Phase-field model for Hele-Shaw flows with arabitrary contrast II: numerical approach

We present a phase-field model for the dynamics of the interface between two inmiscible fluids with arbitrary viscosity contrast in a rectangular Hele-Shaw cell. With asymptotic matching techniques we check the model to yield the right Hele-Shaw equations in the sharp-interface limit, and compute the corrections to these equations to first order in the interface thickness. We also compute the effect of such corrections on the linear dispersion relation of the planar interface. We discuss in detail the conditions on the interface thickness to control the accuracy and convergence of the phase-field model to the limiting Hele-Shaw dynamics. In particular, the convergence appears to be slower for high viscosity contrasts.

Viscous fingering as a paradigm of interfacial pattern formation: Recent results and new challenges

We review recent results on dynamical aspects of viscous fingering. The Saffman¿Taylor instability is studied beyond linear stability analysis by means of a weakly nonlinear analysis and the exact determination of the subcritical branch. A series of contributions pursuing the idea of a dynamical solvability scenario associated to surface tension in analogy with the traditional selection theory is put in perspective and discussed in the light of the asymptotic theory of Tanveer and co-workers. The inherently dynamical singular effects of surface tension are clarified. The dynamical role of viscosity contrast is explored numerically. We find that the basin of attraction of the Saffman¿Taylor finger depends on viscosity contrast, and that the sensitivity to this parameter is maximal in the usual limit of high viscosity contrast. The competing attractors are identified as closed bubble solutions. We briefly report on recent results and work in progress concerning rotating Hele-Shaw flows, topological singularities and wetting effects, and also discuss future directions in the context of viscous fingering

Preisach modeling of hysteresis for a pseudoelastic Cu-Zn-Al single crystal

Stress-strain trajectories associated with pseudoelastic behavior of a Cu¿19.4 Zn¿13.1 Al (at.%) single crystal at room temperature have been determined experimentally. For a constant cross-head speed the trajectories and the associated hysteresis behavior are perfectly reproducible; the trajectories exhibit memory properties, dependent only on the values of return points, where transformation direction is reverted. An adapted version of the Preisach model for hysteresis has been implemented to predict the observed trajectories, using a set of experimental first¿order reversal curves as input data. Explicit formulas have been derived giving all trajectories in terms of this data set, with no adjustable parameters. Comparison between experimental and calculated trajectories shows a much better agreement for descending than for ascending paths, an indication of a dissymmetry between the dissipation mechanisms operative in forward and reverse directions of martensitic transformation.

Elasticity and melting of vortex crystals in anisotropic superconductors: Beyond the continuum regime.

The elastic moduli of vortex crystals in anisotropic superconductors are frequently involved in the investigation of their phase diagram and transport properties. We provide a detailed analysis of the harmonic eigenvalues (normal modes) of the vortex lattice for general values of the magnetic field strength, going beyond the elastic continuum regime. The detailed behavior of these wave-vector-dependent eigenvalues within the Brillouin zone (BZ), is compared with several frequently used approximations that we also recalculate. Throughout the BZ, transverse modes are less costly than their longitudinal counterparts, and there is an angular dependence which becomes more marked close to the zone boundary. Based on these results, we propose an analytic correction to the nonlocal continuum formulas which fits quite well the numerical behavior of the eigenvalues in the London regime. We use this approximate expression to calculate thermal fluctuations and the full melting line (according to Lindeman's criterion) for various values of the anisotropy parameter.

Magnetic properties of Fe-Cu-Nb-Si-B nanocrystaliine magnetic alloys

Several ribbons of composition Fe73.5Cu1Nb 3Si16.5B6 and Fe73.5Cu1 Nb3Si13.5B9 were prepared by annealing the as-quenched samples between 525°C and 700°C; which induced nucleation of nanocrystallites of Fe bcc-type composition. Mean grain sizes were obtained from X-ray diffraction. Static magnetic properties were measured with both a Magnet Physik Hysteresis-Graph (up to 200 Oe) and a SHE SQUID magnetometer (up to 50 kOe). Soft magnetic parameters (coercive field and initial permeability) were very sensitive to grain size. The ZFC magnetization at low field showed a broad peak at a temperature TM, thus signalling a certain distribution of nanocrystalline sizes, and TM strongly decreased when the mean grain size decreased. Isothermal magnetization curves at low temperature showed the expected asymptotic behavior of a random magnet material at low and high fields.

Estimation of the parameters of the gravitational-wage signal of a coalescing binary system

The statistical theory of signal detection and the estimation of its parameters are reviewed and applied to the case of detection of the gravitational-wave signal from a coalescing binary by a laser interferometer. The correlation integral and the covariance matrix for all possible static configurations are investigated numerically. Approximate analytic formulas are derived for the case of narrow band sensitivity configuration of the detector.

Cosmic strings and Einstein-Rosen soliton waves

We consider all generalized soliton solutions of the Einstein-Rosen form in the cylindrical context. They are Petrov type-I solutions which describe solitonlike waves interacting with a line source placed on the symmetry axis. Some of the solutions develop a curvature singularity on the axis which is typical of massive line sources, whereas others just have the conical singularity revealing the presence of a static cosmic string. The analysis is based on the asymptotic behavior of the Riemann and metric tensors, the deficit angle, and a C-velocity associated to Thornes C-energy. The C-energy is found to be radiated along the null directions.

