11,684 research outputs found
Three-Point Statistics from a New Perspective
Multipole expansion of spatial three-point statistics is introduced as a tool
for investigating and displaying configuration dependence. The novel
parametrization renders the relation between bi-spectrum and three-point
correlation function especially transparent as a set of two-dimensional Hankel
transforms. It is expected on theoretical grounds, that three-point statistics
can be described accurately with only a few multipoles. In particular, we show
that in the weakly non-linear regime, the multipoles of the reduced bispectrum,
, are significant only up to quadrupole. Moreover, the non-linear bias in
the weakly non-linear regime only affects the monopole order of these
statistics. As a consequence, a simple, novel set of estimators can be
constructed to constrain galaxy bias. In addition, the quadrupole to dipole
ratio is independent of the bias, thus it becomes a novel diagnostic of the
underlying theoretical assumptions: weakly non-linear gravity and perturbative
local bias. To illustrate the use of our approach, we present predictions based
on both power law, and CDM models. We show that the presently favoured
SDSS-WMAP concordance model displays strong ``baryon bumps'' in the 's.
Finally, we sketch out three practical techniques estimate these novel
quantities: they amount to new, and for the first time edge corrected,
estimators for the bispectrum.Comment: 5 pages 6 figures, ApL accepte
Making electromagnetic wavelets
Electromagnetic wavelets are constructed using scalar wavelets as
superpotentials, together with an appropriate polarization. It is shown that
oblate spheroidal antennas, which are ideal for their production and reception,
can be made by deforming and merging two branch cuts. This determines a unique
field on the interior of the spheroid which gives the boundary conditions for
the surface charge-current density necessary to radiate the wavelets. These
sources are computed, including the impulse response of the antenna.Comment: 29 pages, 4 figures; minor corrections and addition
Global stability analysis of birhythmicity in a self-sustained oscillator
We analyze global stability properties of birhythmicity in a self-sustained
system with random excitations. The model is a multi-limit cycles variation of
the van der Pol oscillatorintroduced to analyze enzymatic substrate reactions
in brain waves. We show that the two frequencies are strongly influenced by the
nonlinear coefficients and . With a random excitation, such as
a Gaussian white noise, the attractor's global stability is measured by the
mean escape time from one limit-cycle. An effective activation energy
barrier is obtained by the slope of the linear part of the variation of the
escape time versus the inverse noise-intensity 1/D. We find that the
trapping barriers of the two frequencies can be very different, thus leaving
the system on the same attractor for an overwhelming time. However, we also
find that the system is nearly symmetric in a narrow range of the parameters.Comment: 17 pages, 8 figures, to appear on Choas, 201
Effective Fokker-Planck Equation for Birhythmic Modified van der Pol Oscillator
We present an explicit solution based on the phase-amplitude approximation of
the Fokker-Planck equation associated with the Langevin equation of the
birhythmic modified van der Pol system. The solution enables us to derive
probability distributions analytically as well as the activation energies
associated to switching between the coexisting different attractors that
characterize the birhythmic system. Comparing analytical and numerical results
we find good agreement when the frequencies of both attractors are equal, while
the predictions of the analytic estimates deteriorate when the two frequencies
depart. Under the effect of noise the two states that characterize the
birhythmic system can merge, inasmuch as the parameter plane of the birhythmic
solutions is found to shrink when the noise intensity increases. The solution
of the Fokker-Planck equation shows that in the birhythmic region, the two
attractors are characterized by very different probabilities of finding the
system in such a state. The probability becomes comparable only for a narrow
range of the control parameters, thus the two limit cycles have properties in
close analogy with the thermodynamic phases
Nuclear energy density functional from chiral pion-nucleon dynamics: Isovector spin-orbit terms
We extend a recent calculation of the nuclear energy density functional in
the systematic framework of chiral perturbation theory by computing the
isovector spin-orbit terms: . The calculation
