Parameter estimation applied to Nimbus 6 wide-angle longwave radiation measurements

A parameter estimation technique was used to analyze the August 1975 Nimbus 6 Earth radiation budget data to demonstrate the concept of deconvolution. The longwave radiation field at the top of the atmosphere is defined from satellite data by a fifth degree and fifth order spherical harmonic representation. The variations of the major features of the radiation field are defined by analyzing the data separately for each two-day duty cycle. A table of coefficient values for each spherical harmonic representation is given along with global mean, gradients, degree variances, and contour plots. In addition, the entire data set is analyzed to define the monthly average radiation field

Isostatic equilibrium in spherical coordinates and implications for crustal thickness on the Moon, Mars, Enceladus, and elsewhere

Isostatic equilibrium is commonly defined as the state achieved when there are no lateral gradients in hydrostatic pressure, and thus no lateral flow, at depth within the lower viscosity mantle that underlies a planetary body's outer crust. In a constant-gravity Cartesian framework, this definition is equivalent to the requirement that columns of equal width contain equal masses. Here we show, however, that this equivalence breaks down when the spherical geometry of the problem is taken into account. Imposing the "equal masses" requirement in a spherical geometry, as is commonly done in the literature, leads to significant lateral pressure gradients along internal equipotential surfaces, and thus corresponds to a state of disequilibrium. Compared with the "equal pressures" model we present here, the "equal masses" model always overestimates the compensation depth--by ~27% in the case of the lunar highlands and by nearly a factor of two in the case of Enceladus.Comment: 23 pages of text; 3 figures; accepted for publication in GR

Left-Invariant Diffusion on the Motion Group in terms of the Irreducible Representations of SO(3)

In this work we study the formulation of convection/diffusion equations on the 3D motion group SE(3) in terms of the irreducible representations of SO(3). Therefore, the left-invariant vector-fields on SE(3) are expressed as linear operators, that are differential forms in the translation coordinate and algebraic in the rotation. In the context of 3D image processing this approach avoids the explicit discretization of SO(3) or $S_2$, respectively. This is particular important for SO(3), where a direct discretization is infeasible due to the enormous memory consumption. We show two applications of the framework: one in the context of diffusion-weighted magnetic resonance imaging and one in the context of object detection

STARRY: Analytic Occultation Light Curves

We derive analytic, closed form, numerically stable solutions for the total flux received from a spherical planet, moon or star during an occultation if the specific intensity map of the body is expressed as a sum of spherical harmonics. Our expressions are valid to arbitrary degree and may be computed recursively for speed. The formalism we develop here applies to the computation of stellar transit light curves, planetary secondary eclipse light curves, and planet-planet/planet-moon occultation light curves, as well as thermal (rotational) phase curves. In this paper we also introduce STARRY, an open-source package written in C++ and wrapped in Python that computes these light curves. The algorithm in STARRY is six orders of magnitude faster than direct numerical integration and several orders of magnitude more precise. STARRY also computes analytic derivatives of the light curves with respect to all input parameters for use in gradient-based optimization and inference, such as Hamiltonian Monte Carlo (HMC), allowing users to quickly and efficiently fit observed light curves to infer properties of a celestial body's surface map.Comment: 55 pages, 20 figures. Accepted to the Astronomical Journal. Check out the code at https://github.com/rodluger/starr

Aspherical gravitational monopoles

We show how to construct non-spherically-symmetric extended bodies of uniform density behaving exactly as pointlike masses. These ``gravitational monopoles'' have the following equivalent properties: (i) they generate, outside them, a spherically-symmetric gravitational potential $M/|x - x_O|$; (ii) their interaction energy with an external gravitational potential $U(x)$ is $- M U(x_O)$; and (iii) all their multipole moments (of order $l \geq 1$) with respect to their center of mass $O$ vanish identically. The method applies for any number of space dimensions. The free parameters entering the construction are: (1) an arbitrary surface $\Sigma$ bounding a connected open subset $\Omega$ of $R^3$; (2) the arbitrary choice of the center of mass $O$ within $\Omega$; and (3) the total volume of the body. An extension of the method allows one to construct homogeneous bodies which are gravitationally equivalent (in the sense of having exactly the same multipole moments) to any given body.Comment: 55 pages, Latex , submitted to Nucl.Phys.

Bogoliubov modes of a dipolar condensate in a cylindrical trap

The calculation of properties of Bose-Einstein condensates with dipolar interactions has proven a computationally intensive problem due to the long range nature of the interactions, limiting the scope of applications. In particular, the lowest lying Bogoliubov excitations in three dimensional harmonic trap with cylindrical symmetry were so far computed in an indirect way, by Fourier analysis of time dependent perturbations, or by approximate variational methods. We have developed a very fast and accurate numerical algorithm based on the Hankel transform for calculating properties of dipolar Bose-Einstein condensates in cylindrically symmetric traps. As an application, we are able to compute many excitation modes by directly solving the Bogoliubov-De Gennes equations. We explore the behavior of the excited modes in different trap geometries. We use these results to calculate the quantum depletion of the condensate by a combination of a computation of the exact modes and the use of a local density approximation

Full-Potential LMTO: Total Energy and Force Calculations

The essential features of a full potential electronic structure method using Linear Muffin-Tin Orbitals (LMTOs) are presented. The electron density and potential in the this method are represented with no inherent geometrical approximation. This method allows the calculation of total energies and forces with arbitrary accuracy while sacrificing much of the efficiency and physical content of approximate methods such as the LMTO-ASA method.Comment: 25 pages, 2 figures, Workshop on the TB-LMTO method, Monastery of Mont St. Odile, October 4-5, 199