Intensity correlation function of dye lasers: Short-time behavior

We propose an equation to calculate the intensity correlation function of a dye-laser model with a pump parameter subject to finite-bandwidth fluctuations. The equation is valid, in the weak-noise limit, for all times. It incorporates novel non-Markovian features. Results are given for the short-time behavior of the correlation function. It exhibits a characteristic initial plateau. Our findings are supported by a numerical simulation of the model.

From nonwetting to prewetting: The asymptotic behavior of 4He drops on alkali substrates

We investigate the spreading of 4He droplets on alkali-metal surfaces at zero temperature, within the frame of finite range density-functional theory. The equilibrium configurations of several 4HeN clusters and their asymptotic trend with increasing particle number N, which can be traced to the wetting behavior of the quantum fluid, are examined for nanoscopic droplets. We discuss the size effects inferring that the asymptotic properties of large droplets correspond to those of the prewetting film.

Effects of small surface tension in Hele-Shaw multifinger dynamics: an analytical and numerical study

We study the singular effects of vanishingly small surface tension on the dynamics of finger competition in the Saffman-Taylor problem, using the asymptotic techniques described by Tanveer [Philos. Trans. R. Soc. London, Ser. A 343, 155 (1993)] and Siegel and Tanveer [Phys. Rev. Lett. 76, 419 (1996)], as well as direct numerical computation, following the numerical scheme of Hou, Lowengrub, and Shelley [J. Comput. Phys. 114, 312 (1994)]. We demonstrate the dramatic effects of small surface tension on the late time evolution of two-finger configurations with respect to exact (nonsingular) zero-surface-tension solutions. The effect is present even when the relevant zero-surface-tension solution has asymptotic behavior consistent with selection theory. Such singular effects, therefore, cannot be traced back to steady state selection theory, and imply a drastic global change in the structure of phase-space flow. They can be interpreted in the framework of a recently introduced dynamical solvability scenario according to which surface tension unfolds the structurally unstable flow, restoring the hyperbolicity of multifinger fixed points.

Dynamical properties of discrete breathers in curved chains with first and second neighbor interaction

We present the study of discrete breather dynamics in curved polymerlike chains consisting of masses connected via nonlinear springs. The polymer chains are one dimensional but not rectilinear and their motion takes place on a plane. After constructing breathers following numerically accurate procedures, we launch them in the chains and investigate properties of their propagation dynamics. We find that breather motion is strongly affected by the presence of curved regions of polymers, while the breathers themselves show a very strong resilience and remarkable stability in the presence of geometrical changes. For chains with strong angular rigidity we find that breathers either pass through bent regions or get reflected while retaining their frequency. Their motion is practically lossless and seems to be determined through local energy conservation. For less rigid chains modeled via second neighbor interactions, we find similarly that chain geometry typically does not destroy the localized breather states but, contrary to the angularly rigid chains, it induces some small but constant energy loss. Furthermore, we find that a curved segment acts as an active gate reflecting or refracting the incident breather and transforming its velocity to a value that depends on the discrete breathers frequency. We analyze the physical reasoning behind these seemingly general breather properties.

Coherence and anticoherence resonance tunned by noise

We present numerical evidence and a theoretical analysis of the appearance of anticoherence resonance induced by noise, not predicted in former analysis of coherence resonance. We have found that this phenomenon occurs for very small values of the intensity of the noise acting on an excitable system, and we claim that this is a universal signature of a nonmonotonous relaxational behavior near its oscillatory regime. Moreover, we demonstrate that this new phenomenon is totally compatible with the standard situation of coherence resonance appearing at intermediate values of noise intensity.

Dynamical scaling of imbibition in columnar geometries

compatible with the usual nonlocal model governed by surface tension that results from a macroscopic description. To explore this discrepancy, we exhaustively analyze numerical integrations of a phase-field model with dichotomic columnar disorder. We find that two distinct behaviors are possible depending on the capillary contrast between the two values of disorder. In a high-contrast case, where interface evolution is mainly dominated by the disorder, an inherent anomalous scaling is always observed. Moreover, in agreement with experimental work, the interface motion has to be described through a local model. On the other hand, in a lower-contrast case, the interface is dominated by interfacial tension and can be well modeled by a nonlocal model. We have studied both spontaneous and forced-flow imbibition situations, giving a complete set of scaling exponents in each case, as well as a comparison to the experimental results.

From subdiffusion to superdiffusion of particles on solid surfaces

We present a numerical and partially analytical study of classical particles obeying a Langevin equation that describes diffusion on a surface modeled by a two-dimensional potential. The potential may be either periodic or random. Depending on the potential and the damping, we observe superdiffusion, large-step diffusion, diffusion, and subdiffusion. Superdiffusive behavior is associated with low damping and is in most cases transient, albeit often long. Subdiffusive behavior is associated with highly damped particles in random potentials. In some cases subdiffusive behavior persists over our entire simulation and may be characterized as metastable. In any case, we stress that this rich variety of behaviors emerges naturally from an ordinary Langevin equation for a system described by ordinary canonical Maxwell-Boltzmann statistics.

