and many other authors and though some researchers claim that the problem is solved, it deserves a further study. In this paper an attempt is performed of the following solution of the irreversibility problem: a formulation of microscopic dynamics is suggested which is irreversible in time. A widely used notion of microscopic state of the system at a given moment of time as a point in the phase space and also a notion of trajectory does not have an immediate physical meaning since arbitrary real numbers are non observable. In the approach presented in this paper the physical meaning is attributed not to an individual trajectory but only to a bunch of trajectories or to the distribution function on the phase space. The fundamental equation of the microscopic dynamics in the proposed "functional" approach is not the Newton equation but the Liouville equation for the distribution function of a single particle. Solutions of the Liouville equation have the property of delocalization which accounts for irreversibility. It is shown that the Newton equation in this approach appears as an approximate equation describing the dynamics of the average values of the position and momenta. Corrections to the Newton equation are computed.

cond-mat.stat-mech↗
arXiv2009

A statistical field theory approach applied to the liquid vapor interface

Last years, there has been a renewed interest in the utilization of statistical field theory methods for the description of systems at equilibrium both in the vicinity and away from critical points, in particular in the field of liquid state physics. These works deal in general with homogeneous systems, although recently the study of liquids in the vicinity of hard walls has also been considered in this way. On the other hand, effective Hamiltonian pertaining to the $ϕ^4$ theory family have been written and extensively used for the description of inhomogeneous systems either at the simple interface between equilibrium phases or for the description of wetting. In the present work, we focus on a field theoretical description of the liquid vapor interface of simple fluids. We start from the representation of the grand partition function obtained from the Hubbard-Stratonovich transform leading to an exact formulation of the problem, namely neither introducing an effective Hamiltonian nor associating the field to the one-body density of the liquid. Using as a reference system the hard sphere fluid and imposing the coexistence condition, the expansion of the Hamiltonian obtained yields a usual $ϕ^4$ theory without unknown parameter. An important point is that the so-called capillary wave theory appears as an approximation of the one-loop theory in the functional expansion of the Hamiltonian, without any need to an underlying phenomenology.

cond-mat.stat-mech↗
arXiv2010

Effective Stochastic Resonance under Heterogeneous Amplitude of Noise

Effective stochastic resonance (SR) is numerically and analytically studied using a model with coupled two particles exposed to heterogeneous, i.e., particles dependent, amplitude of noise. Compared to previous SR models of single particle and to those of coupled two particles exposed to equivalent amplitude of noise, the present model exhibits a more intensive resonance of, at least, one particle exposed to the non-larger amplitude of noise with the assistance of another particle. In a certain range of conditions, this effective resonance of one particle overwhelms the poor resonance of the other particle, meaning that heterogeneous amplitude of noise leads the system, not only locally but also in the average of the whole, to the effective SR.

cond-mat.stat-mech↗
arXiv2010

Is SU(2) lattice gauge theory a spin glass?

A new order parameter is constructed for SU(2) lattice gauge theory in the context of the two-real-replica method normally used for spin glasses. The order parameter is sensitive to a global Z2 subgroup of the gauge symmetry which is seen to break spontaneously at $β= 4/g^2 = 1.96\pm 0.01$. No gauge fixing is required. Finite size scaling is consistent with a high-order paramagnet to spin glass transition with a critical exponent $ν= 0.99 \pm 0.13$. The existence of this transition suggests a second transition from spin glass to ferromagnet should exist at higher $β$.

hep-lat↗
arXiv2013

Fractional Dynamics, Tiling Equilibrium states and Riemann's zeta function

Il is argued that the generalisation of the mechanical principles to other variables than localisation, velocity and momentum leads to the laws of generalized dynamics under the condition of continuous and derivable space time. However, when the fractality arises, the mechanics principles may no more be extended especially because the time and space singularity appears on the boundary and creates curvature. There is no more equilibrium state, but only a horizon which might play a same role as equilibrium but does not close the problem - especially the problem of the invariance of the energy - which requires two complementary factors: a first one related to the closure in the dimensional space, and the second to scan dissymmetry stemming from the default of tilling the space time. A new discreet time arises from fractality. It leads irreversible thermodynamic properties. Space and time singularities lead to the relation between the above mentioned problematic and the Riemann zeta functions as well as its zeros.

