29,893 research outputs found
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
sites, where is the volume of the unit ball in , we show that
the inradius of the set of occupied sites is at least , while the
outradius is at most for any . 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 particles, we show that the inradius is at least , and the
outradius is at most . 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
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