Form Of Avalanches Research Articles

Crackling noise microscopy

Crackling noise is a scale-invariant phenomenon found in various driven nonlinear dynamical material systems as a response to external stimuli such as force or external fields. Jerky material movements in the form of avalanches can span many orders of magnitude in size and follow universal scaling rules described by power laws. The concept was originally studied as Barkhausen noise in magnetic materials and now is used in diverse fields from earthquake research and building materials monitoring to fundamental research involving phase transitions and neural networks. Here, we demonstrate a method for nanoscale crackling noise measurements based on AFM nanoindentation, where the AFM probe can be used to study the crackling of individual nanoscale features, a technique we call crackling noise microscopy. The method is successfully applied to investigate the crackling of individual topological defects, i.e. ferroelectric domain walls. We show that critical exponents for avalanches are altered at these nanoscale features, leading to a suppression of mixed-criticality, which is otherwise present in domains. The presented concept opens the possibility of investigating the crackling of individual nanoscale features in a wide range of material systems.

Microscopic dynamics underlying the stress relaxation of arrested soft materials

Arrested soft materials such as gels and glasses exhibit a slow stress relaxation with a broad distribution of relaxation times in response to linear mechanical perturbations. Although this macroscopic stress relaxation is an essential feature in the application of arrested systems as structural materials, consumer products, foods, and biological materials, the microscopic origins of this relaxation remain poorly understood. Here, we elucidate the microscopic dynamics underlying the stress relaxation of such arrested soft materials under both quiescent and mechanically perturbed conditions through X-ray photon correlation spectroscopy. By studying the dynamics of a model associative gel system that undergoes dynamical arrest in the absence of aging effects, we show that the mean stress relaxation time measured from linear rheometry is directly correlated to the quiescent superdiffusive dynamics of the microscopic clusters, which are governed by a buildup of internal stresses during arrest. We also show that perturbing the system via small mechanical deformations can result in large intermittent fluctuations in the form of avalanches, which give rise to a broad non-Gaussian spectrum of relaxation modes at short times that is observed in stress relaxation measurements. These findings suggest that the linear viscoelastic stress relaxation in arrested soft materials may be governed by nonlinear phenomena involving an interplay of internal stress relaxations and perturbation-induced intermittent avalanches.

Influence of the number of orientational domains on avalanche criticality in ferroelastic transitions.

We study the relationship between avalanche criticality and the number of orientational domains in ferroelastic transitions. To this end, we use a general Ginzburg-Landau model appropriate for displacive transitions of the square lattice. The model includes disorder as a quenched distribution of local transition temperatures. We focus on the square-to-rectangle and the square-to-oblique ferroelastic transitions, which have two and four orientational domains, respectively, which in turn determine the corresponding degeneracy of the ground state of the system. The phase transitions are driven by temperature under the assumption of a strict athermal behavior. That is, we assume that thermal fluctuations do not play any role. Numerical results are obtained using a purely relaxational dynamics, and it is shown that both the square-to-rectangle and the square-to-oblique transitions occur intermittently in the form of avalanches. Avalanche sizes and avalanche energies are found to display power-law distributions, which corroborates avalanche criticality. We compare and contrast the dependence of avalanche criticality on the number of orientational domains of the low-symmetry phase. It is found that the critical exponents depend on that number, in agreement with recent experimental results.

Comparing spatio-temporal networks of intermittent avalanche events: Experiment, model, and empirical data

Abstract Relaxational processes in many complex systems often occur in the form of avalanches resulting from internal cascades from across the system scale. Here, we probe the space, time, and magnitude signatures of avalanching behavior using a network of temporally-directed links subject to a spatial distance criterion between events in the entire catalog. We apply this method onto three systems with avalanche-like characteristics: (i) highly controllable scaled experiments, particularly that of a slowly-driven pile of granular material in a quasi-two-dimensional setup with open edges; (ii) the sandpile, a numerical model of nearest-neighbor interactions in a grid; and (iii) substantially complete empirical data on earthquakes from southern California. Apart from the recovery of the fat-tailed statistics of event sizes, we recover similar power-laws in the spatial and temporal aspects of the networks of these representative systems, hinting at possible common underlying generative mechanisms governing them. By consolidating the results from experiments, numerical models, and empirical data, we can gain a better understanding of these highly nonlinear processes in nature.

