1,574 research outputs found
Asymptotic and exact series representations for the incomplete Gamma function
Using a variational approach, two new series representations for the
incomplete Gamma function are derived: the first is an asymptotic series, which
contains and improves over the standard asymptotic expansion; the second is a
uniformly convergent series, completely analytical, which can be used to obtain
arbitrarily accurate estimates of for any value of or .
Applications of these formulas are discussed.Comment: 8 pages, 4 figure
The period of a classical oscillator
We develop a simple method to obtain approximate analytical expressions for
the period of a particle moving in a given potential. The method is inspired to
the Linear Delta Expansion (LDE) and it is applied to a large class of
potentials. Precise formulas for the period are obtained.Comment: 5 pages, 4 figure
Materials and techniques for spacecraft static charge control
An overview of the design, development, fabrication, and testing of transparent conductive coatings and conductive lattices deposited or formed on high resistivity spacecraft dielectric materials to obtain control static charge buildup on spacecraft external surfaces is presented. Fabrication techniques for the deposition of indium/tin oxide coatings and copper grid networks on Kapton and FEP Teflon films and special frit coatings for OSR and solar cell cover glasses are discussed. The techniques include sputtering, photoetching, silkscreening, and mechanical processes. A facility designed and built to simulate the electron plasma at geosynchronous altitudes is described along with test procedures. The results of material characterizations as well as electron irradiation aging effects in this facility for spacecraft polymers treated to control static charge are presented. The data presents results for electron beam energies up to 30 kV and electron current densities of 30 nA/cm squared. Parameters measured include secondary emission, surface leakage, and through the sample currents as a function of primary beam energy and voltage
Non perturbative regularization of one loop integrals at finite temperature
A method devised by the author is used to calculate analytical expressions
for one loop integrals at finite temperature. A non-perturbative regularization
of the integrals is performed, yielding expressions of non-polynomial nature. A
comparison with previuosly published results is presented and the advantages of
the present technique are discussed.Comment: 7 pages, 2 figures, 2 tables; corrected some typos and simplified eq.
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Inversion of perturbation series
We investigate the inversion of perturbation series and its resummation, and
prove that it is related to a recently developed parametric perturbation
theory. Results for some illustrative examples show that in some cases series
reversion may improve the accuracy of the results
Variational collocation for systems of coupled anharmonic oscillators
We have applied a collocation approach to obtain the numerical solution to
the stationary Schr\"odinger equation for systems of coupled oscillators. The
dependence of the discretized Hamiltonian on scale and angle parameters is
exploited to obtain optimal convergence to the exact results. A careful
comparison with results taken from the literature is performed, showing the
advantages of the present approach.Comment: 14 pages, 10 table
Influence of nucleonic motion in Relativistic Fermi Gas inclusive responses
Impulsive hadronic descriptions of electroweak processes in nuclei involve
two distinctly different elements: one stems from the nuclear many-body physics
--- the medium --- which is rather similar for the various inclusive response
functions, and the other embodies the responses of the hadrons themselves to
the electroweak probe and varies with the channel selected. In this letter we
investigate within the context of the relativistic Fermi gas in both the
quasi-elastic and regimes the interplay between these two
elements. Specifically, we focus on expansions in the one small parameter in
the problem, namely, the momentum of a nucleon in the initial wave function
compared with the hadronic scale, the nucleon mass. Both parity-conserving and
-violating inclusive responses are studied and the interplay between
longitudinal () and transverse ( and ) contributions is highlighted.Comment: 11 pages, 1 figur
Spectroscopy of annular drums and quantum rings: perturbative and nonperturbative results
We obtain systematic approximations to the states (energies and wave
functions) of quantum rings (annular drums) of arbitrary shape by conformally
mapping the annular domain to a simply connected domain. Extending the general
results of Ref.\cite{Amore09} we obtain an analytical formula for the spectrum
of quantum ring of arbirtrary shape: for the cases of a circular annulus and of
a Robnik ring considered here this formula is remarkably simple and precise. We
also obtain precise variational bounds for the ground state of different
quantum rings. Finally we extend the Conformal Collocation Method of
\cite{Amore08,Amore09} to the class of problems considered here and calculate
precise numerical solutions for a large number of states ().Comment: 12 pages, 12 figures, 2 table
Comparative study of quantum anharmonic potentials
We perform a study of various anharmonic potentials using a recently
developed method. We calculate both the wave functions and the energy
eigenvalues for the ground and first excited states of the quartic, sextic and
octic potentials with high precision, comparing the results with other
techniques available in the literature.Comment: 13 pages, 8 figures and 2 tables; revtex
Binding and migration paths of Au adatoms on the GaAs(001) surface
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