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.

Kinematic reduction of reaction-diffusion fronts with multiplicative noise. Derivation of stochastic sharp-interface equations

We study the dynamics of generic reaction-diffusion fronts, including pulses and chemical waves, in the presence of multiplicative noise. We discuss the connection between the reaction-diffusion Langevin-like field equations and the kinematic (eikonal) description in terms of a stochastic moving-boundary or sharp-interface approximation. We find that the effective noise is additive and we relate its strength to the noise parameters in the original field equations, to first order in noise strength, but including a partial resummation to all orders which captures the singular dependence on the microscopic cutoff associated with the spatial correlation of the noise. This dependence is essential for a quantitative and qualitative understanding of fluctuating fronts, affecting both scaling properties and nonuniversal quantities. Our results predict phenomena such as the shift of the transition point between the pushed and pulled regimes of front propagation, in terms of the noise parameters, and the corresponding transition to a non-Kardar-Parisi-Zhang universality class. We assess the quantitative validity of the results in several examples including equilibrium fluctuations and kinetic roughening. We also predict and observe a noise-induced pushed-pulled transition. The analytical predictions are successfully tested against rigorous results and show excellent agreement with numerical simulations of reaction-diffusion field equations with multiplicative noise.

Front propagation in spatially modulated media

A two-dimensional reaction-diffusion front which propagates in a modulated medium is studied. The modulation consists of a spatial variation of the local front velocity in the transverse direction to that of the front propagation. We study analytically and numerically the final steady-state velocity and shape of the front, resulting from a nontrivial interplay between the local curvature effects and the global competition process between different maxima of the control parameter. The transient dynamics of the process is also studied numerically and analytically by means of singular perturbation techniques.

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

Canonical Noether symmetries and commutativity properties for gauge systems

For a dynamical system defined by a singular Lagrangian, canonical Noether symmetries are characterized in terms of their commutation relations with the evolution operators of Lagrangian and Hamiltonian formalisms. Separate characterizations are given in phase space, in velocity space, and through an evolution operator that links both spaces. 2000 American Institute of Physics.

SAFO fragmento 16 V: El Deslumbramiento

E1 fr. 16 V es un breve poema en el que, argumentando con rigurosa lógica y utilizando como ejemplo demostrativo el mito de Helena, Safo formula la más antigua teorización conocida sobre la naturaleza de la belleza. Su modernidad es sorprendente; la belleza no es una cualidad absoluta, sino el producto fantasmático del impulso sexual. Los pormenores de su fenomenalogía se desglosan con el apoyo de la tradición homérica: el deslumbramiento inicial trastorna los sentidos creando apariencias ilusorias, ciega la ruzón, enajena, provoca olvido; pero cuando el deseo se extingue retornan memoria y conciencia, y con ellas el dolor. Se entiende así que la Helena que ya está de vuelta, la de la Odisea, proceda a administrar su seducción como una droga analgésica. El proccso se repite constantemente; sus sujetos somos todos, cualquiera, y su actualización afecta, más alla de la singular experiencia psica-física a las prácticas matrimoniales de la época, donde no se contemplava la elección de pareja y la mujer abandonaba su entorno para inscribirse en el del marido. Así la poesía de Safo, que forma parte de la iniciación a la vida adulta femenina, al poner al descubierto la relatividad de la belleza dentro del mecanismo amoroso, distancia a sus pupilas de sus propias emociones y las protege de la soledad insertándolas en una experiencia religiosa compartida.

Time-resolved imaging of the laser forward transfer of liquids

Time-resolved imaging is carried out to study the dynamics of the laser-induced forward transfer of an aqueous solution at different laser fluences. The transfer mechanisms are elucidated, and directly correlated with the material deposited at the analyzed irradiation conditions. It is found that there exists a fluence range in which regular and well-defined droplets are deposited. In this case, laser pulse energy absorption results in the formation of a plasma, which expansion originates a cavitation bubble in the liquid. After the further expansion and collapse of the bubble, a long and uniform jet is developed, which advances at a constant velocity until it reaches the receptor substrate. On the other hand, for lower fluences no material is deposited. In this case, although a jet can be also generated, it recoils before reaching the substrate. For higher fluences, splashing is observed on the receptor substrate due to the bursting of the cavitation bubble. Finally, a discussion of the possible mechanisms which lead to such singular dynamics is also provided.