cond-mat.stat-mech↗
arXiv2009

Dynamic Phase Structures in the Evolution of Conventions

This paper describes an agent-based model of a finite group of agents in a single population who each choose which convention to advocate, and which convention to practice. Influences or dependencies in agents choice exists in the form of guru effects and what others practice. With payoffs being dependent on cumulative rewards or actual standings in society, we illustrate the evolutionary dynamics of the phase structure of each group in the population via simulations.

physics.soc-ph↗
arXiv2009

Complex networks: A mixture of power-law and Weibull distributions

Complex networks have recently aroused a lot of interest. However, network edges are considered to be the same in almost all these studies. In this paper, we present a simple classification method, which divides the edges of undirected, unweighted networks into two types: p2c and p2p. The p2c edge represents a hierarchical relationship between two nodes, while the p2p edge represents an equal relationship between two nodes. It is surprising and unexpected that for many real-world networks from a wide variety of domains (including computer science, transportation, biology, engineering and social science etc), the p2c degree distribution follows a power law more strictly than the total degree distribution, while the p2p degree distribution follows the Weibull distribution very well. Thus, the total degree distribution can be seen as a mixture of power-law and Weibull distributions. More surprisingly, it is found that in many cases, the total degree distribution can be better described by the Weibull distribution, rather than a power law as previously suggested. By comparing two topology models, we think that the origin of the Weibull distribution in complex networks might be a mixture of both preferential and random attachments when networks evolve.

cs.NI↗
arXiv2011

Study of the Nonequilibrium Critical Quenching and Annealing Dynamics for the Long-Range Ising Model

Extensive Monte Carlo simulations are employed in order to study the dynamic critical behavior of the one-dimensional Ising magnet, with algebraically decaying long-range interactions of the form $\frac{1}{r^{d+σ}}$, with $σ=0.75$. The critical temperature, as well as the critical exponents, is evaluated from the power-law behavior of suitable physical observables when the system is quenched from uncorrelated states, corresponding to infinite temperature, to the critical point. These results are compared with those obtained from the dynamic evolution of the system when it is suddenly annealed at the critical point from the ordered state. Also, the critical temperature in the infinite interaction limit is obtained by means of a finite-range scaling analysis of data measured with different cutoffs of the interaction range. All the estimated static critical exponents ($γ/ν$, $β/ν$, and $1/ν$) are in good agreement with Renormalization Group (RG) predictions and previously reported numerical data obtained under equilibrium conditions. It is found that the dynamic exponent $z$ is different for quenching and annealing experiments, most likely due to the influence of the Kosterlitz-Thouless transition occurring at relatively similar algebraic decay of the interactions with $σ=1$. However, for annealing experiments the measured exponent $z$ is close to the RG predictions. On the other hand, the relevant exponents of the dynamic behavior ($z$ and $θ$) are slightly different than the RG predictions, most likely due to the fact that they may depend on the especific dynamics used (Metropolis in the present paper).

cond-mat.stat-mech↗
arXiv2010

A microscopic model for colloidal gels with directional effective interactions: Network induced glassy dynamics

By means of molecular dynamics, we study the structure and the dynamics of a microscopic model for colloidal gels at low volume fractions. The presence of directional interactions leads to the formation of a persistent interconnected network at temperatures where phase separation does not occur. We find that large scale spatial correlations strongly depend on the volume fraction and characterize the formation of the persistent network. We observe a pre-peak in the static structure factor and relate it to the network structure. The slow dynamics at gelation is characterized by the coexistence of fast collective motion of the mobile parts of the network structure (chains) with large scale rearrangements producing stretched exponential relaxations. We show that, once the network is sufficiently persistent, it induces slow, cooperative processes related to the network nodes. We suggest that this peculiar glassy dynamics is a hallmark of the physics of colloidal gels at low volume fractions.

