2,755 research outputs found
A nonstationary generalization of the Kerr congruence
Making use of the Kerr theorem for shear-free null congruences and of
Newman's representation for a virtual charge ``moving'' in complex space-time,
we obtain an axisymmetric time-dependent generalization of the Kerr congruence,
with a singular ring uniformly contracting to a point and expanding then to
infinity. Electromagnetic and complex eikonal field distributions are naturally
associated with the obtained congruence, with electric charge being
necesssarily unit (``elementary''). We conjecture that the corresponding
solution to the Einstein-Maxwell equations could describe the process of
continious transition of the naked ringlike singularitiy into a rotating black
hole and vice versa, under a particular current radius of the singular ring.Comment: 6 pages, twocolum
Spectral Simplicity of Apparent Complexity, Part II: Exact Complexities and Complexity Spectra
The meromorphic functional calculus developed in Part I overcomes the
nondiagonalizability of linear operators that arises often in the temporal
evolution of complex systems and is generic to the metadynamics of predicting
their behavior. Using the resulting spectral decomposition, we derive
closed-form expressions for correlation functions, finite-length Shannon
entropy-rate approximates, asymptotic entropy rate, excess entropy, transient
information, transient and asymptotic state uncertainty, and synchronization
information of stochastic processes generated by finite-state hidden Markov
models. This introduces analytical tractability to investigating information
processing in discrete-event stochastic processes, symbolic dynamics, and
chaotic dynamical systems. Comparisons reveal mathematical similarities between
complexity measures originally thought to capture distinct informational and
computational properties. We also introduce a new kind of spectral analysis via
coronal spectrograms and the frequency-dependent spectra of past-future mutual
information. We analyze a number of examples to illustrate the methods,
emphasizing processes with multivariate dependencies beyond pairwise
correlation. An appendix presents spectral decomposition calculations for one
example in full detail.Comment: 27 pages, 12 figures, 2 tables; most recent version at
http://csc.ucdavis.edu/~cmg/compmech/pubs/sdscpt2.ht
Spectral properties of a short-range impurity in a quantum dot
The spectral properties of the quantum mechanical system consisting of a
quantum dot with a short-range attractive impurity inside the dot are
investigated in the zero-range limit. The Green function of the system is
obtained in an explicit form. In the case of a spherically symmetric quantum
dot, the dependence of the spectrum on the impurity position and the strength
of the impurity potential is analyzed in detail. It is proven that the
confinement potential of the dot can be recovered from the spectroscopy data.
The consequences of the hidden symmetry breaking by the impurity are
considered. The effect of the positional disorder is studied.Comment: 30 pages, 6 figures, Late
Rare events, escape rates and quasistationarity: some exact formulae
We present a common framework to study decay and exchanges rates in a wide
class of dynamical systems. Several applications, ranging form the metric
theory of continuons fractions and the Shannon capacity of contrained systems
to the decay rate of metastable states, are given
Random walks on the Apollonian network with a single trap
Explicit determination of the mean first-passage time (MFPT) for trapping
problem on complex media is a theoretical challenge. In this paper, we study
random walks on the Apollonian network with a trap fixed at a given hub node
(i.e. node with the highest degree), which are simultaneously scale-free and
small-world. We obtain the precise analytic expression for the MFPT that is
confirmed by direct numerical calculations. In the large system size limit, the
MFPT approximately grows as a power-law function of the number of nodes, with
the exponent much less than 1, which is significantly different from the
scaling for some regular networks or fractals, such as regular lattices,
Sierpinski fractals, T-graph, and complete graphs. The Apollonian network is
the most efficient configuration for transport by diffusion among all
previously studied structure.Comment: Definitive version accepted for publication in EPL (Europhysics
Letters
The dynamics of financial stability in complex networks
We address the problem of banking system resilience by applying
