Force chain splitting in granular materials: a mechanism for large scale pseudo-elastic behaviour

We investigate both numerically and analytically the effect of strong disorder on the large scale properties of the hyperbolic equations for stresses proposed in \protect\cite{bcc,wcc}. The physical mechanism that we model is the local splitting of the force chains (the characteristics of the hyperbolic equation) by packing defects. In analogy with the theory of light diffusion in a turbid medium, we propose a Boltzmann-like equation to describe these processes. We show that, for isotropic packings, the resulting large scale effective equations for the stresses have exactly the same structure as those of an elastic body, despite the fact that no displacement field needs to be introduced at all. Correspondingly, the response function evolves from a two peak structure at short scales to a broad hump at large scales. We find, however, that the Poisson ratio is anomalously large and incompatible with classical elasticity theory that requires the reference state to be thermodynamically stable.Comment: 7 pages, 6 figures, An incorrect definition of the Poisson ratio in dimensions not equal to 3 was amended. The conclusions are unchange

Modelling one-dimensional driven diffusive systems by the Zero-Range Process

The recently introduced correspondence between one-dimensional two-species driven models and the Zero-Range Process is extended to study the case where the densities of the two species need not be equal. The correspondence is formulated through the length dependence of the current emitted from a particle domain. A direct numerical method for evaluating this current is introduced, and used to test the assumptions underlying this approach. In addition, a model for isolated domain dynamics is introduced, which provides a simple way to calculate the current also for the non-equal density case. This approach is demonstrated and applied to a particular two-species model, where a phase separation transition line is calculated

Overlapping resonances in the control of intramolecular vibrational redistribution

Coherent control of bound state processes via the interfering overlapping resonances scenario [Christopher et al., J. Chem. Phys. 123, 064313 (2006)] is developed to control intramolecular vibrational redistribution (IVR). The approach is applied to the flow of population between bonds in a model of chaotic OCS vibrational dynamics, showing the ability to significantly alter the extent and rate of IVR by varying quantum interference contributions.Comment: 10 pages, 7 figure

Strong Spherical Asymptotics for Rotor-Router Aggregation and the Divisible Sandpile

The rotor-router model is a deterministic analogue of random walk. It can be used to define a deterministic growth model analogous to internal DLA. We prove that the asymptotic shape of this model is a Euclidean ball, in a sense which is stronger than our earlier work. For the shape consisting of $n=\omega_d r^d$ sites, where $\omega_d$ is the volume of the unit ball in $\R^d$, we show that the inradius of the set of occupied sites is at least $r-O(\log r)$, while the outradius is at most $r+O(r^\alpha)$ for any $\alpha > 1-1/d$. For a related model, the divisible sandpile, we show that the domain of occupied sites is a Euclidean ball with error in the radius a constant independent of the total mass. For the classical abelian sandpile model in two dimensions, with $n=\pi r^2$ particles, we show that the inradius is at least $r/\sqrt{3}$, and the outradius is at most $(r+o(r))/\sqrt{2}$. This improves on bounds of Le Borgne and Rossin. Similar bounds apply in higher dimensions.Comment: [v3] Added Theorem 4.1, which generalizes Theorem 1.4 for the abelian sandpile. [v4] Added references and improved exposition in sections 2 and 4. [v5] Final version, to appear in Potential Analysi

The Low Quiescent X-Ray Luminosity of the Neutron Star Transient XTE J2123-058

We report on the first X-ray observations of the neutron star soft X-ray transient (SXT) XTE J2123-058 in quiescence, made by Chandra and BeppoSAX, as well as contemporaneous optical observations. In 2002, the Chandra spectrum of XTE J2123-058 is consistent with a power-law model, or the combination of a blackbody plus a power-law, but it is not well-described by a pure blackbody. Using the interstellar column density, the power-law fit gives photon index of 3.1 (+0.7,-0.6) and indicates a 0.3-8 keV unabsorbed luminosity of 9(+4,-3)E31 (d/8.5 kpc)^2 ergs/s (90% confidence errors). Fits with models consisting of thermal plus power-law components indicate that the upper limit on the temperature of a 1.4 solar mass, 10 km radius neutron star with a hydrogen atmosphere is kT_eff < 66 eV, and the upper limit on the bolometric luminosity is L_infinity < 1.4E32 ergs/s, assuming d = 8.5 kpc. Of the neutron star SXTs that exhibit short (< 1 year) outbursts, including Aql X-1, 4U 1608-522, Cen X-4, and SAX J1810.8-2609, the lowest temperatures and luminosities are found for XTE J2123-058 and SAX J1810.8-2609. From the BeppoSAX observation of XTE J2123-058 in 2000, we obtained an upper limit on the 1-10 keV unabsorbed luminosity of 9E32 ergs/s. Although this upper limit allows that the X-ray luminosity may have decreased between 2000 and 2002, that possibility is not supported by our contemporaneous R-band observations, which indicate that the optical flux increased significantly. Motivated by the theory of deep crustal heating by Brown and co-workers, we characterize the outburst histories of the five SXTs. The low quiescent luminosity for XTE J2123-058 is consistent with the theory of deep crustal heating without requiring enhanced neutron star cooling if the outburst recurrence time is >~ 70 years.Comment: 8 pages, accepted by Ap

The effect of curvature and topology on membrane hydrodynamics

We study the mobility of extended objects (rods) on a spherical liquid-liquid interface to show how this quantity is modified in a striking manner by both the curvature and the topology of the interface. We present theoretical calculations and experimental measurements of the interfacial fluid velocity field around a moving rod bound to the crowded interface of a water-in-oil droplet. By using different droplet sizes, membrane viscosities, and rod lengths, we show that the viscosity mismatch between the interior and exterior fluids leads to a suppression of the fluid flow on small droplets that cannot be captured by the flat interface predictions.Comment: 4 pages, 3 figure

An exactly solvable dissipative transport model

We introduce a class of one-dimensional lattice models in which a quantity, that may be thought of as an energy, is either transported from one site to a neighbouring one, or locally dissipated. Transport is controlled by a continuous bias parameter q, which allows us to study symmetric as well as asymmetric cases. We derive sufficient conditions for the factorization of the N-body stationary distribution and give an explicit solution for the latter, before briefly discussing physically relevant situations.Comment: 7 pages, 1 figure, submitted to J. Phys.

Equivariant pretheories and invariants of torsors

In the present paper we introduce and study the notion of an equivariant pretheory: basic examples include equivariant Chow groups, equivariant K-theory and equivariant algebraic cobordism. To extend this set of examples we define an equivariant (co)homology theory with coefficients in a Rost cycle module and provide a version of Merkurjev's (equivariant K-theory) spectral sequence for such a theory. As an application we generalize the theorem of Karpenko-Merkurjev on G-torsors and rational cycles; to every G-torsor E and a G-equivariant pretheory we associate a graded ring which serves as an invariant of E. In the case of Chow groups this ring encodes the information concerning the motivic J-invariant of E and in the case of Grothendieck's K_0 -- indexes of the respective Tits algebras.Comment: 23 pages; this is an essentially extended version of the previous preprint: the construction of an equivariant cycle (co)homology and the spectral sequence (generalizing the long exact localization sequence) are adde

Borel-Moore motivic homology and weight structure on mixed motives

By defining and studying functorial properties of the Borel-Moore motivic homology, we identify the heart of Bondarko-H\'ebert's weight structure on Beilinson motives with Corti-Hanamura's category of Chow motives over a base, therefore answering a question of Bondarko