violation of the fluctuation dissipation theorem in glassy systems basic notions and the numerical evidence this review reports on the research done during past years on violations of the fluctuation dissipation theorem fdt in glassy systems it is focused on the existence of a quasi fluctuation dissipation theorem qfdt in glassy systems and the current supporting knowledge gained from numerical simulation studies it covers a broad range of non stationary aging and stationary driven systems such as structural glasses spin glasses coarsening systems ferromagnetic models at criticality trap models models with entropy barriers kinetically constrained models sheared systems and granular media the review is divided into four main parts 1 an introductory section explaining basic notions related to the existence of the fdt in equilibrium and its possible extension to the glassy regime qfdt 2 a description of the basic analytical tools and results derived in the framework of some exactly solvable models 3 a detailed report of the current evidence in favour of the qfdt and 4 a brief digression on the experimental evidence in its favour this review is intended for inexpert readers who want to learn about the basic notions and concepts related to the existence of the qfdt as well as for the more expert readers who may be interested in more specific results

on hopf cyclicity of planar systems we investigate the maximal number of limit cycles which appear under perturbations in hopf bifurcations by using the first order melnikov function with multiple parameters

exact solution of a 1d asymmetric exclusion model using a matrix formulation several recent works have shown that the one dimensional fully asymmetric exclusion model which describes a system of particles hopping in a preferred direction with hard core interactions can be solved exactly in the case of open boundaries here the authors present a new approach based on representing the weights of each configuration in the steady state as a product of noncommuting matrices with this approach the whole solution of the problem is reduced to finding two matrices and two vectors which satisfy very simple algebraic rules they obtain several explicit forms for these non commuting matrices which are in the general case infinite dimensional their approach allows exact expressions to be derived for the current and density profiles finally they discuss briefly two possible generalizations of their results the problem of partially asymmetric exclusion and the case of a mixture of two kinds of particles

stochastic flow cascades we introduce and explore a stochastic flow cascade sfc model a general statistical model for the unidirectional flow through a tandem array of heterogeneous filters examples include the flow of i liquid through heterogeneous porous layers ii shocks through tandem shot noise systems iii signals through tandem communication filters the sfc model combines together the langevin equation convolution filters and moving averages and poissonian randomizations a comprehensive analysis of the sfc model is carried out yielding closed form results levy laws are shown to universally emerge from the sfc model and characterize both heavy tailed retention times noah effect and long ranged correlations joseph effect

subordinated advection dispersion equation for contaminant transport a mathematical method called subordination broadens the applicability of the classical advection dispersion equation for contaminant transport in this method the time variable is randomized to represent the operational time experienced by different particles in a highly heterogeneous aquifer the operational time captures the fractal properties of the medium this leads to a simple parsimonious model of contaminant transport that exhibits many of the features heavy tails skewness and non fickian growth rate typically seen in real aquifers we employ a stable subordinator that derives from physical models of anomalous diffusion involving fractional derivatives applied to a one dimensional approximation of the made 2 data set the model shows excellent agreement

universal generation of statistical self similarity a randomized central limit theorem a universal mechanism for the generation of statistical self similarity i e fractality in the context of random processes is established we consider a generic system which superimposes independent stochastic signals producing a system output all signals share a common statistical signal pattern yet each signal has its own transmission parameters amplitude frequency and initiation epoch we characterize the class of parameter randomizations yielding statistically self similar outputs in a universal fashion i e for whatever signals fed into the system statistically self similar outputs with finite variance further display i anomalous diffusion behavior characterized by power law temporal variance growth and ii 1 f noise behavior characterized by power law power spectra the mechanism presented is a randomized central limit theorem for fractal statistics of random processes

