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.

Magnetoelastic behavior of the Heusler Ni2MnGa alloy

In this work the effect of the interplay between magnetic and structural degrees of freedom in the structural transitions undergone by Ni2MnGa alloy is investigated. Elastic constant and magnetic susceptibility measurements in a magnetic field are presented. A simple phenomenological model is proposed to account for the experimental observations.

Lattice-gas model of particles with orientational and positional degrees of freedom: Mean-field treatment

We consider a lattice-gas model of particles with internal orientational degrees of freedom. In addition to antiferromagnetic nearest-neighbor (NN) and next-nearest-neighbor (NNN) positional interactions we also consider NN and NNN interactions arising from the internal state of the particles. The system then shows positional and orientational ordering modes with associated phase transitions at Tp and To temperatures at which long-range positional and orientational ordering are, respectively, lost. We use mean-field techniques to obtain a general approach to the study of these systems. By considering particular forms of the orientational interaction function we study coupling effects between both phase transitions arising from the interplay between orientational and positional degrees of freedom. In mean-field approximation coupling effects appear only for the phase transition taking place at lower temperatures. The strength of the coupling depends on the value of the long-range order parameter that remains finite at that temperature.

Lattice-gas model of orientable molecules: Application to liquid crystals

We have analyzed a two-dimensional lattice-gas model of cylindrical molecules which can exhibit four possible orientations. The Hamiltonian of the model contains positional and orientational energy interaction terms. The ground state of the model has been investigated on the basis of Karl¿s theorem. Monte Carlo simulation results have confirmed the predicted ground state. The model is able to reproduce, with appropriate values of the Hamiltonian parameters, both, a smectic-nematic-like transition and a nematic-isotropic-like transition. We have also analyzed the phase diagram of the system by mean-field techniques and Monte Carlo simulations. Mean-field calculations agree well qualitatively with Monte Carlo results but overestimate transition temperatures.

Woody Allen y el espíritu de la tragedia griega: de Crimes and Misdemeanors a Match Point

Numerosos son ya los estudios que se han centrado en el llamado "cine serio" de Woody Allen y, entre ellos, cabe mencionar el que Pau Gilabert Barberà, autor de este artículo, escribió (2006) sobre lo que, en su opinión, es el legado sofístico subyacente en el guión de Crimes and Misdemeanors. En esta ocasión, su objetivo es analizar la trayectoria fluctuante del director americano en relación con la tragedia griega, desde la convicción de que, sólo así, es posible revelar su empatía con el espíritu trágico de los griegos y comprender su necesidad de presentar aquel género literario como un paradigma desde el cual entender las grandezas y miserias del mundo contemporáneo.

Coordenadas clásicas de Shadowlands de Richard Attenborough (sobre la vida y obra de C. S. Lewis)

El objetivo de este artículo es mostrar los parámetros clásicos de Shadowlands de R. Attenborough, con guión de W. Nicholson, sobre la vida y obra de C. S. Lewis. Basándose en un análisis minucioso de los textos de Lewis, el autor propone interpretar la oposición Lewis / Gresham como la traducción en la vida real de la oposición entre los temperamentos platónico o idealista y aristotélico o materialista que ya mencionaba Coleridge. En cualquier caso, son muchas las referencias clásicas que hay que tener en cuenta si se quiere comprender hasta qué punto el cristianismo de Lewis es también un cristianismo clásico, es decir grecolatino.

New York versus la tragedia y Edipo. El legado sofocleo -y sofístico- en Crimes and Misdemeanors de W. Allen

Más allá de la referencia explícita a la tragedia griega y Edipo, el objetivo de este artículo es presentar la estrecha relación, en opinión del autor, entre lo que mantienen los protagonistas en Crimes and Misdemeanors y las teorías de los sofistas griegos sobre Dios, la ley, etc. Una confrontación minuciosa de sus textos con el guión de la película revela claramente unas raíces sofísticas que no pueden ser atribuidas, en este caso, a la presencia constante del legado judío en la obra de W. Allen.

New York versus la tragedia y Edipo. El legado sofocleo -y sofístico- en Crimes and Misdemeanors de W. Allen

Más allá de la referencia explícita a la tragedia griega y Edipo, el objetivo de este artículo es presentar la estrecha relación, en opinión del autor, entre lo que mantienen los protagonistas en Crimes and Misdemeanors y las teorías de los sofistas griegos sobre Dios, la ley, etc. Una confrontación minuciosa de sus textos con el guión de la película revela claramente unas raíces sofísticas que no pueden ser atribuidas, en este caso, a la presencia constante del legado judío en la obra de W. Allen.

Fingerlike aggregates in thin-layer electrodeposition

Electrodeposition experiments conducted in a thin-layer horizontal cell containing a nonbinary aqueous electrolyte prepared with cupric sulfate and sodium sulfate gave rise to fingerlike deposits, a novel and unexpected growth mode in this context. Both the leading instability from which fingers emerge and some distinctive features of their steady evolution are interpreted in terms of a simple model based on the existing theory of fingering in fluids.

Diffraction theory of Fresnel lenses encoded in low-resolution devices

A mathematical model that describes the behavior of low-resolution Fresnel lenses encoded in any low-resolution device (e.g., a spatial light modulator) is developed. The effects of low-resolution codification, such the appearance of new secondary lenses, are studied for a general case. General expressions for the phase of these lenses are developed, showing that each lens behaves as if it were encoded through all pixels of the low-resolution device. Simple expressions for the light distribution in the focal plane and its dependence on the encoded focal length are developed and commented on in detail. For a given codification device an optimum focal length is found for best lens performance. An optimization method for codification of a single lens with a short focal length is proposed.

Diffraction theory of optimized low-resolution Fresnel encoded lenses

A mathematical model describing the behavior of low-resolution Fresnel encoded lenses (LRFEL's) encoded in any low-resolution device (e.g., a spatial light modulator) has recently been developed. From this model, an LRFEL with a short focal length was optimized by our imposing the maximum intensity of light onto the optical axis. With this model, analytical expressions for the light-amplitude distribution, the diffraction efficiency, and the frequency response of the optimized LRFEL's are derived.

Premartensitic and martensitic phase transition in ferromagnetic Ni2MnGa

We present an experimental study of the premartensitic and martensitic phase transitions in a Ni2MnGa single crystal by using ultrasonic techniques. The effect of applied magnetic field and uniaxial compressive stress has been investigated. It has been found that they substantially modify the elastic and magnetic behavior of the alloy. These experimental findings are a consequence of magnetoelastic effects. The measured magnetic and vibrational behavior agrees with the predictions of a recently proposed Landau-type model [A. Planes et al., Phys. Rev. Lett. 79, 3926 (1997)] that incorporates a magnetoelastic coupling as a key ingredient.

Photon spectrum produced by the late decay of a cosmic neutrino background

We obtain the photon spectrum induced by a cosmic background of unstable neutrinos. We study the spectrum in a variety of cosmological scenarios and also we allow for the neutrinos having a momentum distribution (only a critical matter-dominated universe and neutrinos at rest have been considered until now). Our results can be helpful when extracting bounds on neutrino electric and magnetic moments from cosmic photon background observations.