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At least 289 records · Page 16Linked to original sources
arXiv2008

Thermodynamic potential of a mechanical constitutive model for two-phase band flow

Starting from a simple mechanical constitutive model (the non-local diffusive Johnson-Segalman model; DJS model), we provide a rigorous theoretical explanation as to why a unique value of the stress plateau of a highly sheared viscoelastic fluid is stably realized. The present analysis is based on a reduction theory of the degrees of freedom of the model equation in the neighborhood of a critical point, which leads to a time-evolution equation that is equivalent to those for first-order phase transitions.

cond-mat.soft↗
arXiv2009

Superstatistical generalisations of Wishart-Laguerre ensembles of random matrices

Using Beck and Cohen's superstatistics, we introduce in a systematic way a family of generalised Wishart-Laguerre ensembles of random matrices with Dyson index $β$ = 1,2, and 4. The entries of the data matrix are Gaussian random variables whose variances $η$ fluctuate from one sample to another according to a certain probability density $f(η)$ and a single deformation parameter $γ$. Three superstatistical classes for $f(η)$ are usually considered: $χ^2$-, inverse $χ^2$- and log-normal-distributions. While the first class, already considered by two of the authors, leads to a power-law decay of the spectral density, we here introduce and solve exactly a superposition of Wishart-Laguerre ensembles with inverse $χ^2$-distribution. The corresponding macroscopic spectral density is given by a $γ$-deformation of the semi-circle and Marčenko-Pastur laws, on a non-compact support with exponential tails. After discussing in detail the validity of Wigner's surmise in the Wishart-Laguerre class, we introduce a generalised $γ$-dependent surmise with stretched-exponential tails, which well approximates the individual level spacing distribution in the bulk. The analytical results are in excellent agreement with numerical simulations. To illustrate our findings we compare the $χ^2$- and inverse $χ^2$-class to empirical data from financial covariance matrices.

math-ph↗
arXiv2008

Irreversibility and self-organisation in hydrodynamic echo experiments

We discuss the reversible-irreversible transition in low-Reynolds hydrodynamic systems driven by external cycling actuation. We introduce a set of models with no auto-organisation, and show that a sharp crossover is obtained between a Lyapunov regime in which any noise source, such as thermal noise, is amplified exponentially, and a diffusive regime where this no longer holds. In the latter regime, groups of particles are seen to move cooperatively, yet no spatial organization occurs.

cond-mat.stat-mech↗
arXiv2010

Preferential concentration vs. clustering in inertial particle transport by random velocity fields

The concept of preferential concentration in the transport of inertial particles by random velocity fields is extended to account for the possibility of zero correlation time and compressibility of the velocity field. It is shown that, in the case of an uncorrelated in time random velocity field, preferential concentration takes the form of a condition on the field history leading to the current particle positions. This generalized form of preferential concentration appears to be a necessary condition for clustering in the uncorrelated in time case. The standard interpretation of preferential concentration is recovered considering local time averages of the velocity field. In the compressible case, preferential concentration occurs in regions of negative divergence of the field. In the incompressible case, it occurs in regions of simultaneously high strain and negative field skewness.

cond-mat.stat-mech↗
arXiv2008

Glass transitions in 1, 2, 3, and 4 dimensional binary Lennard-Jones systems

We investigate the calorimetric liquid-glass transition by performing simulations of a binary Lennard-Jones mixture in one through four dimensions. Starting at a high temperature, the systems are cooled to T=0 and heated back to the ergodic liquid state at constant rates. Glass transitions are observed in two, three and four dimensions as a hysteresis between the cooling and heating curves. This hysteresis appears in the energy and pressure diagrams, and the scanning-rate dependence of the area and height of the hysteresis can be described by power laws. The one dimensional system does not experience a glass transition but its specific heat curve resembles the shape of the $D\geq 2$ results in the supercooled liquid regime above the glass transition. As $D$ increases, the radial distribution functions reflect reduced geometric constraints. Nearest-neighbor distances become smaller with increasing $D$ due to interactions between nearest and next-nearest neighbors. Simulation data for the glasses are compared with crystal and melting data obtained with a Lennard-Jones system with only one type of particle and we find that with increasing $D$ crystallization becomes increasingly more difficult.