computation of normal forms via a perturbation technique considering qualitative behavior of a non linear dynamical system often leads to first simplifying the differential equations or finding their normal forms a perturbation technique for computing normal forms is presented this technique associated with the method of multiple scales can be used to systematically find a unique form for a given set of differential equations the technique is discussed in detail through the analysis of hopf bifurcation it is shown that for hopf bifurcation the method only requires solving two dimensional matrix systems for any higher order normal forms of a generaln dimensional system with the aid of the symbolic language maple this approach is straightforward and is computationally efficient and fast furthermore a simple verification scheme is given for verifying the normal forms and associated non linear transformations obtained using any methodology examples are presented to demonstrate the applicability of the perturbation technique and the computation efficiency of the maple program

partially asymmetric exclusion process with open boundaries exclusive diffusion on a one dimensional lattice is studied in the model particles hop stochastically in both directions but with different rates at the ends of the lattice particles are injected and removed the exact stationary probability measure is represented in the form of a matrix product as a generalization of the solution given by derrida et al j phys a 26 1493 1993 for the fully asymmetric process the phase diagram of the current on the infinite lattice is obtained analytic expressions for the current in the different phases are derived the model is equivalent to an xxz heisenberg chain with a certain type of boundary terms the ground state of which corresponds to the stationary solution of the master equation

perturbation from an asymmetric cubic hamiltonian this paper concerns with the number of limit cycles from an asymmetric hamiltonian of degree three under cubic perturbation eleven limit cycles are found and three different distributions are given by using the methods of bifurcation theory and qualitative analysis two of which are new

perturbation from an elliptic hamiltonian of degree four iv figure eight loop the paper deals with lienard equations of the form x y y p x yq x with p and q polynomials of degree respectively 3 and 2 attention goes to perturbations of the hamiltonian vector fields with an elliptic hamiltonian of degree four exhibiting a figure eight loop it is proved that the least upper bound of the number of zeros of the related elliptic integral is five and this is a sharp bound multiplicity taken into account moreover if restricting to the level curves inside a saddle loop or outside the figure eight loop the sharp upper bound is respectively two or four also the multiplicity of the zeros is at most four this is the last one in a series of papers on this subject the results of this paper together with j differential equations 176 2001 114 j differential equations 175 2001 209 j differential equations to be published largely finish the study of the cubic perturbations of the elliptic hamiltonians of degree four and presumably provide a complete description of the number and the possible configurations of limit cycles for cubic lienard equations with small quadratic damping as a special case we obtain a configuration of four limit cycles surrounding three singularities together with a small limit cycle which surrounds one of the singularities

bifurcations of limit cycles in complex networks of hamiltonian systems and lloyd s conjecture abstract this paper is motivated by hilbert s sixteenth problem concerning the number and distribution of limit cycles in planar polynomial vector fields we propose an original method inspired by the complex systems framework in order to construct a family of hamiltonian systems admitting non degenerate centers located on the vertices of a planar network we introduce two novel polynomial perturbations adapted to those systems with the aim to produce a high number of limit cycles the first one is oriented along the gradient of the unperturbed system and the second one is again constructed with a complex systems approach using the melnikov integral we reach in a small number of particular cases the lower bound of cubical order for the hilbert number h n conjectured by lloyd in 1988

nonequilibrium temperatures in steady state systems with conserved energy we study a class of nonequilibrium lattice models describing local redistributions of a globally conserved quantity which is interpreted as an energy a particular subclass can be solved exactly allowing us to define a statistical temperature t th along the same lines as in the equilibrium micro canonical ensemble we compute the response function and find that when the fluctuation dissipation relation is linear the slope t fd 1 of this relation differs from the inverse temperature t th 1 we argue that t th is physically more relevant than t fd since in the steady state regime it takes equal values in two subsystems of a large isolated system finally a numerical renormalization group procedure suggests that all models within the class behave similarly at a coarse grained level leading to a parameter that describes the deviation from equilibrium quantitative predictions concerning this parameter are obtained within a mean field framework

