19,341 research outputs found
Convergence towards an asymptotic shape in first-passage percolation on cone-like subgraphs of the integer lattice
In first-passage percolation on the integer lattice, the Shape Theorem
provides precise conditions for convergence of the set of sites reachable
within a given time from the origin, once rescaled, to a compact and convex
limiting shape. Here, we address convergence towards an asymptotic shape for
cone-like subgraphs of the lattice, where . In particular, we
identify the asymptotic shapes associated to these graphs as restrictions of
the asymptotic shape of the lattice. Apart from providing necessary and
sufficient conditions for - and almost sure convergence towards this
shape, we investigate also stronger notions such as complete convergence and
stability with respect to a dynamically evolving environment.Comment: 23 pages. Together with arXiv:1305.6260, this version replaces the
old. The main results have been strengthened and an earlier error in the
statement corrected. To appear in J. Theoret. Proba
Polycyclic aromatic hydrocarbons and molecular hydrogen in oxygen-rich planetary nebulae: the case of NGC6720
Evolved stars are primary sources for the formation of polycyclic aromatic
hydrocarbons (PAHs) and dust grains. Their circumstellar chemistry is usually
designated as either oxygen-rich or carbon-rich, although dual-dust chemistry
objects, whose infrared spectra reveal both silicate- and carbon-dust features,
are also known. The exact origin and nature of this dual-dust chemistry is not
yet understood. Spitzer-IRS mid-infrared spectroscopic imaging of the nearby,
oxygen-rich planetary nebula NGC6720 reveals the presence of the 11.3 micron
aromatic (PAH) emission band. It is attributed to emission from neutral PAHs,
since no band is observed in the 7 to 8 micron range. The spatial distribution
of PAHs is found to closely follow that of the warm clumpy molecular hydrogen
emission. Emission from both neutral PAHs and warm H2 is likely to arise from
photo-dissociation regions associated with dense knots that are located within
the main ring. The presence of PAHs together with the previously derived high
abundance of free carbon (relative to CO) suggest that the local conditions in
an oxygen-rich environment can also become conducive to in-situ formation of
large carbonaceous molecules, such as PAHs, via a bottom-up chemical pathway.
In this scenario, the same stellar source can enrich the interstellar medium
with both oxygen-rich dust and large carbonaceous molecules.Comment: Accepted by MNRAS. 5 page
On alpha stable distribution of wind driven water surface wave slope
We propose a new formulation of the probability distribution function of wind
driven water surface slope with an -stable distribution probability.
The mathematical formulation of the probability distribution function is given
under an integral formulation. Application to represent the probability of time
slope data from laboratory experiments is carried out with satisfactory
results. We compare also the -stable model of the water surface slopes
with the Gram-Charlier development and the non-Gaussian model of Liu et
al\cite{Liu}. Discussions and conclusions are conducted on the basis of the
data fit results and the model analysis comparison.Comment: final version of the manuscript: 25 page
Pressure-Induced Insulating State in Ba1-xRExIrO3 (RE = Gd, Eu) Single Crystals
BaIrO3 is a novel insulator with coexistent weak ferromagnetism, charge and
spin density wave. Dilute RE doping for Ba induces a metallic state, whereas
application of modest pressure readily restores an insulating state
characterized by a three-order-of-magnitude increase of resistivity. Since
pressure generally increases orbital overlap and broadens energy bands, a
pressure-induced insulating state is not commonplace. The profoundly dissimilar
responses of the ground state to light doping and low hydrostatic pressures
signal an unusual, delicate interplay between structural and electronic degrees
of freedom in BaIrO3
Consistency of the Shannon entropy in quantum experiments
The consistency of the Shannon entropy, when applied to outcomes of quantum
experiments, is analysed. It is shown that the Shannon entropy is fully
consistent and its properties are never violated in quantum settings, but
attention must be paid to logical and experimental contexts. This last remark
is shown to apply regardless of the quantum or classical nature of the
experiments.Comment: 12 pages, LaTeX2e/REVTeX4. V5: slightly different than the published
versio
Anomalous aging phenomena caused by drift velocities
We demonstrate via several examples that a uniform drift velocity gives rise
to anomalous aging, characterized by a specific form for the two-time
correlation functions, in a variety of statistical-mechanical systems far from
equilibrium. Our first example concerns the oscillatory phase observed recently
