826 research outputs found
An elliptical tiling method to generate a 2-dimensional set of templates for gravitational wave search
Searching for a signal depending on unknown parameters in a noisy background
with matched filtering techniques always requires an analysis of the data with
several templates in parallel in order to ensure a proper match between the
filter and the real waveform. The key feature of such an implementation is the
design of the filter bank which must be small to limit the computational cost
while keeping the detection efficiency as high as possible. This paper presents
a geometrical method which allows one to cover the corresponding physical
parameter space by a set of ellipses, each of them being associated to a given
template. After the description of the main characteristics of the algorithm,
the method is applied in the field of gravitational wave (GW) data analysis,
for the search of damped sine signals. Such waveforms are expected to be
produced during the de-excitation phase of black holes -- the so-called
'ringdown' signals -- and are also encountered in some numerically computed
supernova signals.Comment: Accepted in PR
Optimum Placement of Post-1PN GW Chirp Templates Made Simple at any Match Level via Tanaka-Tagoshi Coordinates
A simple recipe is given for constructing a maximally sparse regular lattice
of spin-free post-1PN gravitational wave chirp templates subject to a given
minimal match constraint, using Tanaka-Tagoshi coordinates.Comment: submitted to Phys. Rev.
Local statistics for random domino tilings of the Aztec diamond
We prove an asymptotic formula for the probability that, if one chooses a
domino tiling of a large Aztec diamond at random according to the uniform
distribution on such tilings, the tiling will contain a domino covering a given
pair of adjacent lattice squares. This formula quantifies the effect of the
diamond's boundary conditions on the behavior of typical tilings; in addition,
it yields a new proof of the arctic circle theorem of Jockusch, Propp, and
Shor. Our approach is to use the saddle point method to estimate certain
weighted sums of squares of Krawtchouk polynomials (whose relevance to domino
tilings is demonstrated elsewhere), and to combine these estimates with some
exponential sum bounds to deduce our final result. This approach generalizes
straightforwardly to the case in which the probability distribution on the set
of tilings incorporates bias favoring horizontal over vertical tiles or vice
versa. We also prove a fairly general large deviation estimate for domino
tilings of simply-connected planar regions that implies that some of our
results on Aztec diamonds apply to many other similar regions as well.Comment: 42 pages, 7 figure
Tetratic Order in the Phase Behavior of a Hard-Rectangle System
Previous Monte Carlo investigations by Wojciechowski \emph{et al.} have found
two unusual phases in two-dimensional systems of anisotropic hard particles: a
tetratic phase of four-fold symmetry for hard squares [Comp. Methods in Science
and Tech., 10: 235-255, 2004], and a nonperiodic degenerate solid phase for
hard-disk dimers [Phys. Rev. Lett., 66: 3168-3171, 1991]. In this work, we
study a system of hard rectangles of aspect ratio two, i.e., hard-square dimers
(or dominos), and demonstrate that it exhibits a solid phase with both of these
unusual properties. The solid shows tetratic, but not nematic, order, and it is
nonperiodic having the structure of a random tiling of the square lattice with
dominos. We obtain similar results with both a classical Monte Carlo method
using true rectangles and a novel molecular dynamics algorithm employing
rectangles with rounded corners. It is remarkable that such simple convex
two-dimensional shapes can produce such rich phase behavior. Although we have
not performed exact free-energy calculations, we expect that the random domino
tiling is thermodynamically stabilized by its degeneracy entropy, well-known to
be per particle from previous studies of the dimer problem on the
square lattice. Our observations are consistent with a KTHNY two-stage phase
transition scenario with two continuous phase transitions, the first from
isotropic to tetratic liquid, and the second from tetratic liquid to solid.Comment: Submitted for publicatio
Solvent Mediated Assembly of Nanoparticles Confined in Mesoporous Alumina
The controlled self-assembly of thiol stabilized gold nanocrystals in a
mediating solvent and confined within mesoporous alumina was probed in situ
with small angle x-ray scattering. The evolution of the self-assembly process
was controlled reversibly via regulated changes in the amount of solvent
condensed from an undersaturated vapor. Analysis indicated that the
nanoparticles self-assembled into cylindrical monolayers within the porous
template. Nanoparticle nearest-neighbor separation within the monolayer
increased and the ordering decreased with the controlled addition of solvent.
The process was reversible with the removal of solvent. Isotropic clusters of
nanoparticles were also observed to form temporarily during desorption of the
liquid solvent and disappeared upon complete removal of liquid. Measurements of
the absorption and desorption of the solvent showed strong hysteresis upon
thermal cycling. In addition, the capillary filling transition for the solvent
in the nanoparticle-doped pores was shifted to larger chemical potential,
relative to the liquid/vapor coexistence, by a factor of 4 as compared to the
expected value for the same system without nanoparticles.Comment: 9 pages, 9 figures, appeared in Phys. Rev.
Aggregates of two-dimensional vesicles: Rouleaux and sheets
Using both numerical and variational minimization of the bending and adhesion
energy of two-dimensional lipid vesicles, we study their aggregation, and we
find that the stable aggregates include an infinite number of vesicles and that
they arrange either in a columnar or in a sheet-like structure. We calculate
the stability diagram and we discuss the modes of transformation between the
two types of aggregates, showing that they include disintegration as well as
intercalation.Comment: 4 figure
- …