76,305 research outputs found
Peaks in the CMBR power spectrum. I. Mathematical analysis of the associated real space features
The purpose of our study is to understand the mathematical origin in real
space of modulated and damped sinusoidal peaks observed in cosmic microwave
background radiation anisotropies. We use the theory of the Fourier transform
to connect localized features of the two-point correlation function in real
space to oscillations in the power spectrum. We also illustrate analytically
and by means of Monte Carlo simulations the angular correlation function for
distributions of filled disks with fixed or variable radii capable of
generating oscillations in the power spectrum. While the power spectrum shows
repeated information in the form of multiple peaks and oscillations, the
angular correlation function offers a more compact presentation that condenses
all the information of the multiple peaks into a localized real space feature.
We have seen that oscillations in the power spectrum arise when there is a
discontinuity in a given derivative of the angular correlation function at a
given angular distance. These kinds of discontinuities do not need to be abrupt
in an infinitesimal range of angular distances but may also be smooth, and can
be generated by simply distributing excesses of antenna temperature in filled
disks of fixed or variable radii on the sky, provided that there is a non-null
minimum radius and/or the maximum radius is constrained.Comment: accepted to be published in Physica
On the design of optimal input signals in system identification
The problem of designing optimal inputs in the identification of linear systems with unknown random parameters is considered using a Bayesian approach. The information matrix, which is positive definite for the class of systems analyzed, gives a measure of performance for the system inputs. The computation of the optimal closed-loop input mappings is shown to be a nontrivial exercise in adaptive control. Deterministic optimal inputs are shown to be easily computable. Numerical examples are given. A Kalman filter is used to estimate the parameters. A necessary condition for the Kalman filter not to diverge when applying linear feedback is also given
Equation of state of a seven-dimensional hard-sphere fluid. Percus-Yevick theory and molecular dynamics simulations
Following the work of Leutheusser [Physica A 127, 667 (1984)], the solution
to the Percus-Yevick equation for a seven-dimensional hard-sphere fluid is
explicitly found. This allows the derivation of the equation of state for the
fluid taking both the virial and the compressibility routes. An analysis of the
virial coefficients and the determination of the radius of convergence of the
virial series are carried out. Molecular dynamics simulations of the same
system are also performed and a comparison between the simulation results for
the compressibility factor and theoretical expressions for the same quantity is
presented.Comment: 12 pages, 4 figures; v3: Equation (A.19) corrected (see
http://dx.doi.org/10.1063/1.2390712
Boron determination in steels by Inductively-Coupled Plasma spectometry (ICP)
The sample is treated with 5N H2SO4 followed by concentrated HNO3 and the diluted mixture is filtered. Soluble B is determined in the filtrate by Inductively-Coupled Plasma (ICP) spectrometry after addition HCl and extraction of Fe with ethyl-ether. The residue is fused with Na2CO3 and, after treatment with HCl, the insoluble B is determined by ICP spectrometry as before. The method permits determination of ppm amounts of B in steel
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