Related papers: A Breakthrough in Sphere Packing: The Search for M…
In an earlier work, we proposed a generalization for the Apollonian packing in arbitrary dimensions and showed that the resulting object in four, five, and six dimensions have properties consistent with the Apollonian circle and sphere…
This survey of recent developments in cloaking and transformation optics is an expanded version of the lecture by Gunther Uhlmann at the 2008 Annual Meeting of the American Mathematical Society.
We examine packing of $n$ congruent spheres in a cube when $n$ is close but less than the number of spheres in a regular cubic close-packed (ccp) arrangement of $\lceil p^{3}/2\rceil$ spheres. For this family of packings, the previous…
I provide a comprehensive review of indirect searches for New Physics with charmed mesons. I discuss current theoretical and experimental challenges and successes in understanding decays and mixings of those mesons. I argue that in many New…
On March 11, 2013 I talked with Warren Wiscombe about his contributions to scientific computer programming, atmospheric science and radiative transfer. Our conversation is divided into three parts related to light scattering, radiative…
The present work surveys problems in $n$-dimensional space with $n$ large. Early development in the study of packing and covering in high dimensions was motivated by the geometry of numbers. Subsequent results, such as the discovery of the…
This article gives an overview, aimed at theoretical particle physicists, of some recent developments in cosmology.
An overview of recent physics results from the H1 collaboration is given. The covered areas are: rare processes and searches for new physics, structure functions and inclusive measurements, heavy flavour production, QCD and hadronic final…
We give theorems that can be used to upper bound the densities of packings of different spherical caps in the unit sphere and of translates of different convex bodies in Euclidean space. These theorems extend the linear programming bounds…
Throughout this book, we discuss some open problems in various branches of science, including mathematics, theoretical physics, astro-physics, geophysics etc. It is of our hope that some of the problems discussed in this book will find…
An earlier paper describes a program to prove the Kepler conjecture on sphere packings. This paper carries out the second step of that program. A sphere packing leads to a decomposition of $R^3$ into polyhedra. The polyhedra are divided…
We give a simple proof of a recent result by Kleinbock and Merrill concerning intrinsic approximations on sphere, in the simplest case of two-dimensional sphere in $\mathbb{R}^3$.
We show that for certain triangulations of surfaces, circle packings realising the triangulation can be found by solving a system of polynomial equations. We also present a similar system of equations for unbranched circle packings. The…
In a 1983 paper with Frank Warner, we proved that the space of all great circle fibrations of the 3-sphere S^3 deformation retracts to the subspace of Hopf fibrations, and so has the homotopy type of a pair of disjoint two-spheres. Since…
Sphere packings are essential to the development of physical models for powders, composite materials, and the atomic structure of the liquid state. There is a strong scientific need to be able to assess the fit of packing models to data,…
The study of spherical harmonics in superspace, introduced in [J. Phys. A: Math. Theor. 40 (2007) 7193-7212], is further elaborated. A detailed description of spherical harmonics of degree k is given in terms of bosonic and fermionic…
These are exciting times for studies of galaxy formation and the growth of structures. New observatories and advanced simulations are revolutionising our understanding of the cycling of matter into, through, and out of galaxies. This…
Table of contents Editorial. Gravity News: Report on the APS topical group in gravitation, Beverly Berger. Research briefs: Gravitational microlensing and the search for dark matter, Bohdan Paczynski. Laboratory gravity: the G mystery,…
I briefly summarize neutrino oscillation results and discuss their robustness. I mention recent attempts to understand the pattern of neutrino mixing within various seesaw mechanisms, with or without supersymmetry and/or flavor symmetries.…
In the first paper of this series, we introduced Voronoi correlation functions to characterize the structure of maximally random jammed (MRJ) sphere packings across length scales. In the present paper, we determine a variety of correlation…