23,632 research outputs found
Initial-boundary value problems for conservation laws with source terms and the Degasperis-Procesi equation
We consider conservation laws with source terms in a bounded domain with
Dirichlet boundary conditions. We first prove the existence of a strong trace
at the boundary in order to provide a simple formulation of the entropy
boundary condition. Equipped with this formulation, we go on to establish the
well-posedness of entropy solutions to the initial-boundary value problem. The
proof utilizes the kinetic formulation and the compensated compactness method.
Finally, we make use of these results to demonstrate the well-posedness in a
class of discontinuous solutions to the initial-boundary value problem for the
Degasperis-Procesi shallow water equation, which is a third order nonlinear
dispersive equation that can be rewritten in the form of a nonlinear
conservation law with a nonlocal source term.Comment: 24 page
Orientational Melting in Carbon Nanotube Ropes
Using Monte Carlo simulations, we investigate the possibility of an
orientational melting transition within a "rope" of (10,10) carbon nanotubes.
When twisting nanotubes bundle up during the synthesis, orientational
dislocations or twistons arise from the competition between the anisotropic
inter-tube interactions, which tend to align neighboring tubes, and the torsion
rigidity that tends to keep individual tubes straight. We map the energetics of
a rope containing twistons onto a lattice gas model and find that the onset of
a free "diffusion" of twistons, corresponding to orientational melting, occurs
at T_OM > 160 K.Comment: 4 page LaTeX file with 3 figures (10 PostScript files
An Adaptive Algorithm to Optimize the Dynamics of IEEE 802.15.4 Networks
Presentado en ICST 2013IEEE 802.15.4 standard is becoming one of the most popular technologies for the deployment of low rate Wireless Personal Area Networks with strong power constraints. In order to reduce the energy consumption, beacon-enabled networks with long network inactive periods can be employed. However, the duration of these inactivity periods, as some other configuration parameters, are conventionally set to default values and remain fixed during the whole network operation. This implies that if they are misconfigured the network will not adapt to changes in the conditions of the environment, particularly to the most determining one, i.e. the traffic load. This paper proposes a simple procedure for the dynamic adaptation of several key parameters of IEEE 802.15.4 networks. Under this procedure, the 802.15.4 parameters are modified as a function of the existing traffic conditions.Spanish National Project No.TEC2009-13763-C02-01
Anomalous kinetics of attractive reactions
We investigate the kinetics of reaction with the local attractive
interaction between opposite species in one spatial dimension. The attractive
interaction leads to isotropic diffusions inside segregated single species
domains, and accelerates the reactions of opposite species at the domain
boundaries. At equal initial densities of and , we analytically and
numerically show that the density of particles (), the size of domains
(), the distance between the closest neighbor of same species
(), and the distance between adjacent opposite species ()
scale in time as , , and respectively. These dynamical exponents form a new
universality class distinguished from the class of uniformly driven systems of
hard-core particles.Comment: 4 pages, 4 figure
Who Contributes to the Knowledge Sharing Economy?
Information sharing dynamics of social networks rely on a small set of
influencers to effectively reach a large audience. Our recent results and
observations demonstrate that the shape and identity of this elite, especially
those contributing \emph{original} content, is difficult to predict.
Information acquisition is often cited as an example of a public good. However,
this emerging and powerful theory has yet to provably offer qualitative
insights on how specialization of users into active and passive participants
occurs.
This paper bridges, for the first time, the theory of public goods and the
analysis of diffusion in social media. We introduce a non-linear model of
\emph{perishable} public goods, leveraging new observations about sharing of
media sources. The primary contribution of this work is to show that
\emph{shelf time}, which characterizes the rate at which content get renewed,
is a critical factor in audience participation. Our model proves a fundamental
\emph{dichotomy} in information diffusion: While short-lived content has simple
and predictable diffusion, long-lived content has complex specialization. This
occurs even when all information seekers are \emph{ex ante} identical and could
be a contributing factor to the difficulty of predicting social network
participation and evolution.Comment: 15 pages in ACM Conference on Online Social Networks 201
Daytime lidar measurements of tidal winds in the mesospheric sodium layer at Urbana, Illinois
For more than 15 years lidar systems have been used to study the chemistry and dynamics of the mesospheric sodium layer. Because the layer is an excellent tracer of atmospheric wave motions, sodium lidar has proven to be particularly useful for studying the influence of gravity waves and tides on mesospheric dynamics. These waves, which originate in the troposphere and stratosphere, propagate through the mesosphere and dissipate their energy near the mesopause making important contributions to the momentum and turbulence budget in this region of the atmosphere. Recently, the sodium lidar was modified for daytime operation so that wave phenomena and chemical effects could be monitored throughout the complete diurnal cycle. The results of continuous 24 hour lidar observations of the sodium layer structure are presented alond with measurement of the semidiurnal tidal winds
Area spectra of the rotating BTZ black hole from quasinormal modes
Following Bekenstein's suggestion that the horizon area of a black hole
should be quantized, the discrete spectrum of the horizon area has been
investigated in various ways. By considering the quasinormal mode of a black
hole, we obtain the transition frequency of the black hole, analogous to the
case of a hydrogen atom, in the semiclassical limit. According to Bohr's
correspondence principle, this transition frequency at large quantum number is
equal to classical oscillation frequency. For the corresponding classical
system of periodic motion with this oscillation frequency, an action variable
is identified and quantized via Bohr-Sommerfeld quantization, from which the
quantized spectrum of the horizon area is obtained. This method can be applied
for black holes with discrete quasinormal modes. As an example, we apply the
method for the both non-rotating and rotating BTZ black holes and obtain that
the spectrum of the horizon area is equally spaced and independent of the
cosmological constant for both cases
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