cond-mat.soft↗
arXiv2010

Phase Diffusion and Lamb-Shift-Like Spectrum Shift in Classical Oscillators

The phase diffusion in a self-sustained oscillator, which produces oscillator's spectral linewidth, is inherently governed by a nonlinear Langevin equation. Over past 40 years, the equation has been treated with linear approximation, rendering the nonlinearity's effects unknown. Here we solve the nonlinear Langevin equation using the perturbation method borrowed from quantum mechanics, and reveal the physics of the nonlinearity: slower phase diffusion (linewidth narrowing) and a surprising oscillation frequency shift that formally corresponds to the Lamb shift in quantum electrodynamics.

cond-mat.stat-mech↗
arXiv2009

Minimisation of a Free-Energy-Like Potential for Non-Equilibrium Systems at Steady State

This study examines a new formulation of non-equilibrium thermodynamics, which gives a conditional derivation of the ``maximum entropy production'' (MEP) principle for flow and/or chemical reaction systems at steady state. The analysis uses a dimensionless potential function $ϕ_{st}$ for non-equilibrium systems, analogous to the free energy concept of equilibrium thermodynamics. Spontaneous reductions in $ϕ_{st}$ arise from increases in the ``flux entropy'' of the system - a measure of the variability of the fluxes - or in the local entropy production; conditionally, depending on the behaviour of the flux entropy, the formulation reduces to the MEP principle. The inferred steady state is also shown to exhibit high variability in its instantaneous fluxes and rates, consistent with the observed behaviour of turbulent fluid flow, heat convection and biological systems; one consequence is the coexistence of energy producers and consumers in ecological systems. The different paths for attaining steady state are also classified.

q-bio.PE↗
arXiv2009

Model of amplitude modulations induced by phase slips in one-dimensional superconductors

We propose a linear model for the dynamics of amplitudes associated with formation of phase slip centers in a one-dimensional superconductor. The model is derived taking into account the fact that, during the formation of phase slip centers the wave number of the superconducting phase remains practically constant. The model captures various forms of amplitude modulations associated with PSCs in closed analytic forms.

cond-mat.supr-con↗
arXiv2009

Quantum Kinetic Equations and Evolution of Many-Particle Systems

In the paper we discuss possible approaches to the problem of the rigorous derivation of quantum kinetic equations from underlying many-particle dynamics. For the description of a many-particle evolution we construct solutions of the Cauchy problems of the BBGKY hierarchy and the dual BBGKY hierarchy in suitable Banach spaces. In the framework of the conventional approach to the description of kinetic evolution the mean-field asymptotics of the quantum BBGKY hierarchy solution is constructed. We develop also alternative approaches. One method is based on the construction of the solution asymptotics of the initial-value problem of the quantum dual BBGKY hierarchy. One more approach is based on the generalized quantum kinetic equation that is a consequence of the equivalence of the Cauchy problems of such evolution equation and the BBGKY hierarchy with initial data determined by the one-particle density operator.

quant-ph↗
arXiv2009

Mittag-Leffler Functions to Pathway Model to Tsallis Statistics

In reaction rate theory, in input-output type models and in reaction-diffusion problems when the total derivatives are replaced by fractional derivatives the solutions are obtained in terms of Mittag-Leffler functions and their generalizations. When fractional calculus enters into the picture the solutions of these problems, usually available in terms of hypergeometric functions, G and H-functions, switch to Mittag-Leffler functions and their generalizations into Wright functions. In this paper, connections are established among generalized Mittag-Leffler functions, pathway model, Tsallis statistics, superstatisitcs and power law, and among the corresponding entropic measures.

cond-mat.stat-mech↗
arXiv2009

Superclimb of Dislocations and the Anomalous Isochoric Compressibility of Solid He4

In the experiment on superfluid transport in solid He4 [PRL {\bf 100}, 235301 (2008)], Ray and Hallock observed an {\it anomalously large isochoric compressibility}: the supersolid samples demonstrated a significant and apparently spatially uniform response of density and pressure to chemical potential, applied locally through Vycor "electrodes". We propose that the effect is due to {\it superclimb} : edge dislocations can climb because of mass transport along superfluid cores. We corroborate the scenario by {\it ab initio} simulations of an edge dislocation in solid He4 at $T=0.5K$. We argue that at low temperature the effect must be suppressed due to a crossover to the smooth dislocation.

cond-mat.other↗