edwards measures for powders and glasses can one construct a thermodynamics for compact slowly moving powders and grains a few years ago edwards proposed a possible step in this direction raising the fascinating perspective that such systems have a statistical mechanics of their own different from that of maxwell boltzmann and gibbs allowing us to have some information while still ignoring dynamic details recent developments in the theory of glasses have come to confirm these ideas within mean field in order to go beyond we explicitly generate edwards measure in a 3d model comparison of the results with the irreversible compaction data shows very good agreement the present framework immediately suggests new experimental checks

noise cascades and levy correlations we explore a general model of stochastic noise cascades which can be illustrated by the example of rain dropping down on the earth and then seeping through layers of ground pouring down layer by layer the rain represents an input noise that is assumed to be spatially uncorrelated and each ground layer represents a stochastic convolution filter as the input noise percolates through the layered filters spatial correlations which are initially nonexistent build up we study this build up of correlations and focus on the following question are there universally emergent forms of spatial correlations the answer is proved affirmative and is shown to be uniquely characterized by power spectra that coincide with the fourier transform of the spherically symmetric l vy distribution we term these universally emergent spatial correlations l vy correlations

bifurcations and distribution of limit cycles for near hamiltonian polynomial systems this paper concerns with limit cycles through hopf and homoclinic bifurcations for near hamiltonian systems by using the coefficients appeared in melnikov functions at the centers and homoclinic loops some sufficient conditions are obtained to find limit cycles

saddle quantities and applications abstract in this paper we make the connection between the theoretical study of the generalized homoclinic loop bifurcation ghb and the practical computational aspects for this purpose we first compare the dulac normal form with the joyal normal form these forms were both used to prove the ghb theorem but the second one is far more practical from the algorithmic point of view we then show that the information carried by these normal forms can be computed in a much simpler way using what we shall call dual lyapunov constants the coefficients of a normal form or the dual lyapunov quantities are particular cases of what we shall call saddle quantities we calculate the saddle quantities for quadratic systems and we show that no more than three limit cycles can appear in a homoclinic loop bifurcation we also study the homoclinic loop bifurcation of order 5 appearing in a 6 parameter family close to a hamiltonian system to our knowledge this is the first time that one can find a complete description of a ghb of such high order finally we calculate the saddle quantities for a symmetric cubic vector field and we deduce a bound for the number of limit cycles that appear in a ghb

randomized central limit theorems a unified theory the central limit theorems clts characterize the macroscopic statistical behavior of large ensembles of independent and identically distributed random variables the clts assert that the universal probability laws governing ensembles aggregate statistics are either gaussian or levy and that the universal probability laws governing ensembles extreme statistics are frechet weibull or gumbel the scaling schemes underlying the clts are deterministic scaling all ensemble components by a common deterministic scale however there are random environment settings in which the underlying scaling schemes are stochastic scaling the ensemble components by different random scales examples of such settings include holtsmark s law for gravitational fields and the stretched exponential law for relaxation times in this paper we establish a unified theory of randomized central limit theorems rclts in which the deterministic clt scaling schemes are replaced with stochastic scaling schemes and present randomized counterparts to the classic clts the rclt scaling schemes are shown to be governed by poisson processes with power law statistics and the rclts are shown to universally yield the levy frechet and weibull probability laws

paretian poisson processes many random populations can be modeled as a countable set of points scattered randomly on the positive half line the points may represent magnitudes of earthquakes and tornados masses of stars market values of public companies etc in this article we explore a specific class of random such populations we coin paretian poisson processes this class is elemental in statistical physics connecting together in a deep and fundamental way diverse issues including the poisson distribution of the law of small numbers paretian tail statistics the frechet distribution of extreme value theory the one sided levy distribution of the central limit theorem scale invariance renormalization and fractality resilience to random perturbations

the cyclicity of the period annulus of the quadratic hamiltonian triangle abstract the paper studies quadratic hamiltonian centers surrounded by a separatrix contour having a form of a triangle it is proved that in this situation the cyclicity of the period annulus under quadratic perturbations is equal to three