We introduce a modification to Hele-Shaw flows consisting of a rotating cell. A viscous fluid ͑oil͒ is injected at the rotation axis of the cell, which is open to air. The morphological instability of the oil-air interface is thus driven by centrifugal force and is controlled by the density ͑not viscosity͒ difference. We derive the linear dispersion relation and verify the maximum growth rate selection of initial patterns within experimental uncertainty. The nonlinear growth regime is studied in the case of vanishing injection rate. Several characteristic lengths are studied to quantify the patterns obtained. Experimental data exhibit good collapse for two characteristic lengths, namely, the radius of gyration and the radial finger length, which in the nonlinear regime appear to grow linearly in time.

Acoustic emission avalanche distributions are studied in different alloy systems that exhibit a phase transition from a bcc to a close-packed structure. After a small number of thermal cycles through the transition, the distributions become critically stable (exhibit power-law behavior) and can be characterized by an exponent a. The values of a can be classified into universality classes, which depend exclusively on the symmetry of the resulting close-packed structure. [S0031-9007(98) The emission of acoustic waves in the range from kHz to MHz has been acknowledged to be a characteristic of a number of diffusionless first-order structural transitions usually called martensitic. The origin of this acoustic emission (AE) is the sudden change in the local strain field resulting from the phase transition, driven by an external applied field (stress, temperature). Actually, this AE displays many similarities with the seismic waves generated during an earthquake. The amplitude and duration of the acoustic signals generated during martensitic transitions (MT) display power-law distributions, related to the lack of characteristic temporal and spatial scales in the underlying physical mechanism [1,2]. In this respect, the martensitic transition is an example of fluctuationless first-order (FLFO) transition in a disordered system [3]. FLFO phase transitions can be modeled by Ising-type Hamiltonians at T 0 with quenched randomness (fields, bonds, vacancies, etc.). For these models the transition takes place only when the system is driven by an external field. The evolution proceeds by avalanches joining a series of metastable states, until the system is fully transformed. When the external field is reversed, the system returns to the original structure exhibiting history dependence and hysteresis. Because of the absence of thermal fluctuations, the sequence of avalanches determining the hysteresis loop is independent of the driving rate and is reproducible from cycle to cycle if the disorder is quenched. For a particular amount of disorder a critical point has been found [4,5]: At this point the probability distributions of sizes and durations of avalanches are power law and can be characterized by critical exponents. It has been found that these exponents, corresponding to different lattice models, have very similar values, depending only on the system dimensionality [4,5]. This suggests the existence of universality classes. The goal of this Letter is to search for experimental evidence of such universality by studying the amplitude distribution of the AE detected in different systems displaying MT.Besides MT, many first-order transitions display FLFO characteristics. Examples are ferromagnetic materials at low temperature under an applied magnetic field [6,7], precipitation of H in Nb [8], adsorption of liquid He on porous media [9], and superconductivity in granular Al films [10]. In most of these systems critical exponents of the avalanche distribution have been measured. The comparison between the values reported is ...

We present an experimental study of phase-transition avalanches during the stress-induced formation of martensite in a Cu-Zn-Al alloy, with particular attention to the effect of cycling. We have analyzed statistically the amplitudes, durations, and energies of the thermal events accompanying the transition, and found that these magnitudes distribute according to power laws in the first fifty cycles, within experimental error, with exponents ␣ϭ2.3Ϯ0.2, ϭ2.9Ϯ0.7, and ⑀ϭ1.8Ϯ0.3, respectively. However, the extent of power-law behavior is reduced by at least one decade after five hundred transition cycles, and the system is seen to become progressively subcritical. We present a method of measuring the distribution of energy barriers encountered along the transition, which in our case is found to spread over more than four orders of magnitude. Finally, we have observed that repeated cycling leads to a statistical reproducibility of transformation trajectories, and to the remarkable correlation between the cycle-to-cycle trajectory fluctuations and the cycle-averaged response function of the system observed recently in magnetic systems ͓J.S. Urbach, R.C. Madison, and J.T. Markert, Phys. Rev. Lett. 75, 4694 ͑1995͔͒. ͓S0163-1829͑97͒09041-3͔

We have studied the kinetics of thermoelastic martensitic transformations (MT), both experimentally and using spin models. Measurements of acoustic emission and thermal pulses in Cu-Zn-A1 single crystals, during thermally and stress induced MT, show that the transformation takes place as a sequence of avalanches, whose sizes and durations distribute according to power laws in more than one decade. Most features observed are qualitatively reproduced by spin models that incorporate domain interactions and frozen disorder. A systematic simulation of these models at T = 0 (no fluctuations allowed) has shown that there is a critical concentration of disorder for which avalanche sizes and durations distribute following power-laws, which appear to be independent of details of the models other than their dimensionality. We discuss the connection between the experimental results and the simulations.

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