A reduction of order two for infinite-order Lagrangians

Given a Lagrangian system depending on the position derivatives of any order, and assuming that certain conditions are satisfied, a second-order differential system is obtained such that its solutions also satisfy the Euler equations derived from the original Lagrangian. A generalization of the singular Lagrangian formalism permits a reduction of order keeping the canonical formalism in sight. Finally, the general results obtained in the first part of the paper are applied to Wheeler-Feynman electrodynamics for two charged point particles up to order 1/c4.

Open inflation and the singulary boundary

The singularity in the Hawking-Turok model of open inflation has some appealing properties, such as the fact that its action is integrable. Also, if one thinks of the singularity as the boundary of spacetime, then the Gibbons-Hawking term is nonvanishing and finite. Here, we consider a model where the gravitational and scalar fields are coupled to a dynamical membrane. The singular instanton can then be obtained as the limit of a family of no-boundary solutions where both the geometry and the scalar field are regular. Using this procedure, the contribution of the singularity to the Euclidean action is just 1/3 of the Gibbons-Hawking term. Unrelated to this issue, we also point out that the singularity acts as a reflecting boundary for scalar perturbations and gravity waves. Therefore, the quantization of cosmological perturbations seems to be well posed in this background.

Finite energy Dirac-Born-Infeld monopoles and string junctions

It is shown that the world volume field theory of a single D3-brane in a supergravity D3-brane background admits finite energy, and non-singular, Abelian monopoles and dyons preserving 1/2 or 1/4 of the N=4 supersymmetry and saturating a Bogomolnyi-type bound. The 1/4 supersymmetric solitons provide a world volume realization of string-junction dyons. We also discuss the dual M-theory realization of the 1/2 supersymmetric dyons as finite tension self-dual strings on the M5-brane, and of the 1/4 supersymmetric dyons as their intersections.

Exactly solvable phase oscillator models with syncrhonization dynamics

Populations of phase oscillators interacting globally through a general coupling function f(x) have been considered. We analyze the conditions required to ensure the existence of a Lyapunov functional giving close expressions for it in terms of a generating function. We have also proposed a family of exactly solvable models with singular couplings showing that it is possible to map the synchronization phenomenon into other physical problems. In particular, the stationary solutions of the least singular coupling considered, f(x) = sgn(x), have been found analytically in terms of elliptic functions. This last case is one of the few nontrivial models for synchronization dynamics which can be analytically solved.

La ontología del espíritu: principio de epistemología de G. de Ockham

El principio radical de toda la filosofía de Ockham no es ni una metafísica del singular, ni una actitud logicista, teologal oescéptica. El Inceptor es la culminación de una tendencia neoplatónica, también central en el Eriúgena: aun para la creatura humanalo "inteligente" es anterior y ontológicamente superior a lo "inteligible" o "sensible".Heredado de Agustín de Hipona, pero transformado en el análisis hasta ser inmediato precedente de la Modernidad o comienzo de ella, el "yo pienso" es el quicio del sistema de Ockman. De la exacta acotación moderna de "espíritu" arranca todo el sistema; a partir de él se justifican incluso los rasgos que más sorprende hallar en un filósofo del siglo XIV: la centralidad de las nociones opuestas "intuición/evidencia", la plena actividad cognoscitiva del espíritu junto a la pasividad del intelecto, la nula causalidad próxima de las cosas sensibles en el conocimiento humano, e! paradigma perfectamente lingüístico del conocer. El nacimiento de una moderna "teoría del conocimiento", se da a partir de la constatación de que el acto más perfecto y paradigmáticode la vida del espíritu es la intuición de los "intellectualia" que radican en él mismo, y no la captación de los externos "sensibilia" aristotélicos.

Front propagation in spatially modulated media

A two-dimensional reaction-diffusion front which propagates in a modulated medium is studied. The modulation consists of a spatial variation of the local front velocity in the transverse direction to that of the front propagation. We study analytically and numerically the final steady-state velocity and shape of the front, resulting from a nontrivial interplay between the local curvature effects and the global competition process between different maxima of the control parameter. The transient dynamics of the process is also studied numerically and analytically by means of singular perturbation techniques.

Una Cantimplora de fayenza egipcia procedente de la necrópolis de Les Casetes (La Vila Joiosa, Alicante)

La urbanización de unas parcelas en la ciudad de la Vila Joiosa (Alicante), puso al descubierto una interesante necrópolis con ajuares que pueden remontarse hasta finales del siglo VII a.n.e. En una de las tumbas, la número 18, formando parte de su ajuar se encontraba una cantimplora de fayenza que contiene en sus laterales dos cartelas con jeroglíficos egipcios. En este trabajo presentamos el yacimiento, así como el contexto donde se recuperó esta pieza, de la que realizamos un estudio más específico dado su carácter singular.