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

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

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

Adjacency Matrices of Configuration Graphs

In 1960, Hoffman and Singleton \cite{HS60} solved a celebrated equation for square matrices of order $n$, which can be written as $$(\kappa - 1) I_n + J_n - A A^{\rm T} = A$$ where $I_n$, $J_n$, and $A$ are the identity matrix, the all one matrix, and a $(0,1)$--matrix with all row and column sums equal to $\kappa$, respectively. If $A$ is an incidence matrix of some configuration $\cal C$ of type $n_\kappa$, then the left-hand side $\Theta(A):= (\kappa - 1)I_n + J_n - A A^{\rm T}$ is an adjacency matrix of the non--collinearity graph $\Gamma$ of $\cal C$. In certain situations, $\Theta(A)$ is also an incidence matrix of some $n_\kappa$ configuration, namely the neighbourhood geometry of $\Gamma$ introduced by Lef\`evre-Percsy, Percsy, and Leemans \cite{LPPL}. The matrix operator $\Theta$ can be reiterated and we pose the problem of solving the generalised Hoffman--Singleton equation $\Theta^m(A)=A$. In particular, we classify all $(0,1)$--matrices $M$ with all row and column sums equal to $\kappa$, for $\kappa = 3,4$, which are solutions of this equation. As a by--product, we obtain characterisations for incidence matrices of the configuration $10_3F$ in Kantor's list \cite{Kantor} and the $17_4$ configuration #1971 in Betten and Betten's list \cite{BB99}

Turbulence modelling in Titan's zonal wind collapse

International audience1. Context The atmosphere of Titan is interesting by many aspects: it has the thickest atmosphere for a moon in the solar system, an atmosphere in superrotation in the stratosphere, an hemispheric asymmetry of temperature and an haze feedback of haze distribution on circulation between many others. There is another feature by which the atmosphere of Titan is unique, a strong decrease of the zonal wind between 60 and 100 km known as the "zonal wind collapse" (Fig-ure 1). The first measurement of this feature performed by ground-based radio-telescopes recording the Doppler Wind Experiment measurements of the carrier frequency during the Huygens descent [1]. The wind measured above 120 km was approximately of 100 m s −1. Then, below, the wind decreased to about few meters per seconds around 70 km before increasing again to 40 m s −1 at 60 km. 2. Our methodology 2.1 Principle Global Circulation Models (GCM) are powerful tools to study atmospheric circulations and have been employed to study the different planets of the solar system as well as Titan [2, 3, 4]. Although the different models are able to reproduce a realistic atmospheric circulation with superrotation, they fail to reproduce the observed zonal wind collapse characterized by a decrease towards only a few meters per second. We propose here to study for the first time this wind structure using turbulence-resolving model [5]. 2.2 Model description In order to investigate this peculiar wind feature we use the WRF compressible and non-hydrostatic dy-namical core to perform large-eddy simulation (LES) [6]. The timescale of the resolved turbulence is significantly smaller than the radiative timescale, comparable to one Titan year at this altitude [7], so no radiative Figure 1: Huygens temperature (K) and zonal wind profile (m s −1) between 50 and 100 km. processes are taken into account. The model is initialized using pressure, temperature and wind vertical profile as measured by the Huygens probe and shown in Figure 1. The atmospheric and planetary constants (gravity, heat capacity ...) within the model are set to Titan values. The horizontal grid spacing is 20 m spread over a 2 km-wide domain and the vertical grid features 300 levels from 60 to 90 km altitudes. 3. Wave generation Figure 2 displays the vertical wind (top) the associated vertical Eliassen-Palm flux (bottom) ρu w with ρ the density of the atmosphere and u and w the mean perturbation to the mean (domain-averaged) value of the zonal wind u and vertical wind w. The strong decrease of the zonal wind between 65 and 60 km causes a Kelvin-Helmholtz instability that leads to the generation of gravity waves. These waves propagates both towards the ground and towards the upper atmosphere. The dissipation of the wave engenders a momentum transfer to the flow and impacts the zonal wind

Scaling Law in Carbon Nanotube Electromechanical Devices

We report a method for probing electromechanical properties of multiwalled carbon nanotubes(CNTs). This method is based on AFM measurements on a doubly clamped suspended CNT electrostatically deflected by a gate electrode. We measure the maximum deflection as a function of the applied gate voltage. Data from different CNTs scale into an universal curve within the experimental accuracy, in agreement with a continuum model prediction. This method and the general validity of the scaling law constitute a very useful tool for designing actuators and in general conducting nanowire-based NEMS.Comment: 12 pages, 4 figures. To be published in Phys. Rev. Let