Magnetic domain dynamics in an insulating quantum ferromagnet

The statistics and form of avalanches in a driven system reveal the nature of the underlying energy landscape and dynamics. In conventional metallic ferromagnets, eddy-current back action can dominate the dynamics. Here, we study Barkhausen noise in Li(Ho,Y)F4, an insulating Ising ferromagnet that cannot sustain eddy currents. For large avalanches at temperatures approaching the Curie point, we find a symmetric response free of drag effects. In the low temperature limit, drag effects contribute to the dynamics, which we link to enhanced pinning from local random fields that are enabled by the microscopic dipole-coupled Hamiltonian (the Ising model in transverse field).

Bulbous head formation in bidisperse shallow granular flow over an inclined plane

Rapid shallow granular flows over inclined planes are often seen in nature in the form of avalanches, landslides and pyroclastic flows. In these situations the flow develops an inversely graded (large at the top) particle-size distribution perpendicular to the plane. As the surface velocity of such flows is larger than the mean velocity, the larger material is transported to the flow front. This causes size segregation in the downstream direction, resulting in a flow front composed of large particles. Since the large particles are often more frictional than the small, the mobility of the flow front is reduced, resulting in a so-called bulbous head. This study focuses on the formation and evolution of this bulbous head, which we show to emerge in both a depth-averaged continuum framework and discrete particle simulations. Furthermore, our numerical solutions of the continuum model converge to a travelling wave solution, which allows for a very efficient computation of the long-time behaviour of the flow. We use small-scale periodic discrete particle simulations to calibrate (close) our continuum framework, and validate the simple one-dimensional (1-D) model with full-scale 3-D discrete particle simulations. The comparison shows that there are conditions under which the model works surprisingly well given the strong approximations made; for example, instantaneous vertical segregation.

Crackling Dynamics in the Mechanical Response of Knitted Fabrics.

Crackling noise, which occurs in a wide range of situations, is characterized by discrete events of various sizes, often correlated in the form of avalanches. We report experimental evidence that the mechanical response of a knitted fabric displays such broadly distributed events both in the force signal and in the deformation field, with statistics analogous to that of earthquakes or soft amorphous materials. A knit consists of a regular network of frictional contacts, linked by the elasticity of the yarn. When deformed, the fabric displays spatially extended avalanchelike yielding events resulting from collective interyarn contact slips. We measure the size distribution of these avalanches, at the stitch level from the analysis of nonelastic displacement fields and externally from force fluctuations. The two measurements yield consistent power law distributions reminiscent of those found in other avalanching systems. Our study shows that a knitted fabric is not only a thread-based metamaterial with highly sought after mechanical properties, but also an original, model system, with topologically protected structural order, where an intermittent, scale-invariant response emerges from minimal ingredients, and thus a significant landmark in the study of out-of-equilibrium universality.

Austenite avalanche evidenced by uniaxial stress in Ni-Mn-In Heusler single crystal

The martensitic transformation in Ni50Mn34.5In15.5 single crystal was studied by electrical resistivity measurements under controlled and constant uniaxial stress. We observed that the kinetics of the transformation under uniaxial stress, defined as the derivative of the volume fraction of martensite (austenite) with respect to time, present two maxima during heating at a constant rate of 3 K/min. An additional energy is required for the complete transformation to happen and there is a distortion in the hysteretic cycle depending on the rate. The interaction between transformed volume and untransformed volume and inter-variant conversion could be responsible for this distortion adding a local internal stress in the material. The transformation during heating is consequently isothermal. However, a new increase of the austenite restoration rate occurs in an avalanche form when additional superheating leads to an increase in the driving force that does not compensate any more the total strain energy.

Viscoelastic effects in avalanche dynamics: a key to earthquake statistics.