in a model of competitive learning. Further examples, where the proposed theory
is exact, include the voter model and the Ohta-Jasnow-Kawasaki theory for
domain growth in any dimension, and a theory for the smoothing of sandpile
surfaces.Comment: 7 pages, 3 figures. To appear in Europhysics Letter
Strong electron correlations in cobalt valence tautomers
We have examined cobalt based valence tautomer molecules such as
Co(SQ)(phen) using density functional theory (DFT) and variational
configuration interaction (VCI) approaches based upon a model Hamiltonian. Our
DFT results extend earlier work by finding a reduced total energy gap (order
0.6 eV) between high temperature and low temperature states when we fully relax
the coordinates (relative to experimental ones). Futhermore we demonstrate that
the charge transfer picture based upon formal valence arguments succeeds
qualitatively while failing quantitatively due to strong covalency between the
Co 3 orbitals and ligand orbitals. With the VCI approach, we argue that
the high temperature, high spin phase is strongly mixed valent, with about 30 %
admixture of Co(III) into the predominantly Co(II) ground state. We confirm
this mixed valence through a fit to the XANES spectra. Moreover, the strong
electron correlations of the mixed valent phase provide an energy lowering of
about 0.2-0.3 eV of the high temperature phase relative to the low temperature
one. Finally, we use the domain model to account for the extraordinarily large
entropy and enthalpy values associated with the transition.Comment: 10 pages, 4 figures, submitted to J. Chem. Phy
Multichannel pseudogap Kondo model: Large-N solution and quantum-critical dynamics
We discuss a multichannel SU(N) Kondo model which displays non-trivial
zero-temperature phase transitions due to a conduction electron density of
states vanishing with a power law at the Fermi level. In a particular large-N
limit, the system is described by coupled integral equations corresponding to a
dynamic saddle point. We exactly determine the universal low-energy behavior of
spectral densities at the scale-invariant fixed points, obtain anomalous
exponents, and compute scaling functions describing the crossover near the
quantum-critical points. We argue that our findings are relevant to recent
experiments on impurity-doped d-wave superconductors.Comment: 4 pages, 3 figs; extended discussion of large-N spin representations,
added references; accepted for publication in PR
Collaborative Layer-wise Discriminative Learning in Deep Neural Networks
Intermediate features at different layers of a deep neural network are known
to be discriminative for visual patterns of different complexities. However,
most existing works ignore such cross-layer heterogeneities when classifying
samples of different complexities. For example, if a training sample has
already been correctly classified at a specific layer with high confidence, we
argue that it is unnecessary to enforce rest layers to classify this sample
correctly and a better strategy is to encourage those layers to focus on other
samples.
In this paper, we propose a layer-wise discriminative learning method to
enhance the discriminative capability of a deep network by allowing its layers
to work collaboratively for classification. Towards this target, we introduce
multiple classifiers on top of multiple layers. Each classifier not only tries
to correctly classify the features from its input layer, but also coordinates
with other classifiers to jointly maximize the final classification
performance. Guided by the other companion classifiers, each classifier learns
to concentrate on certain training examples and boosts the overall performance.
Allowing for end-to-end training, our method can be conveniently embedded into
state-of-the-art deep networks. Experiments with multiple popular deep
networks, including Network in Network, GoogLeNet and VGGNet, on scale-various
object classification benchmarks, including CIFAR100, MNIST and ImageNet, and
scene classification benchmarks, including MIT67, SUN397 and Places205,
demonstrate the effectiveness of our method. In addition, we also analyze the
relationship between the proposed method and classical conditional random
fields models.Comment: To appear in ECCV 2016. Maybe subject to minor changes before
camera-ready versio
Crystal Field Triplets: A New Route to Non-Fermi Liquid Physics
A model for crystal field triplet ground states on rare earth or actinide
ions with dipolar and quadrupolar couplings to conduction electrons is studied
for the first time with renormalization group methods. The quadrupolar coupling
leads to a new nontrivial, non-Fermi liquid fixed point, which survives in an
intermediate valence Anderson model. The calculated magnetic susceptibility
displays one parameter scaling, going as ()
at intermediate temperatures, reminiscent of the non-Fermi liquid alloy
UCu_{5-x}Pd_x.Comment: 4 pages, 3 figures, REVTe
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