2,571 research outputs found
Geometry of River Networks II: Distributions of Component Size and Number
The structure of a river network may be seen as a discrete set of nested
sub-networks built out of individual stream segments. These network components
are assigned an integral stream order via a hierarchical and discrete ordering
method. Exponential relationships, known as Horton's laws, between stream order
and ensemble-averaged quantities pertaining to network components are observed.
We extend these observations to incorporate fluctuations and all higher moments
by developing functional relationships between distributions. The relationships
determined are drawn from a combination of theoretical analysis, analysis of
real river networks including the Mississippi, Amazon and Nile, and numerical
simulations on a model of directed, random networks. Underlying distributions
of stream segment lengths are identified as exponential. Combinations of these
distributions form single-humped distributions with exponential tails, the sums
of which are in turn shown to give power law distributions of stream lengths.
Distributions of basin area and stream segment frequency are also addressed.
The calculations identify a single length-scale as a measure of size
fluctuations in network components. This article is the second in a series of
three addressing the geometry of river networks.Comment: 16 pages, 13 figures, 4 tables, Revtex4, submitted to PR
Flares and variability from Sagittarius A*: five nights of simultaneous multi-wavelength observations
Aims. We report on simultaneous observations and modeling of mid-infrared
(MIR), near-infrared (NIR), and submillimeter (submm) emission of the source
Sgr A* associated with the supermassive black hole at the center of our Galaxy.
Our goal was to monitor the activity of Sgr A* at different wavelengths in
order to constrain the emitting processes and gain insight into the nature of
the close environment of Sgr A*. Methods. We used the MIR instrument VISIR in
the BURST imaging mode, the adaptive optics assisted NIR camera NACO, and the
sub-mm antenna APEX to monitor Sgr A* over several nights in July 2007.
Results. The observations reveal remarkable variability in the NIR and sub-mm
during the five nights of observation. No source was detected in the MIR, but
we derived the lowest upper limit for a flare at 8.59 microns (22.4 mJy with
A_8.59mu = 1.6+/- 0.5). This observational constraint makes us discard the
observed NIR emission as coming from a thermal component emitting at sub-mm
frequencies. Moreover, comparison of the sub-mm and NIR variability shows that
the highest NIR fluxes (flares) are coincident with the lowest sub-mm levels of
our five-night campaign involving three flares. We explain this behavior by a
loss of electrons to the system and/or by a decrease in the magnetic field, as
might conceivably occur in scenarios involving fast outflows and/or magnetic
reconnection.Comment: 10 pages, 7 figures, published in A&
The two states of Sgr A* in the near-infrared: bright episodic flares on top of low-level continuous variability
In this paper we examine properties of the variable source Sgr A* in the
near-infrared (NIR) using a very extensive Ks-band data set from NACO/VLT
observations taken 2004 to 2009. We investigate the variability of Sgr A* with
two different photometric methods and analyze its flux distribution. We find
Sgr A* is continuously emitting and continuously variable in the near-infrared,
with some variability occurring on timescales as long as weeks. The flux
distribution can be described by a lognormal distribution at low intrinsic
fluxes (<~5 mJy, dereddened with A_{Ks}=2.5). The lognormal distribution has a
median flux of approximately 1.1 mJy, but above 5 mJy the flux distribution is
significantly flatter (high flux events are more common) than expected for the
extrapolation of the lognormal distribution to high fluxes. We make a general
identification of the low level emission above 5 mJy as flaring emission and of
the low level emission as the quiescent state. We also report here the
brightest Ks-band flare ever observed (from August 5th, 2008) which reached an
intrinsic Ks-band flux of 27.5 mJy (m_{Ks}=13.5). This flare was a factor 27
increase over the median flux of Sgr A*, close to double the brightness of the
star S2, and 40% brighter than the next brightest flare ever observed from
Sgr~A*.Comment: 14 pages, 6 figures, accepted for publication in Ap
Stress transmission in granular matter
The transmission of forces through a disordered granular system is studied by
means of a geometrical-topological approach that reduces the granular packing
into a set of layers. This layered structure constitutes the skeleton through
which the force chains set up. Given the granular packing, and the region where
the force is applied, such a skeleton is uniquely defined. Within this
framework, we write an equation for the transmission of the vertical forces
that can be solved recursively layer by layer. We find that a special class of
analytical solutions for this equation are L\'evi-stable distributions. We
discuss the link between criticality and fragility and we show how the
disordered packing naturally induces the formation of force-chains and arches.
