Stirling's formula, the asymptotic expansion of n! for n large, or of Γ(z) for z → ∞, is derived directly from the recursion equationΓ(z + 1) = zΓ(s) and the normalization condition Γ 1 2 = √ π.
Two different physical problems are considered: the magnetic shaping of a liquid metal column and the distortion of a bubble in a corner vortex flow. It is shown that the two problems can be modeled with a virtually identical set of equations. These equations are solved numerically using a conformal mapping and a series truncation method, which permits fast… (More)
This study considers the nonlinear dynamics of stratified immiscible fluids when an electric field acts perpendicular to the direction of gravity. A particular setup is investigated in detail, namely, two stratified fluids inside a horizontal channel of infinite extent. The fluids are taken to be perfect dielectrics, and a constant horizontal field is… (More)
(2015) Multilump symmetric and nonsymmetric gravity-capillary solitary waves in deep water. This version is made available in accordance with publisher policies. Please cite only the published version using the reference above. Abstract. Multilump gravity-capillary solitary waves propagating in a fluid of infinite depth are computed numerically. The study… (More)
Steady solitary and generalized solitary waves of a two-fluid problem where the upper layer is under a flexible elastic sheet are considered as a model for internal waves under an ice-covered ocean. The fluid consists of two layers of constant densities, separated by an interface. The elastic sheet resists bending forces and is mathematically described by a… (More)
Thermodynamic and structural properties of the counterion atmosphere surrounding B-DNA are calculated by Monte Carlo simulation in a spatially inhomogeneous, but piecewise uniform, dielectric continuum cell model - the "barbarous" model. A boundary element formulation is implemented to study the sensitivity of these properties with respect to perturbations… (More)