Related papers: The Volume-of-Tubes Formula: Computational Methods…
A formula of the renormalized volume of tubes over polalized K\"{a}hler-Einstein manifolds is given in terms of the Einstein constant and the volume of the polarization.
There are already quite a few tools for solving the Satisfiability Modulo Theories (SMT) problems. In this paper, we present \texttt{VolCE}, a tool for counting the solutions of SMT constraints, or in other words, for computing the volume…
We apply an algorithm for measuring the volume of polytopes described by Jim Lawrence to polytropes. By using a tropical form of Cramer's rule, we found an efficient way to find all pseudovertices which are necessary for computing the…
Logistic regression models with $n$ observations and $q$ linearly-independent covariates are shown to have Fisher information volumes which are bounded below by $\pi^q$ and above by ${n \choose q} \pi^q$. This is proved with a novel…
We develop the formulation of turbulence in terms of the functional integral over the phase space configurations of the vortex cells. The phase space consists of Clebsch coordinates at the surface of the vortex cells plus the Lagrange…
A variational volume-of-fluid (VVOF) methodology is devised for evolving interfaces under curvature-dependent speed. The interface is reconstructed geometrically using the analytic relations of Scardovelli and Zaleski [1] and the advection…
A formula for the interior epsilon-neighborhood of the classical von Koch snowflake curve is computed in detail. This function of epsilon is shown to match quite closely with earlier predictions of what it should be, but is also much more…
Weil-Petersson and Masur-Veech volumes measure the sizes of moduli spaces of Riemann surfaces equipped with hyperbolic and flat metrics, respectively. Over the past several decades, the computation of these volumes has inspired remarkable…
When query evaluation produces too many tuples, a new approach in query answering is to retrieve a diverse subset of them. The standard approach for measuring the diversity of a set of tuples is to use a distance function between tuples,…
This paper collects some important formulas on hyperbolic volume. To determine concrete values of volume function is a very hard question requiring the knowledge of various methods. Our goal to give a non-elementary integral on the volume…
Analytic relations are derived for finite volume integrals over the radial distribution function of a fluid, so-called Kirkwood-Buff integrals. Closed form expressions are obtained for cubes and cuboids, the system shapes commonly employed…
A calculation formula of volume of revolution with integration by parts of definite integral is derived based on monotone function, and extended to a general case that curved trapezoids is determined by continuous, piecewise strictly…
The calculation of volumes of polyhedra in the three-dimensional Euclidean, spherical and hyperbolic spaces is very old and difficult problem. In particular, an elementary formula for volume of non-euclidean simplex is still unknown. One of…
In this paper we validate the implementation of the numerical scheme proposed in [3]. The validation is made by comparison with an explicit solution here obtained, and the solutions of Riemann problems for several networks. We then perform…
We solve a long-standing set of problems in optics and waves: why does a volume have only so many useful orthogonal wave channels in or out of it, why do coupling strengths fall off dramatically past this number, and, indeed, just what…
We use the self-similar tilings constructed by the second author in "Canonical self-affine tilings by iterated function systems" to define a generating function for the geometry of a self-similar set in Euclidean space. This tubular zeta…
We obtain cubature formulas of volume potentials over bounded domains combining the basis functions introduced in the theory of approximate approximations with their integration over the tangential-halfspace. Then the computation is reduced…
The notion of the flow introduced by Kitaev is a manifestly topological formulation of the winding number on a real lattice. First, we show in this paper that the flow is quite useful for practical numerical computations for systems without…
We present a theory for the three-dimensional evolution of tubes with expandable walls conveying fluid. Our theory can accommodate arbitrary deformations of the tube, arbitrary elasticity of the walls, and both compressible and…
In this work we present, for the first time, a computational fluid dynamics tool for the simulation of the metered discharge in a pressurized metered dose inhaler. The model, based on open-source software, adopts the Volume-Of-Fluid method…