Experimental Mathematics 

About: Experimental Mathematics is an academic journal published by Taylor & Francis. The journal publishes majorly in the area(s): Conjecture & Elliptic curve. It has an ISSN identifier of 1058-6458. Over the lifetime, 1257 publications have been published receiving 27190 citations.

The surface evolver

Abstract: The Surface Evolver is a computer program that minimizes the energy of a surface subject to constraints. The surface is represented as a simplicial complex. The energy can include surface tension, gravity and other forms. Constraints can be geometrical constraints on vertex positions or constraints on integrated quantities such as body volumes. The minimization is done by evolving the surface down the energy gradient. This paper describes the mathematical model used and the operations available to interactively modify the surface.

Computing Discrete Minimal Surfaces and Their Conjugates

Abstract: We present a new algorithm to compute stable discrete minimal surfaces bounded by a number of fixed or free boundary curves in R 3, S 3 and H 3. The algorithm makes no restr iction on the genus and can handl e singular triangulations. Additionally, we present an algorithm that, starting from a discrete harmonic map, gives a conjugate harmonic map. This can be applied to the identity map on a minimal surface to produce its conjugate minimal surface, a procedure that often yields unstable solutions to a free boundary value problem for minimal surfaces. Symmetry properties of boundary curves are respected during conjugation.

Packing lines, planes, etc.: packings in Grassmannian spaces

Abstract: We addressthe question: How should N n-dimensional subspaces of m-dimensional Euclidean space be arranged so that they are as far apart as possible? The resuIts of extensive computations for modest values of N, n, m are described, as well as a reformulation of the problem that was suggested by these computations The reformulation gives a way to describe n-dimensional subspaces of m-space as points on a sphere in dimension ½(m–l)(m+2), which provides a (usually) lowerdimensional representation than the Plucker embedding, and leads to a proof that many of the new packings are optimal The results have applications to the graphical display of multidimensional data via Asimov's grand tour method

A random graph model for power law graphs

Abstract: We propose a random graph model which is a special case of sparserandom graphs with given degree sequences which satisfy a power law. This model involves only a small number of paramo eters, called logsize and log-log growth rate. These parameters capture some universal characteristics of massive graphs. From these parameters, various properties of the graph can be derived. For example, for certai n ranges of the parameters, we wi II compute the expected distribution of the sizes of the connected components which almost surely occur with high probability. We illustrate the consistency of our model with the behavior of some massive graphs derived from data in telecommunications. We also discuss the threshold function, the giant component, and the evolution of random graphs in this model.

Geometry and Dynamics of Quadratic Rational Maps

Abstract: This article is an expository description of quadratic rational maps from the Riemann sphere to itself