12,907 research outputs found
Measuring the Decorrelation Times of Fourier Modes in Simulations
We describe a method to study the rate at which modes decorrelate in
numerical simulations. We study the XY model updated with the Metropolis and
Wolff dynamics respectively and compute the rate at which each eigenvector of
the dynamics decorrelates. Our method allows us to identify the decorrelation
time for each mode separately. We find that the autocorrelation function of the
various modes is markedly different for the `local' Metropolis compared to the
`non-local' Wolff dynamics. Equipped with this new insight, it may be possible
to devise highly efficient algorithms.Comment: 16 pp (LaTeX), PUPT-1378 , IASSNS-HEP-93/
Sub-Riemannian Fast Marching in SE(2)
We propose a Fast Marching based implementation for computing sub-Riemanninan
(SR) geodesics in the roto-translation group SE(2), with a metric depending on
a cost induced by the image data. The key ingredient is a Riemannian
approximation of the SR-metric. Then, a state of the art Fast Marching solver
that is able to deal with extreme anisotropies is used to compute a SR-distance
map as the solution of a corresponding eikonal equation. Subsequent
backtracking on the distance map gives the geodesics. To validate the method,
we consider the uniform cost case in which exact formulas for SR-geodesics are
known and we show remarkable accuracy of the numerically computed SR-spheres.
We also show a dramatic decrease in computational time with respect to a
previous PDE-based iterative approach. Regarding image analysis applications,
we show the potential of considering these data adaptive geodesics for a fully
automated retinal vessel tree segmentation.Comment: CIARP 201
Harmonic oscillator in a background magnetic field in noncommutative quantum phase-space
We solve explicitly the two-dimensional harmonic oscillator and the harmonic
oscillator in a background magnetic field in noncommutative phase-space without
making use of any type of representation. A key observation that we make is
that for a specific choice of the noncommutative parameters, the time reversal
symmetry of the systems get restored since the energy spectrum becomes
degenerate. This is in contrast to the noncommutative configuration space where
the time reversal symmetry of the harmonic oscillator is always broken.Comment: 7 pages Late
Graph Database Solution for Higher Order Spatial Statistics in the Era of Big Data
We present an algorithm for the fast computation of the general -point
spatial correlation functions of any discrete point set embedded within an
Euclidean space of . Utilizing the concepts of kd-trees and graph
databases, we describe how to count all possible -tuples in binned
configurations within a given length scale, e.g. all pairs of points or all
triplets of points with side lengths . Through bench-marking we show
the computational advantage of our new graph based algorithm over more
traditional methods. We show that all 3-point configurations up to and beyond
the Baryon Acoustic Oscillation scale (200 Mpc in physical units) can be
performed on current SDSS data in reasonable time. Finally we present the first
measurements of the 4-point correlation function of 0.5 million SDSS
galaxies over the redshift range .Comment: 9 pages, 8 figures, submitte
Hyperbolic conservation laws on the sphere. A geometry-compatible finite volume scheme
We consider entropy solutions to the initial value problem associated with
scalar nonlinear hyperbolic conservation laws posed on the two-dimensional
sphere. We propose a finite volume scheme which relies on a web-like mesh made
of segments of longitude and latitude lines. The structure of the mesh allows
for a discrete version of a natural geometric compatibility condition, which
arose earlier in the well-posedness theory established by Ben-Artzi and
LeFloch. We study here several classes of flux vectors which define the
conservation law under consideration. They are based on prescribing a suitable
vector field in the Euclidean three-dimensional space and then suitably
projecting it on the sphere's tangent plane; even when the flux vector in the
ambient space is constant, the corresponding flux vector is a non-trivial
vector field on the sphere. In particular, we construct here "equatorial
periodic solutions", analogous to one-dimensional periodic solutions to
one-dimensional conservation laws, as well as a wide variety of stationary
(steady state) solutions. We also construct "confined solutions", which are
time-dependent solutions supported in an arbitrarily specified subdomain of the
sphere. Finally, representative numerical examples and test-cases are
presented.Comment: 22 pages, 10 figures. This is the third part of a series; see also
arXiv:math/0612846 and arXiv:math/061284
