We consider the problem of the escape time (mean first-passage time) from a given interval in the case when the noise is a sum of many independent random telegraph signals. We reduce the problem to the solution of a linear system of algebraic equations valid for arbitrary intensities and correlation times of the noise. The solution allows an easy investigation of the limiting case of the Ornstein-Uhlenbeck process. We find exact scaling laws obeyed by the mean first-passage times in the case of random telegraph signals and the Ornstein-Uhlenbeck process.

The spectral properties of ‘‘chaotic quantum systems’’ are modeled using tridiagonal random matrices. Unlike the Gaussian-orthogonal-ensemble (GOE) method, both the smooth and fluctuating parts of the spectral properties can be modeled simultaneously. We model the recent experiment by Gräf et al. [Phys. Rev. Lett. 69, 1296 (1992)] as an example. This approach also provides an approximate construction of a GOE-type spectrum without any need for unfolding. By changing one control variable, one can bring the model from obeying δ-function level-spacing statistics, to being GOE-like or to being Poisson-like.

The relaxation and stationary properties of the Verhulst-type model with linearly coupled white shot noise are considered. It is found that in spite of the appearance of the noise-induced transitions in the stationary probability density distribution, the moments change continuously. The autocorrelation function is calculated and the relaxation rates are examined. It is shown that the presence of the noise slows down the relaxation. It is found for the true Verhulst model that the integral characteristic, the relaxation time T, is simply proportional to the square of the noise-controlling parameter. The Gaussian-white-noise limit is discussed.

A first-passage-time viewpoint is proposed and formulated as a tool to investigate diffusion in liquids. Application of our theory to a soft-core system shows that a continuous-diffusion model reproduces the observed first-passage-time distribution quite well for liquids in equilibrium and moderately supercooled states. Under a considerable degree of supercooling we find qualitatively different diffusion behavior reflected in the first-passage-time distribution, which cannot be explained by a continuous-diffusion model. Some models, which take into account effects of hopping, are discussed to reveal the diffusion mechanism in highly supercooled liquids.

Experimental studies of positron and positronium decay in dense fluids suggest that these particles are capable of forming self-trapped states in some fluids in a broad region of temperature and density surrounding the liquid-vapor critical point. A central question in understanding the phenomena is whether the light particle (lp) actively creates a static potential well in the fluid in which it localizes, or randomly visits favorable fluctuations. The fact that the experimental measurements yield a single, well-defined decay rate for each decay mode suggests that the environment of the lp is static. Earlier mean-field theories could not shed much light on this question. However, two recent applications of quantum Monte Carlo methods show that substantial fluctuations occur in the lp environment. In this paper, the distribution of fluctuations is described. It is shown that the apparent conflict is resolved if the time scale for fluctuations in the environment is much shorter than the duration of each measurement, and estimates for the different relaxation processes are provided.

A weighted-density-functional theory is developed for inhomogeneous ionic fluids and applied to the structure of the electric double layer using the restricted primitive model where the ions are considered to be charged hard spheres of equal diameter. The formalism is nonperturbative with both hard-sphere and electrical contributions to the one-particle correlation function evaluated through a suitably averaged weighted density, the only input being the second-order direct correlation functions of the corresponding uniform system. Numerical results on the ionic density profile and the mean electrostatic potential near a hard wall at several surface charge densities are shown to compare well with available simulation results.

In a one-dimensional fluid the macroscopic Navier-Stokes equations are no longer valid because of long-time tails and diverging transport coefficients. By performing computer simulations on a one-dimensional cellular automaton fluid we have investigated the ranges of times and densities where the intermediate- and long-time behavior of the velocity correlation function is correctly described by mode-coupling theory. The agreement is in general surprisingly good.

It is shown that the classical entropy of an isolated system does not increase monotonically when the approach to equilibrium is described by hyperbolic equations for the temperature evolution. In contrast, the generalized entropy of extended irreversible thermodynamics does increase monotonically, and is therefore better suited than the classical theory for the description of hyperbolic heat transport.

