3,870 research outputs found
Are gauge shocks really shocks?
The existence of gauge pathologies associated with the Bona-Masso family of
generalized harmonic slicing conditions is proven for the case of simple 1+1
relativity. It is shown that these gauge pathologies are true shocks in the
sense that the characteristic lines associated with the propagation of the
gauge cross, which implies that the name ``gauge shock'' usually given to such
pathologies is indeed correct. These gauge shocks are associated with places
where the spatial hypersurfaces that determine the foliation of spacetime
become non-smooth.Comment: 7 pages, 5 figures, REVTEX 4. Revised version, including corrections
suggested by referee
New invariants for entangled states
We propose new algebraic invariants that distinguish and classify entangled
states. Considering qubits as well as higher spin systems, we obtained complete
entanglement classifications for cases that were either unsolved or only
conjectured in the literature.Comment: published versio
The Visibility Graph: a new method for estimating the Hurst exponent of fractional Brownian motion
Fractional Brownian motion (fBm) has been used as a theoretical framework to
study real time series appearing in diverse scientific fields. Because its
intrinsic non-stationarity and long range dependence, its characterization via
the Hurst parameter H requires sophisticated techniques that often yield
ambiguous results. In this work we show that fBm series map into a scale free
visibility graph whose degree distribution is a function of H. Concretely, it
is shown that the exponent of the power law degree distribution depends
linearly on H. This also applies to fractional Gaussian noises (fGn) and
generic f^(-b) noises. Taking advantage of these facts, we propose a brand new
methodology to quantify long range dependence in these series. Its reliability
is confirmed with extensive numerical simulations and analytical developments.
Finally, we illustrate this method quantifying the persistent behavior of human
gait dynamics.Comment: 5 pages, submitted for publicatio
Number theoretic example of scale-free topology inducing self-organized criticality
In this work we present a general mechanism by which simple dynamics running
on networks become self-organized critical for scale free topologies. We
illustrate this mechanism with a simple arithmetic model of division between
integers, the division model. This is the simplest self-organized critical
model advanced so far, and in this sense it may help to elucidate the mechanism
of self-organization to criticality. Its simplicity allows analytical
tractability, characterizing several scaling relations. Furthermore, its
mathematical nature brings about interesting connections between statistical
physics and number theoretical concepts. We show how this model can be
understood as a self-organized stochastic process embedded on a network, where
the onset of criticality is induced by the topology.Comment: 4 pages, 3 figures. Physical Review Letters, in pres
On the geometry of a class of N-qubit entanglement monotones
A family of N-qubit entanglement monotones invariant under stochastic local
operations and classical communication (SLOCC) is defined. This class of
entanglement monotones includes the well-known examples of the concurrence, the
three-tangle, and some of the four, five and N-qubit SLOCC invariants
introduced recently. The construction of these invariants is based on bipartite
partitions of the Hilbert space in the form with . Such partitions can be given
a nice geometrical interpretation in terms of Grassmannians Gr(L,l) of l-planes
in that can be realized as the zero locus of quadratic polinomials
in the complex projective space of suitable dimension via the Plucker
embedding. The invariants are neatly expressed in terms of the Plucker
coordinates of the Grassmannian.Comment: 7 pages RevTex, Submitted to Physical Review
Asymptotics of Selberg-like integrals: The unitary case and Newton's interpolation formula
We investigate the asymptotic behavior of the Selberg-like integral ,
as for different scalings of the parameters and with .
Integrals of this type arise in the random matrix theory of electronic
scattering in chaotic cavities supporting channels in the two attached
leads. Making use of Newton's interpolation formula, we show that an asymptotic
limit exists and we compute it explicitly
A radio and infrared exploration of the Cygnus X-3 environments
To confirm, or rule out, the possible hot spot nature of two previously
detected radio sources in the vicinity of the Cygnus X-3 microquasar.
We present the results of a radio and near infrared exploration of the
several arc-minute field around the well known galactic relativistic jet source
Cygnus X-3 using the Very Large Array and the Calar Alto 3.5~m telescope.
The data this paper is based on do not presently support the hot spot
hypothesis. Instead, our new observations suggest that these sources are most
likely background or foreground objects. Actually, none of them appears to be
even barely extended as would be expected if they were part of a bow shock
structure. Our near infrared observations also include a search for extended
emission in the Bracket (2.166 m) and (2.122 m)
lines as possible tracers of shocked gas in the Cygnus X-3 surroundings. The
results were similarly negative and the corresponding upper limits are
reported.Comment: Accepted for publication in A&A; 5 pages, 4 figure
Phase transition in a stochastic prime number generator
We introduce a stochastic algorithm that acts as a prime number generator.
The dynamics of such algorithm gives rise to a continuous phase transition
which separates a phase where the algorithm is able to reduce a whole set of
integers into primes and a phase where the system reaches a frozen state with
low prime density. We present both numerical simulations and an analytical
approach in terms of an annealed approximation, by means of which the data are
collapsed. A critical slowing down phenomenon is also outlined.Comment: accepted in PRE (Rapid Comm.
Mathematical modeling of injury healing process under the action of an active pharmaceutical ingredient (API)
In this work we carried out the mathematical modeling of the wound healing process, which is a well documented topic in medical and biological practice; but mathematically speaking there are still too much to be done for a clear understanding of the healing phenomom. Here we contribute to the mathematical modelling by using chemical kinetic concepts and mathematical tools, from which we have been able to formulate a system of ordinary differential equations of initial value, whose solution is presented graphically in front of a case study, where we have tested an active pharmaceutical principle with respect to its effectiveness. Finally, the speed of the healing process for such a case study produced an excellent agreement with experimental data that has been omitted due to confidentiality.En este trabajo llevamos a cabo el modelado matemático del proceso de curación de heridas, que es un tema bien documentado en la práctica médica y biológica; pero matemáticamente hablando, todavía hay mucho por hacer para una comprensión clara del fenómeno curativo. Aquí contribuimos al modelado matemático mediante el uso de conceptos de cinética química y herramientas matemáticas, a partir de los cuales hemos podido formular un sistema de ecuaciones diferenciales ordinarias de valor inicial, cuya solución se presenta gráficamente frente a un estudio de caso, donde hemos probado un principio farmacéuticamente activo con respecto a su eficacia. Finalmente, la velocidad del proceso de curación para tal estudio de caso produjo un excelente acuerdo con los datos experimentales, que se han omitido debido a la confidencialidad
- …