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Register a new userCyclic annealing as an iterated random map
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Disordered magnets, martensitic mixed crystals, and glassy solids can be irreversibly deformed by subjecting them to external deformation. The deformation produces a smooth, reversible response punctuated by abrupt relaxation glitches. Under appropriate repeated forward and reverse deformation producing multiple glitches, a strict repetition of a single sequence of microscopic configurations often emerges. We exhibit these features by describing the evolution of the system configuration from glitch to glitch as a mapping of $mathcal{N}$ states into one-another. A map $mathbf{U}$ controls forward deformation; a second map $mathbf{D}$ controls reverse deformation. Iteration of a given sequence of forward and reverse maps, e.g. $mathbf{DDDDUUU}$ necessarily produces a convergence to a fixed cyclic repetition of states covering multiple glitches. The repetition may have a period of more than one strain cycle, as recently observed in simulations. Using numerical sampling, we characterize the convergence properties of four types of random maps implementing successive physical restrictions. The most restrictive is the much-studied Preisach model. These maps show only the most qualitative resemblance to annealing simulations. However, they suggest further properties needed for a realistic mapping scheme.
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Many materials that are out of equilibrium can learn one or more inputs that are repeatedly applied. Yet, a common framework for understanding such memories is lacking. Here we construct minimal representations of cyclic memory behaviors as directed graphs, and we construct simple physically-motivated models that produce the same graph structures. We show how a model of worn grass between park benches can produce multiple transient memories---a behavior previously observed in dilute suspensions of particles and charge-density-wave conductors---and the Mullins effect. Isolating these behaviors in our simple model allows us to assess the necessary ingredients for these kinds of memory, and to quantify memory capacity. We contrast these behaviors with a simple Preisach model that produces return-point memory. Our analysis provides a unified method for comparing and diagnosing cyclic memory behaviors across different materials.
We explore the compaction dynamics of a granular pile after a hard quench from a liquid into the glassy regime. First, we establish that the otherwise athermal granular pile during tapping exhibits annealing behavior comparable to glassy polymer or colloidal systems. Like those other systems, the pile undergoes a glass transition and freezes into different non-equilibrium glassy states at low agitation for different annealing speeds, starting from the same initial equilibrium state at high agitation. Then, we quench the system instantaneously from the highly-agitated state to below the glass transition regime to study the ensuing aging dynamics. In this classical aging protocol, the density increases (i.e., the potential energy of the pile decreases) logarithmically over several decades in time. Instead of system-wide, thermodynamic measures, here we identify the intermittent, irreversible events (quakes) that actually drive the glassy relaxation process. We find that the event rate decelerates hyperbolically, which explains the observed increase in density when the integrated contribution to the downward displacements is evaluated. We argue that such a hyperbolically decelerating event rate is consistent with a log-Poisson process, also found as a universal feature of aging in many thermal glasses.
The requirement that packings of hard particles, arguably the simplest structural glass, cannot be compressed by rearranging their network of contacts is shown to yield a new constraint on their microscopic structure. This constraint takes the form a bound between the distribution of contact forces P(f) and the pair distribution function g(r): if P(f) sim f^{theta} and g(r) sim (r-{sigma})^(-{gamma}), where {sigma} is the particle diameter, one finds that {gamma} geq 1/(2+{theta}). This bound plays a role similar to those found in some glassy materials with long-range interactions, such as the Coulomb gap in Anderson insulators or the distribution of local fields in mean-field spin glasses. There is ground to believe that this bound is saturated, offering an explanation for the presence of avalanches of rearrangements with power-law statistics observed in packings.
The response to a localized force provides a sensitive test for different models of stress transmission in granular solids. The elasto-plastic models traditionally used by engineers have been challenged by theoretical and experimental results which suggest a wave-like (hyperbolic) propagation of the stress, as opposed to the elliptic equations of static elasticity. Numerical simulations of two-dimensional granular systems subject to a localized external force are employed to examine the nature of stress transmission in these systems as a function of the magnitude of the applied force, the frictional parameters and the disorder (polydispersity). The results indicate that in large systems (typically considered by engineers), the response is close to that predicted by isotropic elasticity whereas the response of small systems (or when sufficiently large forces are applied) is strongly anisotropic. In the latter case the applied force induces changes in the contact network accompanied by frictional sliding. The larger the coefficient of static friction, the more extended is the range of forces for which the response is elastic and the smaller the anisotropy. Increasing the degree of polydispersity (for the range studied, up to 25%) decreases the range of elastic response. This article is an extension of a previously published letter [1].
When subjected to large amplitude oscillatory shear stress, aqueous Laponite suspensions show an abrupt solidification transition after a long delay time tc. We measure the dependence of tc on stress amplitude, frequency, and on the age-dependent initial loss modulus. At first sight our observations appear quantitatively consistent with a simple soft-glassy rheology (SGR)-type model, in which barrier crossings by mesoscopic elements are purely strain-induced. For a given strain amplitude {gamma}0 each element can be classified as fluid or solid according to whether its local yield strain exceeds {gamma}0. Each cycle, the barrier heights E of yielded elements are reassigned according to a fixed prior distribution {rho}(E): this fixes the per-cycle probability R({gamma}0) of a fluid elements becoming solid. As the fraction of solid elements builds up, {gamma}0 falls (at constant stress amplitude), so R({gamma}0) increases. This positive feedback accounts for the sudden solidification after a long delay. The model thus appears to directly link macroscopic rheology with mesoscopic barrier height statistics: within its precepts, our data point towards a power law for {rho}(E) rather than the exponential form usually assumed in SGR. However, despite this apparent success, closer investigation shows that the assumptions of the model cannot be reconciled with the extremely large strain amplitudes arising in our experiments. The quantitative explanation of delayed solidification in Laponite therefore remains an open theoretical challenge.
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