624 research outputs found
Dynamic Vehicle Routing for Data Gathering in Wireless Networks
We consider a dynamic vehicle routing problem in wireless networks where
messages arriving randomly in time and space are collected by a mobile receiver
(vehicle or a collector). The collector is responsible for receiving these
messages via wireless communication by dynamically adjusting its position in
the network. Our goal is to utilize a combination of wireless transmission and
controlled mobility to improve the delay performance in such networks. We show
that the necessary and sufficient condition for the stability of such a system
(in the bounded average number of messages sense) is given by {\rho}<1 where
{\rho} is the average system load. We derive fundamental lower bounds for the
delay in the system and develop policies that are stable for all loads {\rho}<1
and that have asymptotically optimal delay scaling. Furthermore, we extend our
analysis to the case of multiple collectors in the network. We show that the
combination of mobility and wireless transmission results in a delay scaling of
{\Theta}(1/(1- {\rho})) with the system load {\rho} that is a factor of
{\Theta}(1/(1- {\rho})) smaller than the delay scaling in the corresponding
system where the collector visits each message location.Comment: 19 pages, 7 figure
Dynamic Server Allocation over Time Varying Channels with Switchover Delay
We consider a dynamic server allocation problem over parallel queues with
randomly varying connectivity and server switchover delay between the queues.
At each time slot the server decides either to stay with the current queue or
switch to another queue based on the current connectivity and the queue length
information. Switchover delay occurs in many telecommunications applications
and is a new modeling component of this problem that has not been previously
addressed. We show that the simultaneous presence of randomly varying
connectivity and switchover delay changes the system stability region and the
structure of optimal policies. In the first part of the paper, we consider a
system of two parallel queues, and develop a novel approach to explicitly
characterize the stability region of the system using state-action frequencies
which are stationary solutions to a Markov Decision Process (MDP) formulation.
We then develop a frame-based dynamic control (FBDC) policy, based on the
state-action frequencies, and show that it is throughput-optimal asymptotically
in the frame length. The FBDC policy is applicable to a broad class of network
control systems and provides a new framework for developing throughput-optimal
network control policies using state-action frequencies. Furthermore, we
develop simple Myopic policies that provably achieve more than 90% of the
stability region. In the second part of the paper, we extend our results to
systems with an arbitrary but finite number of queues.Comment: 38 Pages, 18 figures. arXiv admin note: substantial text overlap with
arXiv:1008.234
Probing the neutral edge modes in transport across a point contact via thermal effects in the Read-Rezayi non-abelian quantum Hall states
Non-abelian quantum Hall states are characterized by the simultaneous
appearance of charge and neutral gapless edge modes, with the structure of the
latter being intricately related to the existence of bulk quasi-particle
excitations obeying non-abelian statistics. In general, it is hard to probe the
neutral modes in charge transport measurements and a thermal transport
measurement seems to be inevitable. Here we propose a setup which can get
around this problem by having two point contacts in series separated by a
distance set by the thermal equilibration length of the charge mode. We show
that by using the first point contact as a heating device, the excess charge
noise measured at the second point contact carries a non-trivial signature of
the presence of the neutral mode hence leading to its indirect detection. We
also obtain explicit expressions for the thermal conductance and corresponding
Lorentz number for transport across a quantum point contact between two edges
held at different temperatures and chemical potentials
Dynamic stability of crack fronts: Out-of-plane corrugations
The dynamics and stability of brittle cracks are not yet fully understood.
Here we use the Willis-Movchan 3D linear perturbation formalism [J. Mech. Phys.
Solids {\bf 45}, 591 (1997)] to study the out-of-plane stability of planar
crack fronts in the framework of linear elastic fracture mechanics. We discuss
a minimal scenario in which linearly unstable crack front corrugations might
emerge above a critical front propagation speed. We calculate this speed as a
function of Poisson's ratio and show that corrugations propagate along the
crack front at nearly the Rayleigh wave-speed. Finally, we hypothesize about a
possible relation between such corrugations and the long-standing problem of
crack branching.Comment: 5 pages, 2 figures + supplementary informatio
Dynamical Inequality in Growth Models
A recent exponent inequality is applied to a number of dynamical growth
models. Many of the known exponents for models such as the Kardar-Parisi-Zhang
(KPZ) equation are shown to be consistent with the inequality. In some cases,
such as the Molecular Beam Equation, the situation is more interesting, where
the exponents saturate the inequality. As the acid test for the relative
strength of four popular approximation schemes we apply the inequality to the
exponents obtained for two Non Local KPZ systems. We find that all methods but
one, the Self Consistent Expansion, violate the inequality in some regions of
parameter space. To further demonstrate the usefulness of the inequality, we
apply it to a specific model, which belongs to a family of models in which the
inequality becomes an equality. We thus show that the inequality can easily
yield results, which otherwise have to rely either on approximations or general
beliefs.Comment: 6 pages, 4 figure
Anisotropy and periodicity in the density distribution of electrons in a quantum-well
We use low temperature near-field optical spectroscopy to image the electron
density distribution in the plane of a high mobility GaAs quantum well. We find
that the electrons are not randomly distributed in the plane, but rather form
narrow stripes (width smaller than 150 nm) of higher electron density. The
stripes are oriented along the [1-10 ] crystal direction, and are arranged in a
quasi-periodic structure. We show that elongated structural mounds, which are
intrinsic to molecular beam epitaxy, are responsible for the creation of this
electron density texture.Comment: 10 pages, 3 figure
Void Formation and Roughening in Slow Fracture
Slow crack propagation in ductile, and in certain brittle materials, appears
to take place via the nucleation of voids ahead of the crack tip due to plastic
yields, followed by the coalescence of these voids. Post mortem analysis of the
resulting fracture surfaces of ductile and brittle materials on the m-mm
and the nm scales respectively, reveals self-affine cracks with anomalous
scaling exponent in 3-dimensions and in
2-dimensions. In this paper we present an analytic theory based on the method
of iterated conformal maps aimed at modelling the void formation and the
fracture growth, culminating in estimates of the roughening exponents in
2-dimensions. In the simplest realization of the model we allow one void ahead
of the crack, and address the robustness of the roughening exponent. Next we
develop the theory further, to include two voids ahead of the crack. This
development necessitates generalizing the method of iterated conformal maps to
include doubly connected regions (maps from the annulus rather than the unit
circle). While mathematically and numerically feasible, we find that the
employment of the stress field as computed from elasticity theory becomes
questionable when more than one void is explicitly inserted into the material.
Thus further progress in this line of research calls for improved treatment of
the plastic dynamics.Comment: 15 pages, 20 figure
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