Randomly amplified discrete Langevin systems

A discrete stochastic process involving random amplification with additive noise is studied analytically. If the non-negative random amplification factor b is such that =1, where beta is any positive noninteger, then the steady state probability density function for the process will have power law tails of the form p(x) approximately 1/x(beta+1). This is a generalization of recent results for 0相似文献   

Extended acoustic waves in diluted random systems

In this paper we study the propagation of acoustic waves in an one-dimensional diluted random media which is composed of two interpenetrating chains with pure and random elasticity. We considered a discrete one-dimensional version of the wave equation where the elasticity distribution appears as an effective spring constant. By using a matrix recursive reformulation we compute the localization length within the band of allowed frequencies. In addition, we apply a second-order finite difference method for both time and spatial variables, and study the nature of the waves that propagate in the chain. We numerically demonstrate that the diluted random elasticity distribution promotes extended acoustic modes at high-frequencies.     

Ordered and disordered states in magnetically diluted insulating systems

The different kinds of magnetic phases arising in insulating systems are described and discussed. Attention is focussed on semi-disordered phases which retain partially long range order as reentrant properties and local canted states, and disordered phases without long range order as spin glasses and spin cluster states. The properties of some systems are described, choosen among those where Mössbauer spectroscopy has been performed, mainly spinels, glasses, fluorides, Eu-based compounds. Some unsolved problems are shortly pointed out.     

Polaron band collapse in concentrated and diluted polaron systems

The dependence of the character of the phase transition that accompanies the polaron band collapse in Ag _x TiTe₂ on the concentration of polaron centers determining the density of states of the polaron band was studied by differential thermal analysis and by measuring the magnetic susceptibility. In the low-concentration limit, the transition is found to be smooth. As the concentration of impurity centers increases, the transition changes to the first order. On the temperature-concentration diagram, the line along which the change in the phase transition order occurs is determined by percolation laws. It is shown that the thermal effect accompanying the transition can be related to the decrease in the electron free energy due to polaron localization.     

Bond and site diluted Ising-model systems: A unified treatment

A unified effective-field approximation scheme for both quenched bond- and site-diluted Ising magnets is presented. The method, which can systematically include correlation effects, is illustrated by applying to a honeycomb lattice. We also comment on the relation between the present method and that recently proposed by Boccara.     

Phase transition properties of three-dimensional systems described by diluted potts model

Monte Carlo simulations are performed to analyze phase transitions in three-dimensional systems described by the 3-state Potts model with nonmagnetic impurities. Numerical results are presented for systems with spin concentrations p = 1.00, 0.95, 0.90, 0.80, 0.70, and 0.65 on lattices of size L varying between 20 and 44. Binder’s cumulant analysis shows that the introduction of quenched disorder in the form of non-magnetic impurities induces a crossover from first-order to second-order phase transition. The finite-size scaling method is used to calculate the static critical exponents α, γ, β, and ν for specific heat, susceptibility, magnetization, and correlation length, respectively.     

Magnetic field switching between the two orbital-ordered states in DyVO3

The critical phase competition between different spin-orbital-ordered states has been investigated for the DyVO3 single crystal. As temperature is lowered, the compound exhibits a reentrant spin and orbital ordering (SO and OO) transition: C-->G-->C type for SO and G-->C-->G type for OO. It was found that a magnetic field also drives the phase transition from C to G for OO and concomitantly from G to C for SO, the latter of which is coupled with the metamagnetic transition of the Dy 4f moments. The mechanism of this novel magnetic-field-induced orbital switching is discussed.     

Randomly hyperbranched polymers

We describe a model for the structures of randomly hyperbranched polymers in solution, and find a logarithmic growth of radius with polymer mass. We include segmental overcrowding, which puts an upper limit on the density. The model is tested against simulations, against data on amylopectin, a major component of starch, on glycogen, and on polyglycerols. For samples of synthetic polyglycerol and glycogen, our model holds well for all the available data. The model reveals higher-level scaling structure in glycogen, related to the beta particles seen in electron microscopy.     

Randomly forced DNA

We study the effect of random forces on a double-stranded DNA in unzipping the two strands, analogous to the problem of an adsorbed polymer under a random force. The ground state develops bubbles of various lengths as the random force fluctuation is increased. The unzipping phase diagram is shown to be drastically different from the pure case.     

Randomly rattled ratchets

Summary Ratchets are anisotropic periodic potentials. Particles subject to ratchet forces and simultaneously to thermal and nonthermal fluctuations can rectify the nonequilibrium noise, thereby extracting energy from incoherent and otherwise symmetric random forces. In this paper I describe some simple models which illustrate this phenomenon, highlighting two particular mechanisms leading to fluctuation-induced current. Paper presented at the International Workshop ?Fluctuations in Physics and Biology: Stochastic Resonance, Signal Processing and Related Phenomena?, Elba, 5–10 June 1994. Address after July 1, 1994: Center for Nonlinear Studies, MS-B258, Los Alamos National Laboratory, Los Alamos, NM 87545, USA.     

