Microgravity flow regime data and analysis

To utilize the advantageous properties of two-phase flow in microgravity applications, the knowledge base of two-phase flow phenomena must be extended to include the effects of gravity. In the experiment described, data regarding the behavior of two-phase flow in a conduit under microgravity conditions (essentially zero gravity) are explored. Of particular interest, knowledge of the void fraction of the gas and liquid in a conduit is necessary to develop models for heat and mass transfer, pressure drop, and wall shear. An experiment was conducted under reduced gravity conditions to collect data by means of a capacitance void fraction sensor and high speed visual imagery. Independent parameters were varied to map the flow regime regions. These independent parameters include gas and liquid volumetric flow rates and saturation pressures. Void fraction measurements were taken at a rate of 100 Hz with six sensors at two locations along the conduit. Further, statistical parameters were developed from the void fraction measurements. Statistical parameters such as variance, signal-to-noise ratio, half height value, and linear area difference were calculated and found to have characteristics allowing flow regime identification.     

Equifacetted 4-polytopes

Many polyhedra (convex 3-polytopes) are known which occur as facets (3-faces) of convex 4-polytopes. The purpose of this paper is to determine the combinatorial types of infinitely many more polyhedra with this property. This is achieved by determining the facets of polar bicyclic polytopes.     

ISOHEDRAL DELTAHEDRA

A polyhedron is a deltahedron if all its faces are equilateral triangles. It is isohedral if its symmetry group is transitive on the faces. The purpose of this paper is to list the known isohedral deltahedra. This revised version was published online in August 2006 with corrections to the Cover Date.     

Cyclic Product Theorems for Polygons (II) Constructions using Conic Sections

If a point U _i is chosen on each edge of a plane n -gon P , then the product of the n signed ratios in which the points U _i divide the edges of P is called a cyclic product for P . The problem is to find geometric constructions for the U _i such that, for every n -gon P , the cyclic product takes a fixed value. Many constructions are known which use lines or circles. Here we describe constructions that use conic sections. Received August 23, 2000, and in revised form November 27, 2000. Online publication May 4, 2001.     

A review of quantitative ion exchange,high performance liquid and gas chromatographic analysis of amino acids in physiological fluids

Methodologies for quantitative analysis of amino acids in physiological fluids based on classical ion exchange, high performance liquid chromatography, and gas chromatography are analyzed. As judged by the relative number of reports on these techniques, it appears that classical ion exchange continues to be the main method of choice for amino acid determinations and only limited advantage has been taken of the benefits (e.g. lower capital outlay and running costs and shorter analysis times) offered by other techniques. More importantly, however, there appears to be insufficient quantitative evaluation of the methodologies used. As a result, the validity of many reports based on data from amino acid analysis of physiological samples may be questioned.     

Aperiodic tiles

A set of tiles (closed topological disks) is calledaperiodic if there exist tilings of the plane by tiles congruent to those in the set, but no such tiling has any translational symmetry. Several aperiodic sets have been discussed in the literature. We consider a number of aperiodic sets which were briefly described in the recent bookTilings and Patterns, but for which no proofs of their aperiodic character were given. These proofs are presented here in detail, using a technique with goes back to R. M. Robinson and Roger Penrose. The research of Branko Grünbaum was supported in part by NSF Grants MCS8301971 and DMS-8620181.     

Isohedra with nonconvex faces

An isohedron is a 3-dimensional polyhedron all faces of which are equivalent under symmetries of the polyhedron. Many well known polyhedra are isohedra; among them are the Platonic solids, the polars of Archimedean polyhedra, and a variety of polyhedra important in crystallography. Less well known are isohedra with nonconvex faces. We establish that such polyhedra must be starshaped and hence of genus 0, that their faces must be star-shaped pentagons with one concave vertex, and that they are combinatorially equivalent to either the pentagonal dodecahedron, or to the polar of the snub cube or snub dodecahedron.Supported in part by grants from the USA National Science Foundation.     

Limit theorems for multipower variation in the presence of jumps

In this paper we provide a systematic study of how the probability limit and central limit theorem for realised multipower variation changes when we add finite activity and infinite activity jump processes to an underlying Brownian semimartingale.