cond-mat.dis-nn↗
arXiv2009

Dynamic heterogeneities in critical coarsening: Exact results for correlation and response fluctuations in finite-sized spherical models

We study dynamic heterogeneities in the out-of-equilibrium coarsening dynamics of the spherical ferromagnet after a quench from infinite temperature to its critical point. A standard way of probing such heterogeneities is by monitoring the fluctuations of correlation and susceptibility, coarse-grained over mesoscopic regions. We discuss how to define fluctuating coarse-grained correlations (C) and susceptibilities (Chi) in models where no quenched disorder is present. Our focus for the spherical model is on coarse-graining over the whole volume of $N$ spins, which requires accounting for N^{-1/2} non-Gaussian fluctuations of the spin. The latter are treated as a perturbation about the leading order Gaussian statistics. We obtain exact results for these quantities, which enable us to characterise the joint distribution of C and Chi fluctuations. We find that this distribution is qualitatively different, even for equilibrium above criticality, from the spin-glass scenario where C and Chi fluctuations are linked in a manner akin to the fluctuation-dissipation relation between the average C and Chi. Our results show that coarsening at criticality is clearly heterogeneous for d>4 and suggest that, as in other glassy systems, there is a well-defined timescale on which fluctuations across thermal histories are largest. Surprisingly, however, neither this timescale nor the amplitude of the heterogeneities increase with the age of the system, as would be expected from the growing correlation length. For d<4, the strength of the fluctuations varies on a timescale proportional to the age of the system; the corresponding amplitude also grows with age, but does not scale with the correlation volume as might have been expected naively.

cond-mat.dis-nn↗
arXiv2009

Deformed Statistics Formulation of the Information Bottleneck Method

The theoretical basis for a candidate variational principle for the information bottleneck (IB) method is formulated within the ambit of the generalized nonadditive statistics of Tsallis. Given a nonadditivity parameter $ q $, the role of the \textit{additive duality} of nonadditive statistics ($ q^*=2-q $) in relating Tsallis entropies for ranges of the nonadditivity parameter $ q < 1 $ and $ q > 1 $ is described. Defining $ X $, $ \tilde X $, and $ Y $ to be the source alphabet, the compressed reproduction alphabet, and, the \textit{relevance variable} respectively, it is demonstrated that minimization of a generalized IB (gIB) Lagrangian defined in terms of the nonadditivity parameter $ q^* $ self-consistently yields the \textit{nonadditive effective distortion measure} to be the \textit{$ q $-deformed} generalized Kullback-Leibler divergence: $ D_{K-L}^{q}[p(Y|X)||p(Y|\tilde X)] $. This result is achieved without enforcing any \textit{a-priori} assumptions. Next, it is proven that the $q^*-deformed $ nonadditive free energy of the system is non-negative and convex. Finally, the update equations for the gIB method are derived. These results generalize critical features of the IB method to the case of Tsallis statistics.

cond-mat.stat-mech↗
arXiv2009

Supercoil formation in DNA denaturation

We generalize the Poland-Scheraga (PS) model to the case of a circular DNA, taking into account the twisting of the two strains around each other. Guided by recent single-molecule experiments on DNA strands, we assume that the torsional stress induced by denaturation enforces formation of supercoils whose writhe absorbs the linking number expelled by the loops. Our model predicts that, when the entropy parameter of a loop satisfies $c \le 2$, denaturation transition does not take place. On the other hand for $c>2$ a first-order denaturation transition is consistent with our model and may take place in the actual system, as in the case with no supercoils. These results are in contrast with other treatments of circular DNA melting where denaturation is assumed to be accompanied by an increase in twist rather than writhe on the bound segments.

cond-mat.soft↗
arXiv2008

Synchronization of coupled demographic oscillators

Demographic oscillators are individual-based systems exhibiting temporal cycles sustained by the stochastic dynamics of the microscopic interacting particles. We here use the example of coupled predator-prey oscillators to show that synchronization to a common frequency can occur between two such systems, even if they oscillate at different frequencies in the absence of coupling. The power spectra of the separate and the coupled systems are computed within a van Kampen expansion in the inverse system size, and it is found that they exhibit two peaks at separate frequencies at low coupling, but that only one peak is present at large enough coupling strength. We further make predictions on the time behaviour of the phases of the two oscillators, and their phase difference, and confirm the frequency entrainment at sufficiently large coupling. Theoretical results are verified convincingly in numerical simulations.

