Glassy dynamics in granular compaction: sand on random graphs

We discuss the use of a ferromagnetic spin model on a random graph to model granular compaction. A multi-spin interaction is used to capture the competition between local and global satisfaction of constraints characteristic for geometric frustration. We define an athermal dynamics designed to model repeated taps of a given strength. Amplitude cycling and the effect of permanently constraining a subset of the spins at a given amplitude is discussed. Finally we check the validity of Edwards' hypothesis for the athermal tapping dynamics.Comment: 13 pages Revtex, minor changes, to appear in PR

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

Statistics of photodissociation spectra: nonuniversal properties

We consider the two-point correlation function of the photodissociation cross section in molecules where the fragmentation process is indirect, passing through resonances above the dissociation threshold. In the limit of overlapping resonances, a formula is derived, relating this correlation function to the behavior of the corresponding classical system. It is shown that nonuniversal features of the two-point correlation function may have significant experimental manifestations.Comment: 4 pages, 1 figur

The integrated density of states of the random graph Laplacian

We analyse the density of states of the random graph Laplacian in the percolating regime. A symmetry argument and knowledge of the density of states in the nonpercolating regime allows us to isolate the density of states of the percolating cluster (DSPC) alone, thereby eliminating trivially localised states due to finite subgraphs. We derive a nonlinear integral equation for the integrated DSPC and solve it with a population dynamics algorithm. We discuss the possible existence of a mobility edge and give strong evidence for the existence of discrete eigenvalues in the whole range of the spectrum.Comment: 4 pages, 1 figure. Supplementary material available at http://www.theorie.physik.uni-goettingen.de/~aspel/data/spectrum_supplement.pd

Linear response of vibrated granular systems to sudden changes in the vibration intensity

The short-term memory effects recently observed in vibration-induced compaction of granular materials are studied. It is shown that they can be explained by means of quite plausible hypothesis about the mesoscopic description of the evolution of the system. The existence of a critical time separating regimes of ``anomalous'' and ``normal'' responses is predicted. A simple model fitting into the general framework is analyzed in the detail. The relationship between this work and previous studies is discussed.Comment: 10 pages, 6 figures; fixed errata, updtated reference

Vicious walk with a wall, noncolliding meanders, and chiral and Bogoliubov-deGennes random matrices

Spatially and temporally inhomogeneous evolution of one-dimensional vicious walkers with wall restriction is studied. We show that its continuum version is equivalent with a noncolliding system of stochastic processes called Brownian meanders. Here the Brownian meander is a temporally inhomogeneous process introduced by Yor as a transform of the Bessel process that is a motion of radial coordinate of the three-dimensional Brownian motion represented in the spherical coordinates. It is proved that the spatial distribution of vicious walkers with a wall at the origin can be described by the eigenvalue-statistics of Gaussian ensembles of Bogoliubov-deGennes Hamiltonians of the mean-field theory of superconductivity, which have the particle-hole symmetry. We report that the time evolution of the present stochastic process is fully characterized by the change of symmetry classes from the type $C$ to the type $C$I in the nonstandard classes of random matrix theory of Altland and Zirnbauer. The relation between the non-colliding systems of the generalized meanders of Yor, which are associated with the even-dimensional Bessel processes, and the chiral random matrix theory is also clarified.Comment: REVTeX4, 16 pages, 4 figures. v2: some additions and correction

Analysis by x-ray microtomography of a granular packing undergoing compaction

Several acquisitions of X-ray microtomography have been performed on a beads packing while it compacts under vertical vibrations. An image analysis allows to study the evolution of the packing structure during its progressive densification. In particular, the volume distribution of the pores reveals a large tail, compatible to an exponential law, which slowly reduces as the system gets more compact. This is quite consistent, for large pores, with the free volume theory. These results are also in very good agreement with those obtained by a previous numerical model of granular compaction.Comment: 4 pages, 4 figures. Latex (revtex4). to be published in Phys. Rev.

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

Science in Focus: Combining Radiotherapy with Inhibitors of the DNA Damage Response

No abstract available

Moments of vicious walkers and M\"obius graph expansions

A system of Brownian motions in one-dimension all started from the origin and conditioned never to collide with each other in a given finite time-interval $(0, T]$ is studied. The spatial distribution of such vicious walkers can be described by using the repulsive eigenvalue-statistics of random Hermitian matrices and it was shown that the present vicious walker model exhibits a transition from the Gaussian unitary ensemble (GUE) statistics to the Gaussian orthogonal ensemble (GOE) statistics as the time $t$ is going on from 0 to $T$. In the present paper, we characterize this GUE-to-GOE transition by presenting the graphical expansion formula for the moments of positions of vicious walkers. In the GUE limit $t \to 0$, only the ribbon graphs contribute and the problem is reduced to the classification of orientable surfaces by genus. Following the time evolution of the vicious walkers, however, the graphs with twisted ribbons, called M\"obius graphs, increase their contribution to our expansion formula, and we have to deal with the topology of non-orientable surfaces. Application of the recent exact result of dynamical correlation functions yields closed expressions for the coefficients in the M\"obius expansion using the Stirling numbers of the first kind.Comment: REVTeX4, 11 pages, 1 figure. v.2: calculations of the Green function and references added. v.3: minor additions and corrections made for publication in Phys.Rev.