includes the one-pion exchange Fock diagram and the iterated one-pion exchange
Hartree and Fock diagrams. From these few leading order contributions in the
small momentum expansion one obtains already a good equation of state of
isospin-symmetric nuclear matter. We find that the parameterfree results for
the (density-dependent) strength functions and agree
fairly well with that of phenomenological Skyrme forces for densities . At very low densities a strong variation of the strength functions
and with density sets in. This has to do with chiral
singularities and the presence of two competing small mass scales
and . The novel density dependencies of and
as predicted by our parameterfree (leading order) calculation should
be examined in nuclear structure calculations.Comment: 9 pages, 3 figure, published in: Physical Review C68, 014323 (2003
Helicity, polarization, and Riemann-Silberstein vortices
Riemann-Silberstein (RS) vortices have been defined as surfaces in spacetime
where the complex form of a free electromagnetic field given by F=E+iB is null
(F.F=0), and they can indeed be interpreted as the collective history swept out
by moving vortex lines of the field. Formally, the nullity condition is similar
to the definition of "C-lines" associated with a monochromatic electric or
magnetic field, which are curves in space where the polarization ellipses
degenerate to circles. However, it was noted that RS vortices of monochromatic
fields generally oscillate at optical frequencies and are therefore
unobservable while electric and magnetic C-lines are steady. Here I show that
under the additional assumption of having definite helicity, RS vortices are
not only steady but they coincide with both sets of C-lines, electric and
magnetic. The two concepts therefore become one for waves of definite frequency
and helicity. Since the definition of RS vortices is relativistically invariant
while that of C-lines is not, it may be useful to regard the vortices as a
wideband generalization of C-lines for waves of definite helicity.Comment: 5 pages, no figures. Submitted to J of Optics A, special issue on
Singular Optics; minor changes from v.
Complex-Distance Potential Theory and Hyperbolic Equations
An extension of potential theory in R^n is obtained by continuing the
Euclidean distance function holomorphically to C^n. The resulting Newtonian
potential is generated by an extended source distribution D(z) in C^n whose
restriction to R^n is the delta function. This provides a natural model for
extended particles in physics. In C^n, interpreted as complex spacetime, D(z)
acts as a propagator generating solutions of the wave equation from their
initial values. This gives a new connection between elliptic and hyperbolic
equations that does not assume analyticity of the Cauchy data. Generalized to
Clifford analysis, it induces a similar connection between solutions of
elliptic and hyperbolic Dirac equations. There is a natural application to the
time-dependent, inhomogeneous Dirac and Maxwell equations, and the
`electromagnetic wavelets' introduced previously are an example.Comment: 25 pages, submited to Proceedings of 5th Intern. Conf. on Clifford
Algebras, Ixtapa, June 24 - July 4, 199
Probing Dark Energy with Baryonic Acoustic Oscillations from Future Large Galaxy Redshift Surveys
We show that the measurement of the baryonic acoustic oscillations in large
high redshift galaxy surveys offers a precision route to the measurement of
dark energy. The cosmic microwave background provides the scale of the
oscillations as a standard ruler that can be measured in the clustering of
galaxies, thereby yielding the Hubble parameter and angular diameter distance
as a function of redshift. This, in turn, enables one to probe dark energy. We
use a Fisher matrix formalism to study the statistical errors for redshift
surveys up to z=3 and report errors on cosmography while marginalizing over a
large number of cosmological parameters including a time-dependent equation of
state. With redshifts surveys combined with cosmic microwave background
satellite data, we achieve errors of 0.037 on Omega_x, 0.10 on w(z=0.8), and
0.28 on dw(z)/dz for cosmological constant model. Models with less negative
w(z) permit tighter constraints. We test and discuss the dependence of
performance on redshift, survey conditions, and fiducial model. We find results
that are competitive with the performance of future supernovae Ia surveys. We
conclude that redshift surveys offer a promising independent route to the
measurement of dark energy.Comment: submitted to ApJ, 24 pages, LaTe
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