In a harmonically disordered chain with a regular array of quartic nearest-neighbor anharmonicity we have found a constructive or conflicting interplay of Anderson localization and solitary solutions depending on the type of initial excitation (momentum or displacement). In the present work we specifically discuss energy propagation ensuing after the momentum excitation of a single mass. A coexistence of Anderson localization and superdiffusive energy transport is found. Further, it is found that disorder destabilizes the supersonic solitary solution, whereas conversely anharmonicity reduces Anderson localization. A detailed analysis is given.

We present ab initio calculations of the liquid structure of the alkaline-earth metals. Our approach is based on the neutral-pseudoatom method to obtain the interionic pair potential and on the variational-modified-hypernetted-chain integral-equation theory of liquids [Y. Rosenfeld, J. Stat. Phys. 42, 437 (1986)] to obtain the liquid structure. This combination results in a whole theory that is free of adjustable parameters. We find that our pair potentials follow the expected trends for these metals. The predicted static structure factors are in good agreement with the available experimental data [Y. Waseda, The Structure of Non-Crystalline Materials (McGraw-Hill, New York, 1980)].

We experimentally observed the spatiotemporal velocity field of modulated waves (quasiperiodic mode) in a Couette-Taylor system for Reynolds number 9≤R/${\mathit{R}}_{\mathit{c}}$≤28. A power spectrum averaged over four axial wavelengths showed clear evidence of the coexistence of two quasiperiodic modes for a wide range of Reynolds number and the first azimuthal wave mode disappeared at R/${\mathit{R}}_{\mathit{c}}$≊18.

We determine, for a generic dissipative hyperbolic system of balance laws, an upper bound such that for shock velocity greater than this limit no continuous shock-wave-structure solutions may exist. These general results are applied to the old and open problem of shock waves in classical and relativistic nonequilibrium thermodynamics. In this context, for the macroscopic theories of the extended thermodynamics related to the moment Grad procedure for the Boltzmann equation we can prove that, in contrast with a recent paper [D. Jou and D. Pavon, Phys. Rev. A 44, 6496 (1991)], this upper bound for critical Mach numbers is not influenced by adding other nonlinear terms. Moreover, taking into account the results of Weiss (Doctoral dissertation in Physics, Technical University Berlin, 1990), we can verify that our critical upper bound oscillates when the number of moments is increased. Therefore we conclude that the critical Mach number does not increase if we also consider more and more moments. As at the present the experiments do not put in evidence, also for high Mach numbers, a subshock formation in the shock structure, the natural conclusion of our result is that the shock thickness problem is not in the range of any hyperbolic continuum theory compatible with the Boltzmann equation.

We investigate the instability of the anisotropic complex Ginzburg-Landau equation as a function of its parameters. We derive the conditions necessary for the instability of a homogeneous solution. In addition, the analytic geometry of the unstable solutions in wave-number space is investigated. This allows us to establish the most unstable wave (as a function of Reynolds number) whose evolution will eventually dominate the dynamics.

We introduce and analyze a general one-dimensional model for the description of transient patterns which occur in the evolution between two spatially homogeneous states. This phenomenon occurs, for example, during the Fréedericksz transition in nematic liquid crystals. The dynamics leads to the emergence of finite domains that are locally periodic and independent of each other. This picture is substantiated by a finite-size scaling law for the structure factor. The mechanism of evolution towards the final homogeneous state is by local roll destruction and associated reduction of local wave number. The scaling law breaks down for systems of size comparable to the size of the locally periodic domains. For systems of this size or smaller, an apparent nonlinear selection of a global wavelength holds, giving rise to long-lived periodic configurations which do not occur for large systems. We also make explicit unsuitability of a description of transient pattern dynamics in terms of a few Fourier mode amplitudes, even for small systems with a few linearly unstable modes.

The scaling ranges of temperature and velocity fluctuations in thermally driven turbulence are studied by analyzing the various contributions to the equations of motion. The crossover wave number ${\mathit{k}}_{\mathit{B}}$ between Bolgiano-Obukhov and Kolmogorov-Obukhov scaling is estimated in terms of the forcings. By evaluating the thermal and buoyant stirrings and dissipations of Rayleigh-Bénard convection experiments we find ${\mathit{k}}_{\mathit{B}}$ much larger than ${\mathit{L}}^{\mathrm{-}1}$, the energy-containing scale, but smaller than (10η${)}^{\mathrm{-}1}$, the viscous scale. For computer simulation of randomly thermal driven turbulence we find ${\mathit{k}}_{\mathit{B}}$ of the order of ${\mathit{L}}^{\mathrm{-}1}$. This might explain why the Bolgiano-Obukhov scaling was observed in laboratory experiments whereas Kolmogorov-Obukhov scaling was found in computer simulation of thermally driven turbulence.

