Table of contents

We report on measurements of the transverse fluctuations of a string in a turbulent air jet flow. Harmonic modes are excited by the fluctuating drag force, at different wavenumbers. This simple mechanical probe makes it possible to measure excitations of the flow at specific scales, averaged over space and time: it is a scale-resolved, global measurement. We also measure the dissipation associated with the string motion, and we consider the ratio of the fluctuations to the dissipation (FDR). In an exploratory approach, we investigate the concept of effective temperature defined through the FDR. We compare our observations with other definitions of temperature in turbulence. From the theory of Kolmogorov (1941), we derive the exponent −11/3 expected for the spectrum of the fluctuations. This simple model and our experimental results are in good agreement, over the range of wavenumbers and Reynolds number accessible (74 000≤Re≤170 000).

The steady state velocity fluctuations of a movable piston located on the top of a vibrated granular gas are studied by means of molecular dynamics simulations. From the second moment of the distribution, a temperature parameter for the piston is defined and compared with the granular temperature of the gas located just below it. Then the two temperature parameters refer to two interacting macroscopic systems. The equipartition of energy valid in usual molecular systems is strongly violated and the temperature of the piston can be larger or smaller than that of the gas, depending on the parameters defining the system at the particle level. The simulation results for the ratio of temperatures are in agreement with some theoretical predictions from kinetic theory, assuming the validity of a hydrodynamic description in the limit of weak inelasticity of the gas.

We determine the ground-state phase diagram of a Hubbard Hamiltonian with correlated hopping, which is asymmetric under particle–hole transform. By lowering the repulsive Coulomb interaction U at appropriate filling and interaction parameters, the ground state separates into hole and electron conducting phases: two different wavevectors characterize the system and charge–charge correlations become incommensurate. By further decreasing U another transition occurs at which the hole conducting region becomes insulating, and conventional phase separation takes place. Finally, for negative U the whole system eventually becomes a paired insulator. It is speculated that such behavior could be at the origin of the incommensurate superconducting phase recently discovered in the 1D Hirsch model. The exact phase boundaries are calculated in one dimension.

The conventional wisdom is that scale-free networks are prone to epidemic propagation; in the paper we demonstrate that, on the contrary, disease spreading is inhibited in fractal scale-free networks. We first propose a novel network model and show that it simultaneously has the following rich topological properties: scale-free degree distribution, tunable clustering coefficient, 'large-world' behavior, and fractal scaling. Existing network models do not display these characteristics. Then, we investigate the susceptible–infected–removed (SIR) model of the propagation of diseases in our fractal scale-free networks by mapping it to the bond percolation process. We establish the existence of non-zero tunable epidemic thresholds by making use of the renormalization group technique, which implies that power law degree distribution does not suffice to characterize the epidemic dynamics on top of scale-free networks. We argue that the epidemic dynamics are determined by the topological properties, especially the fractality and its accompanying 'large-world' behavior.

Through a series of exact mappings we reinterpret the Bernoulli model of sequence alignment in terms of the discrete-time totally asymmetric exclusion process with backward sequential update and step function initial condition. Using earlier results from the Bethe ansatz we obtain analytically the exact distribution of the length of the longest common subsequence of two sequences of finite lengths X,Y. Asymptotic analysis adapted from random matrix theory allows us to derive the thermodynamic limit directly from the finite-size result.

The celebrated Leibnitz triangle has a remarkable property, namely that each of its elements equals the sum of its south-west and south-east neighbors. In probabilistic terms, this corresponds to a specific form of correlation of N equally probable binary variables which satisfy scale invariance. Indeed, the marginal probabilities of the N-system precisely coincide with the joint probabilities of the (N−1)-system. On the other hand, the non-additive entropy , which grounds non-extensive statistical mechanics, is, under appropriate constraints, extremized by the (q-Gaussian) distribution (q<3; ). These distributions also result, as attractors, from a generalized central limit theorem for random variables which have a finite generalized variance, and are correlated in a specific way called q-independence. In order to provide physical enlightenment as regards this concept, we introduce here three types of asymptotically scale invariant probabilistic models with binary random variables, namely (i) a family, characterized by an index ν = 1,2,3,..., unifying the Leibnitz triangle (ν = 1) and the case of independent variables (); (ii) two slightly different discretizations of q-Gaussians; (iii) a special family, characterized by the parameter χ, which generalizes the usual case of independent variables (recovered for χ = 1/2). Models (i) and (iii) are in fact strictly scale invariant. For models (i), we analytically show that the N → ∞ probability distribution is a q-Gaussian with q = (ν−2)/(ν−1). Models (ii) approach q-Gaussians by construction, and we numerically show that they do so with asymptotic scale invariance. Models (iii), like two other strictly scale invariant models recently discussed by Hilhorst and Schehr, approach instead limiting distributions which are not q-Gaussians. The scenario which emerges is that asymptotic (or even strict) scale invariance is not sufficient but it might be necessary for having strict (or asymptotic) q-independence, which, in turn, mandates q-Gaussian attractors.