The travelling salesman problem on randomly diluted lattices: Results for small-size systems

If one places N cities randomly on a lattice of size L, we find that and vary with the city concentration p=N/L ², where is the average optimal travel distance per city in the Euclidean metric and is the same in the Manhattan metric. We have studied such optimum tours for visiting all the cities using a branch and bound algorithm, giving the exact optimized tours for small system sizes () and near-optimal tours for bigger system sizes (). Extrapolating the results for , we find that for p=1, and and with as . Although the problem is trivial for p=1, for it certainly reduces to the standard travelling salesman problem on continuum which is NP-hard. We did not observe any irregular behaviour at any intermediate point. The crossover from the triviality to the NP-hard problem presumably occurs at p=1. Received 15 April 2000     

Randomly crosslinked macromolecular systems: Vulcanization transition to and properties of the amorphous solid state

As Charles Goodyear discovered in 1839, when he first vulcanized rubber, a macromolecular liquid is transformed into a solid when a sufficient density of permanent crosslinks is introduced at random. At this continuous equilibrium phase transition, the liquid state, in which all macromolecules are delocalized, is transformed into a solid state, in which a non-zero fraction of macromolecules have spontaneously become localized. This solid state is a most unusual one: localization occurs about mean positions that are distributed homogeneously and randomly, and to an extent that varies randomly from monomer to monomer. Thus, the solid state emerging at the vulcanization transition is an equilibrium amorphous solid state: it is properly viewed as a solid state that bears the same relationship to the liquid and crystalline states as the spin glass state of certain magnetic systems bears to the paramagnetic and ferromagnetic states, in the sense that, like the spin glass state, it is diagnosed by a subtle order parameter.

In this article we give a detailed exposition of a theoretical approach to the physical properties of systems of randomly, permanently crosslinked macromolecules. Our primary focus is on the equilibrium properties of such systems, especially in the regime of Goodyear's vulcanization transition. This approach rests firmly on techniques from the statistical mechanics of disordered systems pioneered by Edwards and co-workers in the context of macromolecular systems, and by Edwards and Anderson in the context of magnetic systems. We begin with a review of the semi-microscopic formulation of the statistical mechanics of randomly crosslinked macromolecular systems due to Edwards and co-workers, in particular discussing the role of crosslinks as quenched random variables. Then we turn to the issue of order parameters, and review a version capable, inter alia, of diagnosing the amorphous solid state. To develop some intuition, we examine the order parameter in an idealized situation, which subsequently turns out to be surprisingly relevant. Thus, we are motivated to hypothesize an explicit form for the order parameter in the amorphous solid state that is parametrized in terms of two physical quantities: the fraction of localized monomers, and the statistical distribution of localization lengths of localized monomers. Next, we review the symmetry properties of the system itself, the liquid state and the amorphous solid state, and discuss connections with scattering experiments. Then, we review a representation of the statistical mechanics of randomly crosslinked macromolecular systems from which the quenched disorder has been eliminated via an application of the replica technique. We transform the statistical mechanics into a field-theoretic representation, which exhibits a close connection with the order parameter, and analyse this representation at the saddle-point level. This analysis reveals that sufficient crosslinking causes an instability of the liquid state, this state giving way to the amorphous solid state. To address the properties of the amorphous solid state itself, we solve the self-consistent equation for the order parameter by adopting the hypothesis discussed earlier. Hence, we find that the vulcanization transition is marked by the appearance of a non-zero fraction of localized monomers, which we compute, the dependence of this fraction on the crosslink density indicating a connection with random graph theory and percolation. We also compute the distribution of localization lengths that characterizes the ordered state, which we find to be expressible in terms of a universal scaling function of a single variable, at least in the vicinity of the transition. Finally, we analyse the consequences of incorporating a certain specific class of correlations associated with the excluded-volume interaction.     

Half-metallic diluted antiferromagnetic semiconductors

The possibility of half-metallic antiferromagnetism, a special case of ferrimagnetism with a compensated magnetization, in the diluted magnetic semiconductors is highlighted on the basis of the first-principles electronic structure calculation. As typical examples, the electrical and magnetic properties of II-VI compound semiconductors doped with 3d transition metal ion pairs--(V, Co) and (Fe, Cr)--are discussed.     

IR Properties of Randomly Sea Surfaces

Sea surfaces should be considered as randomly rough surfaces at the infrared(IR) and optical bands. The geometric model of sea surfaces has been obtained by using image processing. Based on the electromagnetic scattering theory, the Laser Radar Cross Section(LRCS) for the sea surfaces is analyzed at IR band and the scattering properties of the sea surfaces have been gotten.     

Randomly flashing diffusion: Asymptotic properties

The theory of abstract Markov operators and semigroups is applied for studying asymptotics of a randomly flashing diffusion process. The probability distribution of the process is determined by a set of two partial differential equations and sufficient conditions for the existence of a stationary solution of the equations are formulated, and convergence of solutions to the stationary solution is proved.