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The jerky motion of twin boundaries in the ferromagnetic shape memory alloy Ni-Mn-Ga is studied by simultaneous measurements of stress and magnetic emissions (ME). A careful design of the experimental conditions results in an approximately linear relationship between the measured ME voltage and the nm-scale volumes exhibiting twinning transformation during microsecondscale abrupt "avalanche" events. This study shows that the same distributions of ME avalanches, related to features of jerky twin boundary motion, are found both during and between stress drop events. Maximum likelihood analysis of statistical distributions of several variables reveals a good fit to power laws truncated by exponential functions. Interestingly, the characteristic cutoffs described by the exponential functions are in the middle of the distribution range. Further, the cutoff values can be related to the physical characteristics of the studied problem. Particularly, the cutoff of amplitudes of ME avalanches matches the value predicted by high rate magnetic pulse tests performed under much larger driving force values. This observation implies that avalanches during slow rate twin boundary motion and velocity changes observed by high rate tests represent the same behavior and can be described by the same theory.

Temporal average shapes of crackling noise avalanches, U(t) (U is the detected parameter proportional to the interface velocity), have self-similar behavior, and it is expected that by appropriate normalization, they can be scaled together according to a universal scaling function. There are also universal scaling relations between the avalanche parameters (amplitude, A, energy, E, size (area), S, and duration, T), which in the mean field theory (MFT) have the form E∝A3, S∝A2, S∝T2. Recently, it turned out that normalizing the theoretically predicted average U(t) function at a fixed size, U(t)=atexp−bt2 (a and b are non-universal, material-dependent constants) by A and the rising time, R, a universal function can be obtained for acoustic emission (AE) avalanches emitted during interface motions in martensitic transformations, using the relation R~A1−φ too, where φ is a mechanism-dependent constant. It was shown that φ also appears in the scaling relations E~A3−φ and S~A2−φ, in accordance with the enigma for AE, that the above exponents are close to 2 and 1, respectively (in the MFT limit, i.e., with φ= 0, they are 3 and 2, respectively). In this paper, we analyze these properties for acoustic emission measurements carried out during the jerky motion of a single twin boundary in a Ni50Mn28.5Ga21.5 single crystal during slow compression. We show that calculating from the above-mentioned relations and normalizing the time axis of the average avalanche shapes with A1−φ, and the voltage axis with A, the averaged avalanche shapes for the fixed area are well scaled together for different size ranges. These have similar universal shapes as those obtained for the intermittent motion of austenite/martensite interfaces in two different shape memory alloys. The averaged shapes for a fixed duration, although they could be acceptably scaled together, showed a strong positive asymmetry (the avalanches decelerate much slower than they accelerate) and thus did not show a shape reminiscent of an inverted parabola, predicted by the MFT. For comparison, the above scaling exponents were also calculated from simultaneously measured magnetic emission data. It was obtained that the φ values are in accordance with theoretical predictions going beyond the MFT, but the AE results for φ are characteristically different from these, supporting that the well-known enigma for AE is related to this deviation.

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Dynamic mode decomposition (DMD) is a leading tool for equation-free analysis of high-dimensional dynamical systems from observations. In this work, we focus on a combination of DMD and delay-coordinates embedding, which is termed delay-coordinates DMD and is based on augmenting observations from current and past time steps, accommodating the analysis of a broad family of observations. An important utility of DMD is the compact and reduced-order spectral representation of observations in terms of the DMD eigenvalues and modes, where the temporal information is separated from the spatial information. From a spatiotemporal viewpoint, we show that when DMD is applied to delay-coordinates embedding, temporal information is intertwined with spatial information, inducing a particular spectral structure on the DMD components. We formulate and analyze this structure, which we term the spatiotemporal coupling in delay-coordinates DMD. Based on this spatiotemporal coupling, we propose a new method for DMD components selection. When using delay-coordinates DMD that comprises redundant modes, this selection is an essential step for obtaining a compact and reduced-order representation of the observations. We demonstrate our method on noisy simulated signals and various dynamical systems and show superior component selection compared to a commonly used method that relies on the amplitudes of the modes.

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