A Multidomain Spectral Method for Scalar and Vectorial Poisson Equations with Noncompact Sources

We study the convergence of exact and inexact versions of the proximal point method with a generalized regularization function in Hadamard manifolds for solving scalar and vectorial optimization problems involving Lipschitz functions. We consider a local dominance property of the directional derivative of the objective function over the regularization term in order to obtain that cluster points of the sequence are stationary points. Under an additional assumption, we prove that every cluster point of the sequence is a minimizer in the scalar case and a weak efficient point in the vectorial case. Our results extend some of the existing ones in the literature about optimization on manifolds.

A pseudospectral matrix method for time-dependent tensor fields on a spherical shell

<p style='text-indent:20px;'>We consider weak boundary layer solutions to the singularly perturbed ODE systems of the type <inline-formula><tex-math id="M1">\begin{document}$ \varepsilon^2\left(A(x, u(x), \varepsilon)u'(x)\right)' = f(x, u(x), \varepsilon) $\end{document}</tex-math></inline-formula>. The new features are that we do not consider one scalar equation, but systems, that the systems are allowed to be quasilinear, and that the systems are spatially non-smooth. Although the results about existence, asymptotic behavior, local uniqueness and stability of boundary layer solutions are similar to those known for semilinear, scalar and smooth problems, there are at least three essential differences. First, the asymptotic convergence rates valid for smooth problems are not true anymore, in general, in the non-smooth case. Second, a specific local uniqueness condition from the scalar case is not sufficient anymore in the vectorial case. And third, the monotonicity condition, which is sufficient for stability of boundary layers in the scalar case, must be adjusted to the vectorial case.</p>

A threshold voltage model for mesa-isolated fully depleted silicon-on-insulator (FDSOI) MOSFETs, based on the analytical solution of three-dimensional (3-D) Poisson's equation is presented for the first time in this paper. The separation of variables technique is used to solve the 3-D Poisson's equation analytically with appropriate boundary conditions. Simple and accurate analytical expressions for the threshold voltage of the front and the back gate are derived. The model is able to predict short channel as well as narrow width effects in mesa-isolated FDSOI MOSFETs. The model is validated by comparing with the experimental results as well as with the numerical results available in the literature.

Negative VTEC with spherical harmonic expansion model under different solar activity conditions

view Abstract Citations (12) References (23) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Second-Order Perturbation Theory in an Expanding Universe: Spherical Harmonics Expansion Zaroubi, Saleem ; Hoffman, Yehuda Abstract The formalism of gravitational instability in an expanding universe is developed here to second order in terms of the spherical harmonics representation and is applied to study the evolution of single localized perturbations to an otherwise flat Einstein-de Sitter universe. A simple analytical form of the radial dependence of the various harmonics is used to model the structure expected for a scale-free Gaussian perturbation field. The general formalism is applied to study the dynamics of the monopole terms, i.e., the spherically averaged variables, of a proto- object made of monopole and quadrupole terms only. Our main result is that at the inner part, i.e., the core, the dynamics is dominated by the monopole term, and it reproduces the exact spherical top-hat model. However, the outer region, i.e., the halo, is dominated by the quadrupole terms, and its dynamics differs significantly from the top-hat model. The l = 2 terms lead to the formation of a secondary maximum in the run of the density (averaged over spherical shells) versus radius. This is a pure second-order effect whose very clear signature is that it occurs at a radius of the transition to the nonlinear regime. Indeed, such a secondary maximum has been observed in the outer parts of real clusters of galaxies and in N-body numerical simulations. Another pure second- order effect discovered here is the case of a pure quadrupole primordial perturbation. For such a perturbation the vanishing monopole does not grow in the linear regime, but is unstable to second order. We find a considerable growth for typical values of parameters, and conjecture that this is the main dynamical factor in the formation of filaments in the large-scale structure of the universe. Publication: The Astrophysical Journal Pub Date: September 1993 DOI: 10.1086/173052 Bibcode: 1993ApJ...414...20Z Keywords: Cosmology; Galactic Clusters; Hubble Constant; Perturbation Theory; Spherical Harmonics; Computational Astrophysics; Digital Simulation; Universe; Astrophysics; COSMOLOGY: THEORY; GALAXIES: CLUSTERING; COSMOLOGY: LARGE-SCALE STRUCTURE OF UNIVERSE full text sources ADS |

A method of solving the Stokes equation for a spherical mantle model by expansion in spherical harmonics was developed by Hager and O’Connell [1979]. However, this method is applicable only if the viscosity depends solely on depth. In this case, the Stokes equation reduces to a system of independent equations for each harmonic. Given lateral variations in viscosity, the Stokes equation contains terms in the form of products of harmonics, which invalidates all advantages of harmonic expansion. Zhang and Christensen [1993] developed a perturbation method for the case when terms containing products of lateral viscosity variations are small. These terms are first calculated from the preceding iteration and are then expanded in a series of harmonic functions. As a result, equations for harmonics remain independent. An evident advantage of the spectral method is the simplicity of the technique of incorporating the self-gravitation and compressibility effects. Moreover, this method partially eliminates difficulties related to the singularities at poles. As yet, it has not been applied in practice, possibly because the equations presented in [Zhang and Christensen, 1993] contain misprints that have not been elucidated in the literature. In the present work, a system of equations is derived for the spectral-iterative method of solving the Stokes equation and the errata present in formulas of Zhang and Christensen [1993] and significantly affecting results of calculations are analyzed.

