Related papers: Tube Volumes via Functional Equations
We show that for optical cavities with any finite dissipation, the term "cavity mode" should be understood as a solution to the Helmholtz equation with outgoing wave boundary conditions. This choice of boundary condition renders the problem…
The authors showed in a preceding paper that in a connected locally harmonic manifold, the volume of a tube of small radius about a regularly parameterized simple arc depends only on the length of the arc and the radius. In this paper, we…
Within the framework of Gaussian equivalent representation method a new procedure of obtaining equations of state for simple liquids is discussed in some technical details. The developed approach permits one to compute partition and…
We give a direct, pointwise proof for the tube formula of Lapidus-Pearse for self-similar fractals, where we allow non-convex, non-Steiner-like generators.
We establish pointwise and distributional fractal tube formulas for a large class of compact subsets of Euclidean spaces of arbitrary dimensions. These formulas are expressed as sums of residues of suitable meromorphic functions over the…
This note provides a simple proof for the equality between the normalized volume of a convex polytope with $m$ vertices and the mixed volume of $m$ simplices and thus shows the seemingly restrictive problem of computing mixed volume of…
In this paper we outline methods for calculating the pressure field inside flow conduits in the one-dimensional flow models where the pressure is dependent on the axial coordinate only. The investigation is general with regard to the tube…
The aim of this work is to introduce several different volume computation methods of the graph polytope associated with various type of finite simple graphs. Among them, we obtained the recursive volume formula (RVF) that is fundamental and…
This paper proposes a new volume function for calculation of the entropy of planar granular assemblies. This function is extracted from the antisymmetric part of a new geometric tensor and is rigorously additive when summed over grains. It…
We provide a closed formula for the volume of a simple compact Lie group in terms of the universal Vogel parameters. For the unitary groups SU_n this reduces to the integral representation of the classical Barnes G-function.
We give upper bounds for volume of sublevel sets of real polynomials. Our method is to combine a version of global Lojasiewicz inequality with some well known estimate on volume of tubes around real algebraic sets. Some applications to…
We study the approximation by a semi-discrete finite-volume scheme of the Gross-Pitaevskii equation with time-dependent potential in two dimensions, performing a two-point flux approximation scheme in space. We rigorously analyze the error…
In this work we derive a class of geometric flow equations for metric-scalar systems. Thereafter, we construct them from some general string frame action by performing volume-preserving fields variations and writing down the associated…
Using combinatorial methods, we derive several formulas for the volume of convex bodies obtained by intersecting a unit hypercube with a halfspace, or with a hyperplane of codimension 1, or with a flat defined by two parallel hyperplanes.…
We derive analytical expressions for the flow of Newtonian and power law fluids in elastic circularly-symmetric tubes based on a lubrication approximation where the flow velocity profile at each cross section is assumed to have its…
We define covering and separation numbers for functions. We investigate their properties, and show that for some classes of functions there is exact equality of separation and covering. We provide analogues for various geometric…
The article describes the CFD software tool FlowVision (OOO "Tesis", Moscow). The model equations used for this research are the set of Reynolds and continuity equations and equations of the standard k - e turbulence model. The aim of the…
We have derived an analytical formulation for estimating the volume of geometries enclosed by implicitly defined surfaces. The novelty of this work is due to two aspects. First we provide a general analytical formulation for all…
In this paper we consider the approximation of a function by its interpolating multilinear spline and the approximation of its derivatives by the derivatives of the corresponding spline. We derive formulas for the uniform approximation…
A way to derive an explicit formulae in terms of the potentials, if they are finite-gap, for the solutions of spectral problems and corresponding algebraic curves is presented.