Tapping Thermodynamics of the One Dimensional Ising Model

We analyse the steady state regime of a one dimensional Ising model under a tapping dynamics recently introduced by analogy with the dynamics of mechanically perturbed granular media. The idea that the steady state regime may be described by a flat measure over metastable states of fixed energy is tested by comparing various steady state time averaged quantities in extensive numerical simulations with the corresponding ensemble averages computed analytically with this flat measure. The agreement between the two averages is excellent in all the cases examined, showing that a static approach is capable of predicting certain measurable properties of the steady state regime.Comment: 11 pages, 5 figure

First ozone reanalysis on Mars using SPICAM data

To further our understanding of important photochemical processes in the Martian atmosphere, a synthesis can be used to investigate the temporal and spatial agreement between model and observations and determine any possible causes of identified differences. In this study [1], we have assimilated, for the first time, total ozone into a Mars Global Circulation model (GCM) to study the ozone cycle

Finite Element Simulation of Smart Lightweight Structures for Active Vibration and Interior Acoustic Control

The paper presents a numerical approach to active vibration and noise control of smart lightweight structures. The structure is provided with thin piezoelectric wafers as actuators and sensors to control vibrations of the structure. Fully coupled electromechanical field equations were taken into account where model based controllers are applied for design purposes. The objective of vibration control of elastic structures is to reduce interior noise levels. Hence, the mechanical field is also coupled with the acoustic field, and consequently a fully coupled electro-mechanical-acoustical problem needs to be solved. The numerical solution is based on the finite element method, introducing a velocity potential for the acoustic fluid to receive overall symmetric system matrices of the semi-discrete form of the equation of motion. It is shown that the vibro-acoustic coupling can be neglected for controller design purposes, and consequently the modal truncation technique considering only the uncoupled structural modes, can be adapted to vibro-acoustic systems. The behaviour of a smart plate structure coupled with an acoustic cavity is studied as a reference example

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

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

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