The Hele-Shaw cell involves two immiscible fluids separated by an interface. Possible topology changes in the interface are investigated. In particular, we ask whether a thin neck between two masses of the fluid can develop, get thinner, and finally break. To study this, we employ the lubrication approximation, which implies for a symmetrical neck that the neck thickness h obeys ${\mathit{h}}_{\mathit{t}}$+(${\mathit{hh}}_{\mathit{x}\mathit{x}\mathit{x}}$${)}_{\mathit{x}}$=0. The question is whether, starting with smooth positive initial data for h, one can achieve h=0, and hence a possible broken neck within a finite time. One possibility is that, instead of breaking, the neck gets continually thinner and finally goes to zero thickness only at infinite time. Here, we investigate one set of initial data and argue that in this case the system does indeed realize this infinite-time breakage scenario.

We investigate the behavior of the interface between two fluids in a two-dimensional flow driven by surface tension. The geometry is chosen so that one can apply a variant of the lubrication approximation and so that the more-viscous fluid will have a tendency to change its topology by separating into two masses. Simulations are used to show that, with appropriate initial and boundary conditions, this separation can occur in a finite time. We particularly focus our attention at the pinch point, i.e., the space-time point at which the width of the viscous fluid first goes to zero. The lubrication approximation used contains a parameter ρ which measures the strength of the inertial forces. Since the fluid velocity diverges as the pinch is approached, the behavior is qualitatively different for small ρ and for ρ=0. Simulations and asymptotic analyses are used to isolate this difference. For ρ=0, at the pinch time there is a region of space in which the width grows quadratically as one moves away from the pinch. The curvatures, however, are different on the two sides of the pinch. In contrast, when ρ is different from zero, the width rises nearly linearly with distance from the pinch.

This paper addresses the question as to the differences between weakly and strongly structured mixtures of water (A), oils (${\mathit{B}}_{\mathit{k}}$), and nonionic amphiphiles such as alkylpolyglycol ether (${\mathrm{C}}_{\mathit{i}}$${\mathrm{E}}_{\mathit{j}}$). Starting with weak short-chain amphiphiles, it is shown that the three-phase body in such mixtures evolves from a tricritical point upon increasing either the carbon number k of the oil, or the amphiphilicity (i,j) of ${\mathrm{C}}_{\mathit{i}}$${\mathrm{E}}_{\mathit{j}}$. In the first case, the three-phase bodies grow monotonically with increasing distance from the tricritical point, with the mixtures, however, remaining weakly structured, whereas in the second case, the three-phase bodies first grow, then pass through maxima in the range of medium-chain amphiphiles, and shrink again as one proceeds to long-chain amphiphiles. In that range in which the three-phase bodies pass their maxima, one observes a gradual evolution of properties that distinguish weakly from strongly structured mixtures. This permits drawing a rather well-defined border line between weakly and strongly structured mixtures in (i,j)-k space.

We have examined the temperature dependence of the integrated intensity of the broad spectral contribution to the depolarized light scattered from liquids in four different experiments analyzed by four different approaches. Although the quantitative results depend upon the method of analysis, in all cases the integrated intensity, which is an equilibrium property, diminishes rapidly with decreasing temperature. This rapid decrease can be understood if the broad spectral line is associated with dipole-induced dipole interactions, which are known to exhibit a cancellation effect and which, in turn, are dependent upon the structure of and degree of order in the liquid. Therefore the integrated intensity of the broad spectral line may be an experimentally determined indicator of the degree of order in liquids and supercooled liquids.

The combined analysis of x-ray- and neutron-diffraction data of liquid water and heavy water exhibits distinct molecular tetrahedral pentamer clusters (in ${\mathit{C}}_{2\mathit{v}}$ symmetry) in water due to hydrogen bonding. The center structure is derived from the diffraction data and used to evaluate through the model intermolecular partial structures and partial correlations in water. The results are compared with the available experimental and computer-simulated data.