We point out that critical regimes, with power law distributions, are
associated with the roughness of the topological layers. Whereas, fragility is
associated with local changes in the force network induced by local granular
rearrangements or by changes in the applied force. The results are compared
with recent experimental observations in particulate matter and with computer
simulations.Comment: 14 pages, Latex, 5 EPS figure
Positivity of the English language
Over the last million years, human language has emerged and evolved as a
fundamental instrument of social communication and semiotic representation.
People use language in part to convey emotional information, leading to the
central and contingent questions: (1) What is the emotional spectrum of natural
language? and (2) Are natural languages neutrally, positively, or negatively
biased? Here, we report that the human-perceived positivity of over 10,000 of
the most frequently used English words exhibits a clear positive bias. More
deeply, we characterize and quantify distributions of word positivity for four
large and distinct corpora, demonstrating that their form is broadly invariant
with respect to frequency of word use.Comment: Manuscript: 9 pages, 3 tables, 5 figures; Supplementary Information:
12 pages, 3 tables, 8 figure
Geometry of River Networks I: Scaling, Fluctuations, and Deviations
This article is the first in a series of three papers investigating the
detailed geometry of river networks. Large-scale river networks mark an
important class of two-dimensional branching networks, being not only of
intrinsic interest but also a pervasive natural phenomenon. In the description
of river network structure, scaling laws are uniformly observed. Reported
values of scaling exponents vary suggesting that no unique set of scaling
exponents exists. To improve this current understanding of scaling in river
networks and to provide a fuller description of branching network structure, we
report here a theoretical and empirical study of fluctuations about and
deviations from scaling. We examine data for continent-scale river networks
such as the Mississippi and the Amazon and draw inspiration from a simple model
of directed, random networks. We center our investigations on the scaling of
the length of sub-basin's dominant stream with its area, a characterization of
basin shape known as Hack's law. We generalize this relationship to a joint
probability density and show that fluctuations about scaling are substantial.
We find strong deviations from scaling at small scales which can be explained
by the existence of linear network structure. At intermediate scales, we find
slow drifts in exponent values indicating that scaling is only approximately
obeyed and that universality remains indeterminate. At large scales, we observe
a breakdown in scaling due to decreasing sample space and correlations with
overall basin shape. The extent of approximate scaling is significantly
restricted by these deviations and will not be improved by increases in network
resolution.Comment: 16 pages, 13 figures, Revtex4, submitted to PR
Clinical Spectrum of HLA-B27-associated Ocular Inflammation
Human leukocyte antigen (HLA)-B27-associated anterior uveitis (AU) is the most commonly diagnosed form of AU and represents the largest entity of non-infectious uveitis around the world. The most typical ocular manifestation associated with HLA-B27 consists of unilateral AU of acute onset. The HLA-B27-associated acute AU represents a distinct clinical entity occurring typically in young adults between the ages of 20 and 40 years. HLA-B27-associated acute AU is typically unilateral and lasts usually several weeks and diminishes within 3 months in the majority of patients. The anterior chamber shows typically severe cellular reaction and flare, as well as a fibrinous exudate. Frequently, posterior synechiae are formed and occasionally hypopyon is present. The pattern of the disease is recurrent with a full remission between the attacks. Intraocular pressure during active periods is typically low due to inflammation of ciliary body and decreased aqueous production. Less typical presentations are also recognized and include the development of chronic inflammation, posterior segmen
On Random Bubble Lattices
We study random bubble lattices which can be produced by processes such as
first order phase transitions, and derive characteristics that are important
for understanding the percolation of distinct varieties of bubbles. The results
are relevant to the formation of topological defects as they show that infinite
domain walls and strings will be produced during appropriate first order
transitions, and that the most suitable regular lattice to study defect
formation in three dimensions is a face centered cubic lattice. Another
application of our work is to the distribution of voids in the large-scale
structure of the universe. We argue that the present universe is more akin to a
system undergoing a first-order phase transition than to one that is
crystallizing, as is implicit in the Voronoi foam description. Based on the
picture of a bubbly universe, we predict a mean coordination number for the
voids of 13.4. The mean coordination number may also be used as a tool to
distinguish between different scenarios for structure formation.Comment: several modifications including new abstract, comparison with froth
models, asymptotics of coordination number distribution, further discussion
of biased defects, and relevance to large-scale structur
Stochastic analysis of surface roughness
For the characterization of surface height profiles we present a new
stochastic approach which is based on the theory of Markov processes. With this
analysis we achieve a characterization of the complexity of the surface
roughness by means of a Fokker-Planck or Langevin equation, providing the
complete stochastic information of multiscale joint probabilities. The method
was applied to different road surface profiles which were measured with high
resolution. Evidence of Markov properties is shown. Estimations for the
parameters of the Fokker-Planck equation are based on pure, parameter free data
analysis
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