The Ljapunov-Schmidt reduction for some critical problems
This is a survey about the application of the Ljapunov-Schmidt reduction for
some critical problems
Genetic Correlations in Mutation Processes
We study the role of phylogenetic trees on correlations in mutation
processes. Generally, correlations decay exponentially with the generation
number. We find that two distinct regimes of behavior exist. For mutation rates
smaller than a critical rate, the underlying tree morphology is almost
irrelevant, while mutation rates higher than this critical rate lead to strong
tree-dependent correlations. We show analytically that identical critical
behavior underlies all multiple point correlations. This behavior generally
characterizes branching processes undergoing mutation.Comment: revtex, 8 pages, 2 fig
Steering proton migration in hydrocarbons using intense few-cycle laser fields
Proton migration is a ubiquitous process in chemical reactions related to
biology, combustion, and catalysis. Thus, the ability to control the movement
of nuclei with tailored light, within a hydrocarbon molecule holds promise for
far-reaching applications. Here, we demonstrate the steering of hydrogen
migration in simple hydrocarbons, namely acetylene and allene, using
waveform-controlled, few-cycle laser pulses. The rearrangement dynamics are
monitored using coincident 3D momentum imaging spectroscopy, and described with
a quantum-dynamical model. Our observations reveal that the underlying control
mechanism is due to the manipulation of the phases in a vibrational wavepacket
by the intense off-resonant laser field.Comment: 5 pages, 4 figure
Universal scaling in sports ranking
Ranking is a ubiquitous phenomenon in the human society. By clicking the web
pages of Forbes, you may find all kinds of rankings, such as world's most
powerful people, world's richest people, top-paid tennis stars, and so on and
so forth. Herewith, we study a specific kind, sports ranking systems in which
players' scores and prize money are calculated based on their performances in
attending various tournaments. A typical example is tennis. It is found that
the distributions of both scores and prize money follow universal power laws,
with exponents nearly identical for most sports fields. In order to understand
the origin of this universal scaling we focus on the tennis ranking systems. By
checking the data we find that, for any pair of players, the probability that
the higher-ranked player will top the lower-ranked opponent is proportional to
the rank difference between the pair. Such a dependence can be well fitted to a
sigmoidal function. By using this feature, we propose a simple toy model which
can simulate the competition of players in different tournaments. The
simulations yield results consistent with the empirical findings. Extensive
studies indicate the model is robust with respect to the modifications of the
minor parts.Comment: 8 pages, 7 figure
Time-Dependent Behavior of Linear Polarization in Unresolved Photospheres, With Applications for The Hanle Effect
Aims: This paper extends previous studies in modeling time varying linear
polarization due to axisymmetric magnetic fields in rotating stars. We use the
Hanle effect to predict variations in net line polarization, and use geometric
arguments to generalize these results to linear polarization due to other
mechanisms. Methods: Building on the work of Lopez Ariste et al., we use simple
analytic models of rotating stars that are symmetric except for an axisymmetric
magnetic field to predict the polarization lightcurve due to the Hanle effect.
We highlight the effects for the variable line polarization as a function of
viewing inclination and field axis obliquity. Finally, we use geometric
arguments to generalize our results to linear polarization from the weak
transverse Zeeman effect. Results: We derive analytic expressions to
demonstrate that the variable polarization lightcurve for an oblique magnetic
rotator is symmetric. This holds for any axisymmetric field distribution and
arbitrary viewing inclination to the rotation axis. Conclusions: For the
situation under consideration, the amplitude of the polarization variation is
set by the Hanle effect, but the shape of the variation in polarization with
phase depends largely on geometrical projection effects. Our work generalizes
the applicability of results described in Lopez Ariste et al., inasmuch as the
assumptions of a spherical star and an axisymmetric field are true, and
provides a strategy for separating the effects of perspective from the Hanle
effect itself for interpreting polarimetric lightcurves.Comment: 6 pages; 4 figures. Includes an extra figure found only in this
preprint versio
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