In many complex systems a continuous input of energy over time can be suddenly relaxed in the form of avalanches. Conventional avalanche models disregard the possibility of internal dynamical effects in the interavalanche periods, and thus miss basic features observed in some real systems. We address this issue by studying a model with viscoelastic relaxation, showing how coherent oscillations of the stress field can emerge spontaneously. Remarkably, these oscillations generate avalanche patterns that are similar to those observed in seismic phenomena.

Inhibition causes ceaseless dynamics in networks of excitable nodes.

The collective dynamics of a network of excitable nodes changes dramatically when inhibitory nodes are introduced. We consider inhibitory nodes which may be activated just like excitatory nodes but, upon activating, decrease the probability of activation of network neighbors. We show that, although the direct effect of inhibitory nodes is to decrease activity, the collective dynamics becomes self-sustaining. We explain this counterintuitive result by defining and analyzing a "branching function" which may be thought of as an activity-dependent branching ratio. The shape of the branching function implies that, for a range of global coupling parameters, dynamics are self-sustaining. Within the self-sustaining region of parameter space lies a critical line along which dynamics take the form of avalanches with universal scaling of size and duration, embedded in a ceaseless time series of activity. Our analyses, confirmed by numerical simulation, suggest that inhibition may play a counterintuitive role in excitable networks.

Gas-discharge diagnostics of text on paper

Barrier gas discharge in avalanche form has been used to study a hand-written text on paper with various ages of records. A comparison of the optical images of this text with gas-discharge patterns showed that the latter possess certain advantages. It is demonstrated that barrier discharge can be used for forensic diagnostics of hand-written paper documents with the aim of revealing additions written at various times.

Power-law statistics for avalanches in a martensitic transformation.

We devise a two-dimensional model that mimics the recently observed power-law distributions for the amplitudes and durations of the acoustic emission signals observed during martensitic transformation [Vives et al., Phys. Rev. Lett. 72, 1694 (1994)]. We include a threshold mechanism, long-range interaction between the transformed domains, inertial effects, and dissipation arising due to the motion of the interface. The model exhibits thermal hysteresis and, more importantly, it shows that the energy is released in the form of avalanches with power-law distributions for their amplitudes and durations. Computer simulations also reveal morphological features similar to those observed in real systems.

Pierres écrites et dessinées

Madeleine Pinault Sorensen : Stones in writing and art. This article attempts to show the diverse forms of representation used by artists to introduce into their works different subjects linked to mineralogy, which almost became a leitmotiv in the second half of the 18th Century, with volcanoes, glaciers, grottos, waterfalls and streams. Artists tackled these subjects after having studied mineralogy, when accompanying a travelling scientist, when travelling alone, or when working on the illustrations for a book or catalogue. Thus we can see the diversity of artists' views of mineralogy, from a panorama of nature to a detailed study of a sample, for example. A whole aspect of landscape painting was thereby transformed, and even more so at the end of the century when sensibility moved towards a clear taste for the unchained elements, in the form of avalanches, storms, eruptions of Vesuvius and earthquakes. These nightmare visions emphasize humain frailty and precarity in the face of nature.

ＭｎＡｌ?S６?T相を中心とするＭｎ‐Ａｌ同時蒸着膜の結晶化

Mn-Al films with different compositions ranging from 8 to 21 at. % Mn were prepared by simultaneous vacuum deposition and their crystallization occurring in the temperature rise and their crystal structures were investigated through transmission electron micrographs and the diffraction patterns. Shape of the crystals emerging in the films depends on their composition. MnAl6 crystals grow in complete circular form when the composition is exactly at that of MnAl6, i.e. 14 at. % Mn. As the composition increases from this ideal value, crystals grow in circular, blade-like and avalanche form respectively. Diffraction patterns of these crystals also show a dependence of disorder in MnAl6 crystal lattice on the film composition. Extra spots, diffuse streaks and deficiency of spots were observed and some of them are interpreted to be due to disorder of stacking of atomic planes parallel to (001) MnAl6 lattice. A model of the disordered atomic arrangement is proposed to account for the deficiency of the diffraction spots.