off-equilibrium statistical physics to a system of particles, representing the
economic agents, modelled according to the theoretical foundation of the
current banking regulation, the so called Merton-Vasicek model. Economic agents
are attracted to each other to exchange `economic energy', forming a network of
trades. When the capital level of one economic agent drops below a minimum, the
economic agent becomes insolvent. The insolvency of one single economic agent
affects the economic energy of all its neighbours which thus become susceptible
to insolvency, being able to trigger a chain of insolvencies (avalanche). We
show that the distribution of avalanche sizes follows a power-law whose
exponent depends on the minimum capital level. Furthermore, we present evidence
that under an increase in the minimum capital level, large crashes will be
avoided only if one assumes that agents will accept a drop in business levels,
while keeping their trading attitudes and policies unchanged. The alternative
assumption, that agents will try to restore their business levels, may lead to
the unexpected consequence that large crises occur with higher probability
Gamma-ray absorption and the origin of the gamma-ray flare in Cygnus X-1
The high-mass microquasar Cygnus X-1, the best-established candidate for a
stellar-mass black hole in the Galaxy, has been detected in a flaring state at
very high energies (VHE), E > 200 GeV, by the Atmospheric Cherenkov Telescope
MAGIC. The flare occurred at orbital phase 0.91, where phase 1 is the
configuration with the black hole behind the companion high-mass star, when the
absorption of gamma-ray photons by photon-photon annihilation with the stellar
field is expected to be highest. We aim to set up a model for the high-energy
emission and absorption in Cyg X-1 that can explain the nature of the observed
gamma-ray flare. We study the gamma-ray opacity due to pair creation along the
whole orbit, and for different locations of the emitter. Then we consider a
possible mechanism for the production of the VHE emission. We present detailed
calculations of the gamma-ray opacity and infer from these calculations the
distance from the black hole where the emitting region was located. We suggest
that the flare was the result of a jet-clump interaction where the decay
products of inelastic proton-proton collisions dominate the VHE outcome. We are
able to reproduce the spectrum of Cyg X-1 during the observed flare under
reasonable assumptions. The flare may be the first event of jet-cloud
interaction ever detected at such high energies.Comment: 9 pages, 7 figure
The Gaia-ESO Survey: Separating disk chemical substructures with cluster models
(Abridged) Recent spectroscopic surveys have begun to explore the Galactic
disk system outside the solar neighborhood on the basis of large data samples.
In this way, they provide valuable information for testing spatial and temporal
variations of disk structure kinematics and chemical evolution. We used a
Gaussian mixture model algorithm, as a rigurous mathematical approach, to
separate in the [Mg/Fe] vs. [Fe/H] plane a clean disk star subsample from the
Gaia-ESO survey internal data release 2. We find that the sample is separated
into five groups associated with major Galactic components; the metal-rich end
of the halo, the thick disk, and three subgroups for the thin disk sequence.
This is confirmed with a sample of red clump stars from the Apache Point
Observatory Galactic Evolution Experiment (APOGEE) survey. The two
metal-intermediate and metal-rich groups of the thin disk decomposition
([Fe/H]>-0.25 dex) highlight a change in the slope at solar metallicity. This
holds true at different radial regions. The distribution of Galactocentric
radial distances of the metal-poor part of the thin disk ([Fe/H]<-0.25 dex) is
shifted to larger distances than those of the more metal-rich parts. Moreover,
the metal-poor part of the thin disk presents indications of a scale height
intermediate between those of the thick and the rest of the thin disk, and it
displays higher azimuthal velocities than the latter. These stars might have
formed and evolved in parallel and/or dissociated from the inside-out formation
taking place in the internal thin disk. Their enhancement levels might be due
to their origin from gas pre-enriched by outflows from the thick disk or the
inner halo. The smooth trends of their properties (their spatial distribution
with respect to the plane, in particular) with [Fe/H] and [Mg/Fe] suggested by
the data indicates a quiet dynamical evolution, with no relevant merger events
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