Spatially heterogeneous dynamics in granular compaction

We prove the emergence of spatially correlated dynamics in slowly compacting dense granular media by analyzing analytically and numerically multi-point correlation functions in a simple particle model characterized by slow non-equilibrium dynamics. We show that the logarithmically slow dynamics at large times is accompanied by spatially extended dynamic structures that resemble the ones observed in glass-forming liquids and dense colloidal suspensions. This suggests that dynamic heterogeneity is another key common feature present in very different jamming materials.Comment: 4 pages, 3 figure

Experimental Study of Iron Losses Generated by a Uniform Rotating Field

This paper introduces a mock-up with a solid iron cylinder rotating in a fixed excitation frame powered by dc current. A uniform field is created in the rotating cylinder, which is driven by an external motor. The braking torque is measured, allowing the study of iron losses generated by a uniform rotating field. The aim is to advance toward a vector iron loss model that takes into account different magnetization directions and their interdependency. The eddy current losses are the dominant loss source in the mock-up, rendering it easier to model. A standard eddy currents model is proposed. It models well the losses at low and medium magnetic flux density, but lower losses are measured near saturation levels. This could be due to the high thickness to radius ratio changing the eddy current paths near the edges of the rotor, which can be later analyzed by a full 3-D finite-element method analysis. A 2-D finite-element method simulation is performed, which estimates the magnetic flux heterogeneity in the rotor. Several lessons are drawn from this mock-up, which prepares a second version with a higher speed and a longer laminated stack rotor. A higher air gap will decrease the voltage fluctuation in the primary winding, a smaller angular opening of the excitation frame will improve the uniformity of the flux in the rotor

Phase transitions in the steady state behavior of mechanically perturbed spin glasses and ferromagnets

We analyze the steady state regime of systems interpolating between spin glasses and ferromagnets under a tapping dynamics recently introduced by analogy with the dynamics of mechanically perturbed granular media. A crossover from a second order to first order ferromagnetic transition as a function of the spin coupling distribution is found. The flat measure over blocked states introduced by Edwards for granular media is used to explain this scenario. Annealed calculations of the Edwards entropy are shown to qualitatively explain the nature of the phase transitions. A Monte-Carlo construction of the Edwards measure confirms that this explanation is also quantitatively accurate

Modeling quasi-static magnetic hysteresis: a new implementation of the play model based on experimental asymmetrical B(H) loops

This paper relates a new model of quasi-static magnetic hysteresis based on the Play model hysterons, which builds the magnetic field density B from the magnetic field H. In the original model, H is discretized into temporal values H(t m ), which is itself modeled by a hysteron chain of m sub-values. B is then reconstructed from these sub-values through a function experimentally determined by measuring B(H) centered cycles, using a constraint optimization method. The new proposed method is to measure asymmetrical B(H) loops, which give additional equations leading to a fully determined linear square invertible system. The asymmetrical B(H) loop is included in a bigger symmetrical loop with a magnetic flux density turnaround in order to be regulatable

Tapping Spin Glasses

We consider a tapping dynamics, analogous to that in experiments on granular media, on spin glasses and ferromagnets on random thin graphs. Between taps, zero temperature single spin flip dynamics takes the system to a metastable state. Tapping, corresponds to flipping simultaneously any spin with probability $p$. This dynamics leads to a stationary regime with a steady state energy $E(p)$. We analytically solve this dynamics for the one dimensional ferromagnet and $\pm J$ spin glass. Numerical simulations for spin glasses and ferromagnets of higher connectivity are carried out, in particular we find a novel first order transition for the ferromagnetic systems.Comment: 5 pages, 3 figures, RevTe

Steady State Behavior of Mechanically Perturbed Spin Glasses and Ferromagnets

A zero temperature dynamics of Ising spin glasses and ferromagnets on random graphs of finite connectivity is considered, like granular media these systems have an extensive entropy of metastable states. We consider the problem of what energy a randomly prepared spin system falls to before becoming stuck in a metastable state. We then introduce a tapping mechanism, analogous to that of real experiments on granular media, this tapping, corresponding to flipping simultaneously any spin with probability $p$, leads to stationary regime with a steady state energy $E(p)$. We explicitly solve this problem for the one dimensional ferromagnet and $\pm J$ spin glass and carry out extensive numerical simulations for spin systems of higher connectivity. The link with the density of metastable states at fixed energy and the idea of Edwards that one may construct a thermodynamics with a flat measure over metastable states is discussed. In addition our simulations on the ferromagnetic systems reveal a novel first order transition, whereas the usual thermodynamic transition on these graphs is second order.Comment: 11 pages, 7 figure