Correlations in avalanche critical points

Acoustic Emissions during Structural Changes in Shape Memory Alloys

Structural changes (martensitic transformation, rearrangements of martensitic variants) in shape memory alloys have an intermittent character that is accompanied by the emission of different (thermal, acoustic, and magnetic) noises, which are fingerprints of the driven criticality, resulting in a damped power-law behaviour. We will illustrate what kinds of important information can be obtained on the structural changes in shape memory alloys. It was established that the power exponents of distributions of acoustic emission (AE) parameters (energy, amplitude, etc.), belonging to martensitic transformations, show quite a universal character and depend only on the symmetry of the martensite. However, we have shown that the asymmetry of the transformation (the exponents are different for the forward and reverse transformations) results in as large differences as those due to the martensite symmetry. We will also demonstrate how the recently introduced AE clustering method can help to identify the different contributions responsible for the asymmetry. The usefulness of the investigations of time correlations between the subsequent events and correlations between acoustic and magnetic noise events in ferromagnetic shape memory alloys will be demonstrated too. Finally, examples of acoustic and magnetic emissions during variant rearrangements (superplastic or superelastic behaviour) in the martensitic state will be described.

Dynamical properties of random-field Ising model

Extensive Monte Carlo simulations are performed on a two-dimensional random field Ising model. The purpose of the present work is to study the disorder-induced changes in the properties of disordered spin systems. The time evolution of the domain growth, the order parameter, and the spin-spin correlation functions are studied in the nonequilibrium regime. The dynamical evolution of the order parameter and the domain growth shows a power law scaling with disorder-dependent exponents. It is observed that for weak random fields, the two-dimensional random field Ising model possesses long-range order. Except for weak disorder, exchange interaction never wins over pinning interaction to establish long-range order in the system.

Tuning coupling: discrete changes in runaway avalanche sizes in disordered media

Hysteretic systems may exhibit a runaway avalanche in which a large fraction of the constituents of the system collectively change state. It would be very valuable to understand the role that interaction strength between constituents plays in the size of such catastrophic runaway avalanches. We use a simple model, the random field Ising model, to study how the size of the runaway avalanche changes as the coupling between spins, J, is tuned. In particular, we calculate P(S), the distribution of size changes S in the runaway avalanche size as J comes close to a critical value J(c), and find that the distribution scales as P(S)∼S(-τ)D(S(σ)(J/J(c)-1)), with τ and σ critical exponents and D(x) a universal scaling function. In mean field theory we find τ=3/2, σ=1/2, and D(x)=exp[-(3x)(1/σ)/2]. On the basis of these results and previous studies, we also predict that for three dimensions τ=1.6 and σ=0.24.