Internal and external fluctuations around nonequilibrium steady states in one-dimensional heat-conduction problems

Thermal fluctuations around inhomogeneous nonequilibrium steady states of one-dimensional rigid heat conductors are analyzed in the framework of generalized fluctuating hydrodynamics. The effect of an external source of noise is also considered. External fluctuations come from temperature and position fluctuations of the source. Contributions of each kind of noise to the temperature correlation function are computed and compared through the study of its asymptotic behavior.

Bistability driven by white shot noise

We consider mean-first-passage times and transition rates in bistable systems driven by white shot noise. We obtain closed analytical expressions, asymptotic approximations, and numerical simulations in two cases of interest: (i) jumps sizes exponentially distributed and (ii) jumps of the same size.

Bistability driven by dichotomous noise

We consider mean-first-passage times and transition rates in bistable systems driven by dichotomous colored noise. We carry out an asymptotic expansion for short correlation times ¿c of the colored noise and find results that differ from those reported earlier. In particular, to retain corrections to O(¿c) we find that it is necessary to retain up to four derivatives of the potential function. We compare our asymptotic results to existing ones and also to exact ones obtained from numerical integration.

Exact solution to the exit-time problem for an undamped free particle driven by Gaussian white noise

In a recent paper [Phys. Rev. Lett. 75, 189 (1995)] we have presented the exact analytical expression for the mean exit time, T(x,v), of a free inertial process driven by Gaussian white noise out of a region (0,L) in space. In this paper we give a detailed account of the method employed and present results on asymptotic properties and averages of T(x,v).

Damage spreading transition in glasses: A probe for the ruggedness of the configurational landscape

We consider damage spreading transitions in the framework of mode-coupling theory. This theory describes relaxation processes in glasses in the mean-field approximation which are known to be characterized by the presence of an exponentially large number of metastable states. For systems evolving under identical but arbitrarily correlated noises, we demonstrate that there exists a critical temperature T0 which separates two different dynamical regimes depending on whether damage spreads or not in the asymptotic long-time limit. This transition exists for generic noise correlations such that the zero damage solution is stable at high temperatures, being minimal for maximal noise correlations. Although this dynamical transition depends on the type of noise correlations, we show that the asymptotic damage has the good properties of a dynamical order parameter, such as (i) independence of the initial damage; (ii) independence of the class of initial condition; and (iii) stability of the transition in the presence of asymmetric interactions which violate detailed balance. For maximally correlated noises we suggest that damage spreading occurs due to the presence of a divergent number of saddle points (as well as metastable states) in the thermodynamic limit consequence of the ruggedness of the free-energy landscape which characterizes the glassy state. These results are then compared to extensive numerical simulations of a mean-field glass model (the Bernasconi model) with Monte Carlo heat-bath dynamics. The freedom of choosing arbitrary noise correlations for Langevin dynamics makes damage spreading an interesting tool to probe the ruggedness of the configurational landscape.

Extreme times for volatility processes

Extreme times techniques, generally applied to nonequilibrium statistical mechanical processes, are also useful for a better understanding of financial markets. We present a detailed study on the mean first-passage time for the volatility of return time series. The empirical results extracted from daily data of major indices seem to follow the same law regardless of the kind of index thus suggesting an universal pattern. The empirical mean first-passage time to a certain level L is fairly different from that of the Wiener process showing a dissimilar behavior depending on whether L is higher or lower than the average volatility. All of this indicates a more complex dynamics in which a reverting force drives volatility toward its mean value. We thus present the mean first-passage time expressions of the most common stochastic volatility models whose approach is comparable to the random diffusion description. We discuss asymptotic approximations of these models and confront them to empirical results with a good agreement with the exponential Ornstein-Uhlenbeck model.

An AdS/QCD model from tachyon condensation: II

A simple holographic model is presented and analyzed that describes chiral symmetry breaking and the physics of the meson sector in QCD. This is a bottom-up model that incorporates string theory ingredients like tachyon condensation which is expected to be the main manifestation of chiral symmetry breaking in the holographic context. As a model for glue the Kuperstein-Sonnenschein background is used. The structure of the flavor vacuum is analyzed in the quenched approximation. Chiral symmetry breaking is shown at zero temperature. Above the deconfinement transition chiral symmetry is restored. A complete holographic renormalization is performed and the chiral condensate is calculated for different quark masses both at zero and non-zero temperatures. The 0++, 0¿+, 1++, 1¿¿ meson trajectories are analyzed and their masses and decay constants are computed. The asymptotic trajectories are linear. The model has one phenomenological parameter beyond those of QCD that affects the 1++, 0¿+ sectors. Fitting this parameter we obtain very good agreement with data. The model improves in several ways the popular hard-wall and soft wall bottom-up models.

On the nucleolus of 2 x 2 assignment games

[spa] En este artículo hallamos fórmulas para el nucleolo de juegos de asignación arbitrarios con dos compradores y dos vendedores. Se analizan cinco casos distintos, dependiendo de las entradas en la matriz de asignación. Los resultados se extienden a los casos de juegos de asignación de tipo 2 x m o m x 2.