Dynamics of the two-dimensional gonihedric spin model

In this paper, we study dynamical aspects of the two-dimensional (2D) gonihedric spin model using both numerical and analytical methods. This spin model has vanishing microscopic surface tension and it actually describes an ensemble of loops living on a 2D surface. The self-avoidance of loops is parametrized by a parameter ¿. The ¿=0 model can be mapped to one of the six-vertex models discussed by Baxter, and it does not have critical behavior. We have found that allowing for ¿¿0 does not lead to critical behavior either. Finite-size effects are rather severe, and in order to understand these effects, a finite-volume calculation for non-self-avoiding loops is presented. This model, like his 3D counterpart, exhibits very slow dynamics, but a careful analysis of dynamical observables reveals nonglassy evolution (unlike its 3D counterpart). We find, also in this ¿=0 case, the law that governs the long-time, low-temperature evolution of the system, through a dual description in terms of defects. A power, rather than logarithmic, law for the approach to equilibrium has been found.

Studying Avalanches in the ground-state of the two-dimensional random field Ising model driven by an external field

We study the exact ground state of the two-dimensional random-field Ising model as a function of both the external applied field B and the standard deviation ¿ of the Gaussian random-field distribution. The equilibrium evolution of the magnetization consists in a sequence of discrete jumps. These are very similar to the avalanche behavior found in the out-of-equilibrium version of the same model with local relaxation dynamics. We compare the statistical distributions of magnetization jumps and find that both exhibit power-law behavior for the same value of ¿. The corresponding exponents are compared.

Noise-enhanced excitability in bistable activator-inhibitor media

We show that external fluctuations induce excitable behavior in a bistable spatially extended system with activator-inhibitor dynamics of the FitzHugh-Nagumo type. This can be understood as a mechanism for sustained signal propagation in bistable media. The phase diagram of the stochastic system is analytically obtained and numerically verified. For small-noise intensities, front propagation becomes unstable, and excitable pulses arise as the only possible spatiotemporal behavior of the system. For large-noise intensities, on the other hand, the system enters an effective regime of oscillatory behavior, where it exhibits spontaneous nucleation of pulses and synchronized firing.

Slow Dynamics of Ising Models with Energy Barriers

Using Monte Carlo simulations we study the dynamics of three-dimensional Ising models with nearest-, next-nearest-, and four-spin (plaquette) interactions. During coarsening, such models develop growing energy barriers, which leads to very slow dynamics at low temperature. As already reported, the model with only the plaquette interaction exhibits some of the features characteristic of ordinary glasses: strong metastability of the supercooled liquid, a weak increase of the characteristic length under cooling, stretched-exponential relaxation, and aging. The addition of two-spin interactions, in general, destroys such behavior: the liquid phase loses metastability and the slow-dynamics regime terminates well below the melting transition, which is presumably related with a certain corner-rounding transition. However, for a particular choice of interaction constants, when the ground state is strongly degenerate, our simulations suggest that the slow-dynamics regime extends up to the melting transition. The analysis of these models leads us to the conjecture that in the four-spin Ising model domain walls lose their tension at the glassy transition and that they are basically tensionless in the glassy phase.

Colored noise in spatially extended systems

We study the effects of time and space correlations of an external additive colored noise on the steady-state behavior of a time-dependent Ginzburg-Landau model. Simulations show the existence of nonequilibrium phase transitions controlled by both the correlation time and length of the noise. A Fokker-Planck equation and the steady probability density of the process are obtained by means of a theoretical approximation.

Dynamical Systems approach to Saffman-Taylor fingering. A Dynamical Solvability Scenario

A dynamical systems approach to competition of Saffman-Taylor fingers in a Hele-Shaw channel is developed. This is based on global analysis of the phase space flow of the low-dimensional ordinary-differential-equation sets associated with the classes of exact solutions of the problem without surface tension. Some simple examples are studied in detail. A general proof of the existence of finite-time singularities for broad classes of solutions is given. Solutions leading to finite-time interface pinchoff are also identified. The existence of a continuum of multifinger fixed points and its dynamical implications are discussed. We conclude that exact zero-surface tension solutions taken in a global sense as families of trajectories in phase space are unphysical because the multifinger fixed points are nonhyperbolic, and an unfolding does not exist within the same class of solutions. Hyperbolicity (saddle-point structure) of the multifinger fixed points is argued to be essential to the physically correct qualitative description of finger competition. The restoring of hyperbolicity by surface tension is proposed as the key point to formulate a generic dynamical solvability scenario for interfacial pattern selection.

Nonequilibrium transitions induced by multiplicative noise

A simple model exhibiting a noise-induced ordering transition (NIOT) and a noise-induced disordering transition (NIDT), in which the noise is purely multiplicative, is presented. Both transitions are found in two dimensions as well as in one dimension. We show analytically and numerically that the critical behavior of these two transitions is described by the so called multiplicative noise (MN) universality class. A computation of the set of critical exponents is presented in both d=1 and d=2.

Fluctuations in Saffman-Taylor fingers with quenched disorder

We make an experimental characterization of the effect that static disorder has on the shape of a normal Saffman-Taylor finger. We find that static noise induces a small amplitude and long wavelength instability on the sides of the finger. Fluctuations on the finger sides have a dominant wavelength, indicating that the system acts as a selective amplifier of static noise. The dominant wavelength does not seem to be very sensitive to the intensity of static noise present in the system. On the other hand, at a given flow rate, rms fluctuations of the finger width, decrease with decreasing intensity of static noise. This might explain why the sides of the fingers are flat for typical Saffman-Taylor experiments. Comparison with previous numerical studies of the effect that temporal noise has on the Saffman-Taylor finger, leads to conclude that the effect of temporal noise and static noise are similar. The behavior of fluctuations of the finger width found in our experiments, is qualitatively similar to one recently reported, in the sense that, the magnitude of the width fluctuations decays as a power law of the capillary number, at low flow rates, and increases with capillary number for larger flow rates.