10,790 research outputs found
On the dependence of the avalanche angle on the granular layer thickness
A layer of sand of thickness h flows down a rough surface if the inclination
is larger than some threshold value theta which decreases with h. A tentative
microscopic model for the dependence of theta with h is proposed for rigid
frictional grains, based on the following hypothesis: (i) a horizontal layer of
sand has some coordination z larger than a critical value z_c where mechanical
stability is lost (ii) as the tilt angle is increased, the configurations
visited present a growing proportion $_s of sliding contacts. Instability with
respect to flow occurs when z-z_s=z_c. This criterion leads to a prediction for
theta(h) in good agreement with empirical observations.Comment: 6 pages, 2 figure
Dynamical instabilities in density-dependent hadronic relativistic models
Unstable modes in asymmetric nuclear matter (ANM) at subsaturation densities
are studied in the framework of relativistic mean-field density-dependent
hadron models. The size of the instabilities that drive the system are
calculated and a comparison with results obtained within the non-linear Walecka
model is presented. The distillation and anti-distillation effects are
discussed.Comment: 8 pages, 8 Postscript figures. Submitted for publication in Phys.
Rev.
The distribution of forces affects vibrational properties in hard sphere glasses
We study theoretically and numerically the elastic properties of hard sphere
glasses, and provide a real-space description of their mechanical stability. In
contrast to repulsive particles at zero-temperature, we argue that the presence
of certain pairs of particles interacting with a small force soften elastic
properties. This softening affects the exponents characterizing elasticity at
high pressure, leading to experimentally testable predictions. Denoting
the force distribution of such pairs and the
packing fraction at which pressure diverges, we predict that (i) the density of
states has a low-frequency peak at a scale , rising up to it as
, and decaying above as where and is the frequency,
(ii) shear modulus and mean-squared displacement are inversely proportional
with where
, and (iii) continuum elasticity breaks down on a
scale where
and , where is the
coordination and the spatial dimension. We numerically test (i) and provide
data supporting that in our bi-disperse system,
independently of system preparation in two and three dimensions, leading to
, , and . Our results for the
mean-square displacement are consistent with a recent exact replica computation
for , whereas some observations differ, as rationalized by the
present approach.Comment: 5 pages + 4 pages supplementary informatio
A symmetric quantum calculus
We introduce the -symmetric difference derivative and the
-symmetric N\"orlund sum. The associated symmetric quantum
calculus is developed, which can be seen as a generalization of the forward and
backward -calculus.Comment: Submitted 26/Sept/2011; accepted in revised form 28/Dec/2011; to
Proceedings of International Conference on Differential & Difference
Equations and Applications, in honour of Professor Ravi P. Agarwal, to be
published by Springer in the series Proceedings in Mathematics (PROM
On the Modeling of Droplet Evaporation on Superhydrophobic Surfaces
When a drop of water is placed on a rough surface, there are two possible
extreme regimes of wetting: the one called Cassie-Baxter (CB) with air pockets
trapped underneath the droplet and the one characterized by the homogeneous
wetting of the surface, called the Wenzel (W) state. A way to investigate the
transition between these two states is by means of evaporation experiments, in
which the droplet starts in a CB state and, as its volume decreases, penetrates
the surface's grooves, reaching a W state. Here we present a theoretical model
based on the global interfacial energies for CB and W states that allows us to
predict the thermodynamic wetting state of the droplet for a given volume and
surface texture. We first analyze the influence of the surface geometric
parameters on the droplet's final wetting state with constant volume, and show
that it depends strongly on the surface texture. We then vary the volume of the
droplet keeping fixed the geometric surface parameters to mimic evaporation and
show that the drop experiences a transition from the CB to the W state when its
volume reduces, as observed in experiments. To investigate the dependency of
the wetting state on the initial state of the droplet, we implement a cellular
Potts model in three dimensions. Simulations show a very good agreement with
theory when the initial state is W, but it disagrees when the droplet is
initialized in a CB state, in accordance with previous observations which show
that the CB state is metastable in many cases. Both simulations and theoretical
model can be modified to study other types of surface.Comment: 23 pages, 7 figure
Non-Markovian incoherent quantum dynamics of a two-state system
We present a detailed study of the non-Markovian two-state system dynamics
for the regime of incoherent quantum tunneling. Using perturbation theory in
the system tunneling amplitude , and in the limit of strong system-bath
coupling, we determine the short time evolution of the reduced density matrix
and thereby find a general equation of motion for the non-Markovian evolution
at longer times. We relate the nonlocality in time due to the non-Markovian
effects with the environment characteristic response time. In addition, we
study the incoherent evolution of a system with a double-well potential, where
each well consists several quantized energy levels. We determine the crossover
temperature to a regime where many energy levels in the wells participate in
the tunneling process, and observe that the required temperature can be much
smaller than the one associated with the system plasma frequency. We also
discuss experimental implications of our theoretical analysis.Comment: 10 pages, published versio
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