The previous calculations of Abragam and Van Vleck on the $g$ factors of the $2{p}^{4}^{3}P$ terms of atomic oxygen are refined by including exchange, using better wave functions, and not assuming that the charge distribution in which a $2p$ electron moves is spherically symmetric. In Sec. 2, a general technique is developed for calculating the relativistic and diamagnetic corrections to the $g$ factors of complex atoms (Breit-Margenau and Lamb terms, etc.) by an expansion in spherical harmonics which is an extension of the well-known Slater procedure for computing the angular dependence of electrostatic energy. The integrals encountered are usually either of the Condon and Shortley $F$, $G$ type, or variants thereof. The most important members are computed by means of the wave functions of Hartree, Hartree, and Swirles, based on a Fock self-consistent field, but some of the minor contributions are estimated with Slater wave functions improved by introducing slightly different screening constants for the $2s$ and $2p$ terms. When all corrections are comprised, including also the Schwinger electrodynamic shift, motion of nucleus, and deviations from Russell-Saunders coupling, the calculated values of the $g$ factors for the $^{3}P_{1}$ and $^{3}P_{2}$ terms are, respectively, 1.500974, 1.500913, in excellent agreement with Rawson and Beringer's experimental determinations 1.500971, 1.500905.

Measurement of a 4π angular pattern for α-decay of 12C excited by inelastic deuteron scattering

A method for generation of a wave-field that is a plane wave is described. This method uses an array of loudspeakers phased so that the field in the wave-number domain is nearly concentrated at a point, this point being at the wave-number vector of the desired plane wave. The method described here for such a wave-number concentration makes use of an expansion in spherical harmonics, and requires a relatively small number of measurement points for a good approximate achievement of a plane wave. The measurement points are on a spherical surface surrounding the array of loudspeakers. The input signals for the individual loudspeakers can be derived without a matrix inversion or without explicit assumptions about the loudspeakers. The mathematical development involves spherical harmonics and three-dimensional Fourier transforms. Some numerical examples are given, with various assumptions concerning the nature of the loudspeakers, that support the premise that the method described in the present paper may be useful in applications.

A theory is developed, within the context of the Davydov-Filippov model of the nucleus, to describe the even-parity alpha decay of nonaxial nuclei. The wave equation of the system consisting of a daughter nucleus and an alpha particle is solved under the boundary conditions that on the nuclear surface the wave function shall be equal to a given function and that the function shall represent only an outgoing wave for large values of $r$. It is found that if the given function is assumed to be equal to a constant, the observed variations of the alpha transition probabilities with respect to $Z$ in even-even nuclei cannot be explained. But if one assumes that this given function can be represented as an expansion in spherical harmonics, keeping only quadrupole terms, the expansion coefficients being determined by the empirical data (that is, setting the boundary conditions by the empirical data), the observed variations can be theoretically reproduced. Even-parity alpha transitions in odd-$A$ nuclei are also considered. The comparison between theory and the empirical data is quite satisfactory.

A spin spatial distribution in terms of an expansion in spherical harmonics containing deviation parameters from the symmetry axis P (0, ϕ) is used to describe the moment distribution of amorphous ribbon alloys. According to the theoretical analysis and Mossbauer measurement, P (0, ϕ) values and squareness Sxy (0, ϕ) and Sz can be obtained. The P (0, ϕ) distribution of FeNiSiBC and hydrided FeCrSiB amorphous alloys are studied.

10.1119/5.0074846.1The Earth's magnetic field can be decomposed into spherical harmonics, and the exact coefficients of the decomposition can be determined through a few measurements of its value at different locations. Using measurements from a magnetometer on board the International Space Station, we computed the multipolar moments of an expansion in spherical harmonics to order 3, calculated the location of the magnetic dip poles, and produced an intensity map of the magnetic field across the globe. The accuracy of the results was evaluated by comparison with data from the International Geomagnetic Reference Field.

The convergence of spherical harmonic expansions is studied through projection operators and various summability methods. We start with translation and convolution operators on the sphere in the first section, which are essential for the rest of the book. In particular, the projection operators and the Poisson integrals for the Fourier expansion in spherical harmonics, discussed in the second section, are convolution operators, which are also multiplier operators. The convolution and translation operators are used to define and study the Hardy–Littlewood maximal function on the sphere in the third section.

This is a review of some of the more effective means for calculating the distribution of radiance in the sea. The first section reviews the fundamentals of scattering and absorption. The second section briefly reviews the concepts of irradiance and radiance. The third and fourth sections describe a method of estimating radiance near the surface, where little of the power has scattered more than once through a large angle. The fifth section describes the exact solution for radiance transport by expansion in spherical harmonics, and approximate means for simplifying this solution. Finally, the sixth gives some mathematical background for the fifth.