1,721,068 research outputs found
Large deviations, condensation and giant response in a statistical system
Full text linkWe study the probability distribution P of the sum of a large number of non-identically distributed random variables n_m . Condensation of fluctuations, the phenomenon whereby one of such variables provides a macroscopic contribution to the global probability, is discussed and interpreted by analogy with phase-transitions in statistical mechanics. A general expression for P is derived, and its sensitivity to the details of the distribution of a single n_m is worked out. These general results are verified by the analytical and numerical solution of some specific examples
STATIC PROPERTIES OF CHARGE-DENSITY WAVES AT THE DEPINNING TRANSITION
No full textWe study the static properties of charge density waves, in the presence of quenched random impurities, at the depinning transition. We develop an analytical approach based on a simple assumption for the fluctuations that are compatible with a static solution; this allows us to deduce approximate equations for the threshold field, in the limit of strong pinning. These equations admit an approximate perturbative solution in any dimension, which results in an excellent agreement with the data of the simulations in the strong pinning regime, while it is qualitatively correct for weak pinning
Gaussian solution of a charge-density-wave model
No full textWe study the static and dynamic properties of the Fukuyama-Lee-Rice model for charge-density waves pinned by random impurities by means of a self-consistent Gaussian approximation. A depinning transition is observed, from an insulating to a conductive phase, when the external field E is raised above a critical value Ec, which depends both on the elastic coupling constant and on the disorder strength. The dynamics are characterized by an early stage followed by a crossover to an asymptotic regime. In the depinned phase a stationary periodic state is attained for long times characterized by a scaling behavior of the average current J̄, namely, J̄∼(E-Ec)ω, with ω=0.497±0.004
STATIC AND DYNAMIC PHASE-TRANSITION IN PINNED CHARGE-DENSITY WAVES
No full textWe study the analytical properties of charge density waves, in presence of quenched random impurities, at the depinning transition. We deduce the equation for the threshold field, as a function of the coupling constant, in the strong pinning regime, by means of a mean field approach. The results are in excellent agreement with previous calculations and numerical simulations. The concept of criticality is carefully examined. showing the presence of different critical lines, corresponding to the static and dynamic definition of the phase transition.
A qualitative interpretation of the effects of temperature on the critical field is also proposed, which agrees with the experimental behaviour of quasi-unidimensional metals
Development and regression of a large fluctuation
No full textWe study the evolution leading to (or regressing from) a large fluctuation in a statistical mechanical system. We introduce and study analytically a simple model of many identically and independently distributed microscopic variables nm (m=1,M) evolving by means of a master equation. We show that the process producing a nontypical fluctuation with a value of N= m=1Mnm well above the average (N) is slow. Such process is characterized by the power-law growth of the largest possible observable value of N at a given time t. We find similar features also for the reverse process of the regression from a rare state with N (N) to a typical one with N≃(N)
Phase ordering of conserved vectorial systems with field-dependent mobility
No full textThe dynamics of phase-separation in conserved systems with an O(N) continuous symmetry is investigated in the presence of an order-parameter-dependent mobility M{phi} = 1-a phi(2). The model is studied analytically in the framework of the large-N approximation and by numerical simulations of the N=2, N=3, and N=4 cases in d=2, for both critical and off-critical quenches. We show the existence of a universality class for a=1 characterized by a growth law of the typical length L(t)similar to t(1/z) with dynamical exponent z=6 as opposed to the usual value z=4, which is recovered for a<1
Foreword
No full textWe started thinking about a dossier on coarsening because, although many excellent reviews exist, a collection of papers where the diverse manifestations of this phenomenon were gathered together and discussed at a relatively broad and basic level, addressing both theory and experiments, would have been useful.
Coarsening certainly plays an important role in physical sciences, where phenomena of phase ordering and phase sepa- ration are widespread [1–3]. But it is also relevant in biology, characterizing for instance the motion of birds flocks [4] or bacterial suspensions [5]; in social sciences, with several implications in finance and opinion making [6]; in chemistry [7], being a possible outcome of sustained reactions. Coarsening is also important for a wealth of applications in metallurgical and plastic productions, food [8] and drug preparations, construction industry and many other areas.
The pattern formation observed in driven systems [9] is also very often the outcome of a coarsening process, although many other dynamical features such as traveling waves and chaos, non-equilibrium stationary and oscillating states may be observed. In particular, coarsening has been recognized to be widespread in surface science where Ostwald ripen- ing [10]—a phenomenon at the historical roots of coarsening studies—is observed
Ordering kinetics of the two-dimensional voter model with long-range interactions
Full text linkWe study analytically the ordering kinetics of the two-dimensional long-range voter model on a two-dimensional lattice, where agents on each vertex take the opinion of others at distance r with probability P(r)∝ r-α. The model is characterized by different regimes, as α is varied. For α>4, the behavior is similar to that of the nearest-neighbor model, with the formation of ordered domains of a typical size growing as L(t) ∝ t, until consensus is reached in a time of the order of NlnN, with N being the number of agents. Dynamical scaling is violated due to an excess of interfacial sites whose density decays as slowly as ρ(t) ∝ 1/lnt. Sizable finite-time corrections are also present, which are absent in the case of nearest-neighbor interactions. For 0<α≤4, standard scaling is reinstated and the correlation length increases algebraically as L(t) ∝ t1/z, with 1/z=2/α for 3<α<4 and 1/z=2/3 for 0<α<3. In addition, for α≤3, L(t) depends on N at any time t>0. Such coarsening, however, only leads the system to a partially ordered metastable state where correlations decay algebraically with distance, and whose lifetime diverges in the N→∞ limit. In finite systems, consensus is reached in a time of the order of N for any α<4
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