Distributions of avalanches in martensitic transformations

An experimental study of the acoustic emission generated during a martensitic transformation is presented. A statistical analysis of the amplitude and lifetime of a large number of signals has revealed power-law behavior for both magnitudes. The exponents of these distributions have been evaluated and, through independent measurements of the statistical lifetime to amplitude dependence, we have checked the scaling relation between the exponents. Our results are discussed in terms of current ideas on avalanche dynamics.

Phase-field model of Hele-Shaw flows in the high-viscosity contrast regime

A one-sided phase-field model is proposed to study the dynamics of unstable interfaces of Hele-Shaw flows in the high viscosity contrast regime. The corresponding macroscopic equations are obtained by means of an asymptotic expansion from the phase-field model. Numerical integrations of the phase-field model in a rectangular Hele-Shaw cell reproduce finger competition with the final evolution to a steady-state finger.

Influence of disorder strength on phase-field models of interfacial growth

We study the influence of disorder strength on the interface roughening process in a phase-field model with locally conserved dynamics. We consider two cases where the mobility coefficient multiplying the locally conserved current is either constant throughout the system (the two-sided model) or becomes zero in the phase into which the interface advances (one-sided model). In the limit of weak disorder, both models are completely equivalent and can reproduce the physical process of a fluid diffusively invading a porous media, where super-rough scaling of the interface fluctuations occurs. On the other hand, increasing disorder causes the scaling properties to change to intrinsic anomalous scaling. In the limit of strong disorder this behavior prevails for the one-sided model, whereas for the two-sided case, nucleation of domains in front of the invading front are observed.

Side-branch growth in two-dimensional dendrits. Part II: Phase-field model

The development of side-branching in solidifying dendrites in a regime of large values of the Peclet number is studied by means of a phase-field model. We have compared our numerical results with experiments of the preceding paper and we obtain good qualitative agreement. The growth rate of each side branch shows a power-law behavior from the early stages of its life. From their birth, branches which finally succeed in the competition process of side-branching development have a greater growth exponent than branches which are stopped. Coarsening of branches is entirely defined by their geometrical position relative to their dominant neighbors. The winner branches escape from the diffusive field of the main dendrite and become independent dendrites.

Phase-field approach to spatial perturbations in normal Saffman-Taylor fingers

We make a numerical study of the effect that spatial perturbations have in normal Saffman-Taylor fingers driven at constant pressure gradients. We use a phase field model that allows for spatial variations in the Hele-Shaw cell. We find that, regardless of the specific way in which spatial perturbations are introduced, a lateral instability develops on the sides of the propagating Saffman-Taylor finger. Moreover, the instability exists regardless of the intensity of spatial perturbations in the cell as long as the perturbations are felt by the finger tip. If, as the finger propagates, the spatial perturbations felt by the tip change, the instability is nonperiodic. If, as the finger propagates, the spatial perturbations felt by the tip are persistent, the instability developed is periodic. In the later case, the instability is symmetrical or asymmetrical depending on the intensity of the perturbation.

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.

Gauge transformations in Einstein-Yang-Mills theories

We discuss the relation between spacetime diffeomorphisms and gauge transformations in theories of the YangMills type coupled with Einsteins general relativity. We show that local symmetries of the Hamiltonian and Lagrangian formalisms of these generally covariant gauge systems are equivalent when gauge transformations are required to induce transformations which are projectable under the Legendre map. Although pure YangMills gauge transformations are projectable by themselves, diffeomorphisms are not. Instead, the projectable symmetry group arises from infinitesimal diffeomorphism-inducing transformations which must depend on the lapse function and shift vector of the spacetime metric plus associated gauge transformations. Our results are generalizations of earlier results by ourselves and by Salisbury and Sundermeyer. 2000 American Institute of Physics.

Noether's theorem and gauge transformations. Application to the bosonic string and CP(2,n-1) model

New results on the theory of constrained systems are applied to characterize the generators of Noethers symmetry transformations. As a byproduct, an algorithm to construct gauge transformations in Hamiltonian formalism is derived. This is illustrated with two relevant examples.

Poincar wave equations as Fourier transformations of Galilei wave equations

The relationship between the Poincar and Galilei groups allows us to write the Poincar wave equations for arbitrary spin as a Fourier transform of the Galilean ones. The relation between the Lagrangian formulation for both cases is also studied.

Lee HWA Chung theorem for presympectic manifolds. Canonical transformations for constrained systems

We generalize the analogous of Lee Hwa Chungs theorem to the case of presymplectic manifolds. As an application, we study the canonical transformations of a canonical system (M, S, O). The role of Dirac brackets as a test of canonicity is clarified.