This paper investigates the applicability of classical, Gibbs–Boltzmann statistical mechanics to the phenomenon of non-thermal damage. As an example, a non-thermal fiber-bundle model with the global uniform (mean field) load sharing is considered. Stochastic topological behavior in the system is described in terms of an effective temperature parameter that thermalizes the system. An equation of state and a topological analogue of the energy-balance equation are obtained. The formalism of the free energy potential is developed, and the nature of the first-order phase transition and spinodal is demonstrated.

We analyze the evolution of the particle spectrum of the tricritical Ising model by varying the couplings of the energy and vacancy density fields. The particle content changes from the spectrum of a supersymmetric theory (either of an exact or a spontaneously broken supersymmetric theory) to the spectrum of seven particles related to the underlying E₇ structure. In the low temperature phase some of these excitations are topologically charged particles that are stable under an arbitrary variation of the parameters. The high and low temperature phases of the model are related by duality. In some regions of the two couplings there are also present false vacua and sequences of bound states. In order to study the non-integrable features of this model we employ the form factor perturbation theory and the truncated conformal space approach.

We study in this work the transport properties of an impurity immersed in a granular gas under stationary nonlinear Couette flow. The starting point is a kinetic model for low-density granular mixtures recently proposed by the authors (Vega Reyes et al 2007 Phys. Rev. E 75 061306). Two routes have been considered. First, a hydrodynamic or normal solution is found by exploiting a formal mapping between the kinetic equations for the gas particles and for the impurity. We show that the transport properties of the impurity are characterized by the ratio between the temperatures of the impurity and gas particles and by five generalized transport coefficients: three related to the momentum flux (a nonlinear shear viscosity and two normal stress differences) and two related to the heat flux (a nonlinear thermal conductivity and a cross-coefficient measuring a component of the heat flux orthogonal to the thermal gradient). Second, by means of a Monte Carlo simulation method we numerically solve the kinetic equations and show that our hydrodynamic solution is valid in the bulk of the fluid when realistic boundary conditions are used. Furthermore, the hydrodynamic solution applies to arbitrarily (inside the continuum regime) large values of the shear rate, of the inelasticity, and of the rest of the parameters of the system. Preliminary simulation results of the true Boltzmann description show the reliability of the nonlinear hydrodynamic solution of the kinetic model. This shows again the validity of a hydrodynamic description for granular flows, even under extreme conditions, beyond the Navier–Stokes domain.

We introduce a one-parameter deformation of the Wishart–Laguerre or chiral ensembles of positive definite random matrices with Dyson index β = 1,2 and 4. Our generalized model has a fat-tailed distribution while preserving the invariance under orthogonal, unitary or symplectic transformations. The spectral properties are derived analytically for finite matrix size N × M for all three values of β, in terms of the orthogonal polynomials of the standard Wishart–Laguerre ensembles. For large N in a certain double-scaling limit we obtain a generalized Marčenko–Pastur distribution on the macroscopic scale, and a generalized Bessel law at the hard edge which is shown to be universal. Both macroscopic and microscopic correlations exhibit power law tails, where the microscopic limit depends on β and the difference M−N. In the limit where our parameter governing the power law goes to infinity we recover the correlations of the Wishart–Laguerre ensembles. To illustrate these findings, the generalized Marčenko–Pastur distribution is shown to be in very good agreement with empirical data from financial covariance matrices.

Fluctuations and noise may alter the behaviour of dynamical systems considerably. For example, oscillations may be sustained by demographic fluctuations in biological systems where a stable fixed point is found in the absence of noise. We here extend the theoretical analysis of such stochastic effects to models which have a limit cycle for some range of the model parameters. We formulate a description of fluctuations about the periodic orbit which allows the relation between the stochastic oscillations in the fixed-point phase and the oscillations in the limit cycle phase to be elucidated. In the case of the limit cycle, a suitable transformation into a co-moving frame allows fluctuations transverse and longitudinal with respect to the limit cycle to be effectively decoupled. While longitudinal fluctuations are of a diffusive nature, those in the transverse direction follow a stochastic path more akin to that of an Ornstein–Uhlenbeck process. Their power spectrum is computed analytically within a van Kampen expansion in the inverse system size. The subsequent comparison with numerical simulations, carried out in two different ways, illustrates the effects that can occur due to diffusion in the longitudinal direction.