At each shade point, the spherical visibility function encodes occlusion from surrounding geometry, in all directions. Computing this function is difficult and point-sampling approaches, such as ray-tracing or hardware shadow mapping, are traditionally used to efficiently approximate it. We propose a semi-analytic solution to the problem where the spherical silhouette of the visibility is compu...

A nonlinear semi-analytic filtering method to sequentially estimate spacecraft states and their associated uncertainties is presented. We first discuss the state transition tensors that characterize the localized nonlinear behavior of the spacecraft trajectory and illustrate the importance of higher order effects on orbit uncertainty propagation. We then present the semi-analytic filtering meth...

Nonlinear semi-analytic filtering methods to sequentially estimate spacecraft states and their associated uncertainties are presented. We first discuss the state transition tensors that characterize the localized nonlinear behavior of the trajectory statistics and illustrate the importance of higher-order effects on orbit uncertainty propagation. We then present a semi-analytic filtering method...

Various analytic expressions have been proposed for the density profile of dark matter halos. We consider six of these expressions for which the density profile has a power-law fall-off ρ ∝ r−3 at large radii and a power-law cusp ρ ∝ r−γ (γ = 0, 1 2 , 1, 3 2) at small radii. The phase-space distribution function for these models is calculated assuming spherical symmetry and either an isotropic ...

V. L. Rvachev called R-functions “logically-charged functions” because they encode complete logical information within the standard setting of real analysis. He invented them in the 1960s as a means for unifying logic, geometry, and analysis within a common computational framework – in an effort to develop a new computationally effective language for modeling and solving boundary value problems...

Abstract. We have developed a new semi-analytic model for the formation and evolution of structure on galaxy, group and cluster scales. The model combines merger trees with a detailed, spatially resolved description of the dynamical evolution of halo substructure. It reproduces the results of numerical simulations of mergers and halo formation at a fraction of the computational expense. We use ...

We investigate the secular dynamics of a planetary system composed of the parent star and two massive planets in mutually inclined orbits. The dynamics are investigated in wide ranges of semi-major axes ratios (0.1–0.667), and planetary masses ratios (0.25–2) as well as in the whole permitted ranges of the energy and total angular momentum. The secular model is constructed by semi-analytic aver...