nlin.AO↗
arXiv2008

Polaron Properties of an Impurity in Bose-Einstein-Condensation

In this paper we study an impurity in Bose-Einstein-Condensate system at $T=0K$ and suppose the contact forms for boson-boson and boson-impurity interactions. Using Bogoliubov theory and a further approximation corresponding to only think over the forward scattering of impurity by bosons, we derive a reduced Hamiltonian whose form is the same as the Fröhlich Hamiltonian for large polaron. By using Lee-Low-Pines (LLP) theory for large polaron, we obtain the effective mass of impurity, the phonon number carried by impurity and the energy related to the existence of impurity. In addition, we also discuss the valid range for forward-scattering approximation.

cond-mat.stat-mech↗
arXiv2009

Recent developments in superstatistics

We provide an overview on superstatistical techniques applied to complex systems with time scale separation. Three examples of recent applications are dealt with in somewhat more detail: the statistics of small-scale velocity differences in Lagrangian turbulence experiments, train delay statistics on the British rail network, and survival statistics of cancer patients once diagnosed with cancer. These examples correspond to three different universality classes: Lognormal superstatistics, chi-square superstatistics and inverse chi-square superstatistics.

cond-mat.stat-mech↗
arXiv2008

Matrix Ansatz, lattice paths and rook placements

We give two combinatorial interpretations of the Matrix Ansatz of the PASEP in terms of lattice paths and rook placements. This gives two (mostly) combinatorial proofs of a new enumeration formula for the partition function of the PASEP. Besides other interpretations, this formula gives the generating function for permutations of a given size with respect to the number of ascents and occurrences of the pattern 13-2, the generating function according to weak exceedances and crossings, and the n-th moment of certain q-Laguerre polynomials.

math.CO↗
arXiv2010

Generalised Kramers model

We study a particular generalisation of the classical Kramers model describing Brownian particles in the external potential. The generalised model includes the stochastic force which is modelled as an additive random noise that depends upon the position of the particle, as well as time. The stationary solution of the Fokker-Planck equation is analysed in two limits: weak external forcing, where the solution is equivalent to the increase of the potential compared to the classical model, and strong external forcing, where the solution yields a non-zero probability flux for the motion in a periodic potential with a broken reflection symmetry.

cond-mat.stat-mech↗
arXiv2008

Self-organization in nonadditive systems with external noise

A nonadditive generalization of Klimontovich's S-theorem [G. B. Bagci, Int.J. Mod. Phys. B 22, 3381 (2008)] has recently been obtained by employing Tsallis entropy. This general version allows one to study physical systems whose stationary distributions are of the inverse power law in contrast to the original S-theorem, which only allows exponential stationary distributions. The nonadditive S-theorem has been applied to the modified Van der Pol oscillator with inverse power law stationary distribution. By using nonadditive S-theorem, it is shown that the entropy decreases as the system is driven out of equilibrium, indicating self-organization in the system. The allowed values of the nonadditivity index $q$ are found to be confined to the regime (0.5,1].

cond-mat.stat-mech↗
arXiv2008

Magnetism of frustrated regular networks

We consider a regular random network where each node has exactly three neighbours. Ising spins at the network nodes interact antiferromagnetically along the links. The clustering coefficient $C$ is tuned from zero to 1/3 by adding new links. At the same time, the density of geometrically frustrated links increases. We calculate the magnetic specific heat, the spin susceptibility and the Edwards-Anderson order parameter $q$ by means of the heat-bath Monte Carlo simulations. The aim is the transition temperature $T_x$ dependence on the clustering coefficient $C$. The results are compared with the predictions of the Bethe approximation. At C=0, the network is bipartite and the low temperature phase is antiferromagnetic. When $C$ increases, the critical temperature falls down towards the values which are close to the theoretical predictions for the spin-glass phase.

cond-mat.dis-nn↗