3,737 research outputs found
Coupled frustrated quantum spin-1/2 chains with orbital order in volborthite Cu3V2O7(OH)2(H2O)2
We present a microscopic magnetic model for the spin-liquid candidate
volborthite Cu3V2O7(OH)2(H2O)2. The essentials of this DFT-based model are (i)
the orbital ordering of Cu(1) 3d 3z2-r2 and Cu(2) 3d 3x2-y2, (ii) three
relevant couplings J_ic, J_1 and J_2, (iii) the ferromagnetic nature of J_1 and
(iv) frustration governed by the next-nearest-neighbor exchange interaction
J_2. Our model implies magnetism of frustrated coupled chains in contrast to
the previously proposed anisotropic kagome model. Exact diagonalization studies
reveal agreement with experiments.Comment: 5 pages, 4 figures + supplementar
Fully Analyzing an Algebraic Polya Urn Model
This paper introduces and analyzes a particular class of Polya urns: balls
are of two colors, can only be added (the urns are said to be additive) and at
every step the same constant number of balls is added, thus only the color
compositions varies (the urns are said to be balanced). These properties make
this class of urns ideally suited for analysis from an "analytic combinatorics"
point-of-view, following in the footsteps of Flajolet-Dumas-Puyhaubert, 2006.
Through an algebraic generating function to which we apply a multiple
coalescing saddle-point method, we are able to give precise asymptotic results
for the probability distribution of the composition of the urn, as well as
local limit law and large deviation bounds.Comment: LATIN 2012, Arequipa : Peru (2012
Maximum relative height of one-dimensional interfaces : from Rayleigh to Airy distribution
We introduce an alternative definition of the relative height h^\kappa(x) of
a one-dimensional fluctuating interface indexed by a continuously varying real
paramater 0 \leq \kappa \leq 1. It interpolates between the height relative to
the initial value (i.e. in x=0) when \kappa = 0 and the height relative to the
spatially averaged height for \kappa = 1. We compute exactly the distribution
P^\kappa(h_m,L) of the maximum h_m of these relative heights for systems of
finite size L and periodic boundary conditions. One finds that it takes the
scaling form P^\kappa(h_m,L) = L^{-1/2} f^\kappa (h_m L^{-1/2}) where the
scaling function f^\kappa(x) interpolates between the Rayleigh distribution for
\kappa=0 and the Airy distribution for \kappa=1, the latter being the
probability distribution of the area under a Brownian excursion over the unit
interval. For arbitrary \kappa, one finds that it is related to, albeit
different from, the distribution of the area restricted to the interval [0,
\kappa] under a Brownian excursion over the unit interval.Comment: 25 pages, 4 figure
A network-based threshold model for the spreading of fads in society and markets
We investigate the behavior of a threshold model for the spreading of fads
and similar phenomena in society. The model is giving the fad dynamics and is
intended to be confined to an underlying network structure. We investigate the
whole parameter space of the fad dynamics on three types of network models. The
dynamics we discover is rich and highly dependent on the underlying network
structure. For some range of the parameter space, for all types of substrate
networks, there are a great variety of sizes and life-lengths of the fads --
what one see in real-world social and economical systems
Terrestrial planets across space and time
The study of cosmology, galaxy formation and exoplanets has now advanced to a
stage where a cosmic inventory of terrestrial planets may be attempted. By
coupling semi-analytic models of galaxy formation to a recipe that relates the
occurrence of planets to the mass and metallicity of their host stars, we trace
the population of terrestrial planets around both solar-mass (FGK type) and
lower-mass (M dwarf) stars throughout all of cosmic history. We find that the
mean age of terrestrial planets in the local Universe is Gyr for FGK
hosts and Gyr for M dwarfs. We estimate that hot Jupiters have
depleted the population of terrestrial planets around FGK stars by no more than
, and that only of the terrestrial planets at the
current epoch are orbiting stars in a metallicity range for which such planets
have yet to be confirmed. The typical terrestrial planet in the local Universe
is located in a spheroid-dominated galaxy with a total stellar mass comparable
to that of the Milky Way. When looking at the inventory of planets throughout
the whole observable Universe, we argue for a total of and terrestrial planets around FGK and M
stars, respectively. Due to light travel time effects, the terrestrial planets
on our past light cone exhibit a mean age of just Gyr. These
results are discussed in the context of cosmic habitability, the Copernican
principle and searches for extraterrestrial intelligence at cosmological
distances.Comment: 11 pages, 8 figures. v.2: Accepted for publication in ApJ. Some
changes in quantitative results compared to v.1, mainly due to differences in
IMF assumption
Flows on Graphs with Random Capacities
We investigate flows on graphs whose links have random capacities. For binary
trees we derive the probability distribution for the maximal flow from the root
to a leaf, and show that for infinite trees it vanishes beyond a certain
threshold that depends on the distribution of capacities. We then examine the
maximal total flux from the root to the leaves. Our methods generalize to
simple graphs with loops, e.g., to hierarchical lattices and to complete
graphs.Comment: 8 pages, 6 figure
Monotone graph limits and quasimonotone graphs
The recent theory of graph limits gives a powerful framework for
understanding the properties of suitable (convergent) sequences of
graphs in terms of a limiting object which may be represented by a symmetric
function on , i.e., a kernel or graphon. In this context it is
natural to wish to relate specific properties of the sequence to specific
properties of the kernel. Here we show that the kernel is monotone (i.e.,
increasing in both variables) if and only if the sequence satisfies a
`quasi-monotonicity' property defined by a certain functional tending to zero.
As a tool we prove an inequality relating the cut and norms of kernels of
the form with and monotone that may be of interest in its
own right; no such inequality holds for general kernels.Comment: 38 page
Quicksort with unreliable comparisons: a probabilistic analysis
We provide a probabilistic analysis of the output of Quicksort when
comparisons can err.Comment: 29 pages, 3 figure
High-contrast Imaging with Spitzer: Deep Observations of Vega, Fomalhaut, and epsilon Eridani
Stars with debris disks are intriguing targets for direct imaging exoplanet
searches, both due to previous detections of wide planets in debris disk
systems, as well as commonly existing morphological features in the disks
themselves that may be indicative of a planetary influence. Here we present
observations of three of the most nearby young stars, that are also known to
host massive debris disks: Vega, Fomalhaut, and eps Eri. The Spitzer Space
Telescope is used at a range of orientation angles for each star, in order to
supply a deep contrast through angular differential imaging combined with
high-contrast algorithms. The observations provide the opportunity to probe
substantially colder bound planets (120--330 K) than is possible with any other
technique or instrument. For Vega, some apparently very red candidate point
sources detected in the 4.5 micron image remain to be tested for common proper
motion. The images are sensitive to ~2 Mjup companions at 150 AU in this
system. The observations presented here represent the first search for planets
around Vega using Spitzer. The upper 4.5 micron flux limit on Fomalhaut b could
be further constrained relative to previous data. In the case of eps Eri,
planets below both the effective temperature and the mass of Jupiter could be
probed from 80 AU and outwards, although no such planets were found. The data
sensitively probe the regions around the edges of the debris rings in the
systems where planets can be expected to reside. These observations validate
previous results showing that more than an order of magnitude improvement in
performance in the contrast-limited regime can be acquired with respect to
conventional methods by applying sophisticated high-contrast techniques to
space-based telescopes, thanks to the high degree of PSF stability provided in
this environment.Comment: 11 pages, 12 figures, accepted for publication in A&
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