Related papers: A Breakthrough in Sphere Packing: The Search for M…
The packing of hard spheres (HS) of diameter $\sigma$ in a cylinder has been used to model experimental systems, such as fullerenes in nanotubes and colloidal wire assembly. Finding the densest packings of HS under this type of confinement,…
On 2 October 2018 Goran Hansson, Secretary General of the Royal Swedish Academy of Sciences, announced that the Nobel Prize in Physics would be jointly awarded to Arthur Ashkin, Gerard Mourou and Donna Strickland, for their groundbreaking…
The recent observation of neutrino oscillations with atmospheric and solar neutrinos, implying that neutrinos are not massless, is a discovery of paramount importance for particle physics and particle astrophysics. This invited lecture…
During the last decade the Subspace Theorem found several quite unexpected applications, mainly in the Diophantine Analysis and in the Transcendence Theory. Among the great variety of spectacular results, I have chosen several which are…
The ``N-Box Experiment'' is a much-discussed thought experiment in quantum mechanics. It is claimed by some authors that a single particle prepared in a superposition of N+1 box locations and which is subject to a final ``post-selection''…
This symposium has revealed considerable new progress on nuclei of galaxies over the last three years. In this talk, I will try to point out the advances since the last meeting on exactly the same subject held three years ago at Ringberg…
We improve upper bounds on sphere packing densities and sizes of spherical codes in high dimensions. In particular, we prove that the maximal sphere packing densities $\delta_n$ in $\mathbb{R}^n$ satisfy \[\delta_n\leq \frac{1+o(1)}{e}\cdot…
I review at the non-specialist level recent progress in the study of the large-scale structure of the Universe, covering the following areas: (1) Results from recently completed or ongoing redshift surveys of galaxies and X-ray clusters;…
Global celebration greeted the 2012 discovery at CERN's Large Hadron Collider of a particle that matches the textbook description of the Higgs boson. That achievement validated a remarkable chain of theoretical reasoning that combined the…
New examples of noncommutative 4-spheres are introduced.
We show that very clear answers to the queries raised by D. Chen and R. Ni in their Comment on our recent paper [A. Zaccone, Phys. Rev. Lett. 128, 028002 (2022)] can be found in our original paper already. The paper [A. Zaccone, Phys. Rev.…
Building on Viazovska's recent solution of the sphere packing problem in eight dimensions, we prove that the Leech lattice is the densest packing of congruent spheres in twenty-four dimensions and that it is the unique optimal periodic…
This survey discusses recent developments in the context of spherical designs and minimal energy point configurations on spheres. The recent solution of the long standing problem of the existence of spherical $t$-designs on $\mathbb{S}^d$…
Sphere packing problems have a rich history in both mathematics and physics; yet, relatively few analytical analyses of sphere packings exist, and answers to seemingly simple questions are unknown. Here, we present an analytical method for…
Ideas from quantum field theory and topology have proved remarkably fertile in suggesting new phenomena in the quantum physics of condensed matter. Here I'll supply some broad, unifying context, both conceptual and historical, for the…
Starting from the early works by Weizsaecker and Bethe about fusion cycles and energy conversion in stars, a brief survey of thermonuclear processes in stars leading to contemporary research problems in this field is given. Special emphasis…
This is the fifth in a series of papers giving a proof of the Kepler conjecture, which asserts that the density of a packing of congruent spheres in three dimensions is never greater than $\pi/\sqrt{18}\approx 0.74048...$. This is the…
A review of the recent achievements in high energy neutrino physics and, partly, neutrino astrophysics is presented. It is argued that experiments with high energy neutrinos of natural origin can be used for a search of new physics effects…
A new formalism is presented for analytically obtaining the probability density function, \( P_{n}(s) \), for the distance between two random points in an \( n \)-dimensional sphere of radius \( R \). Our formalism allows \( P_{n}(s) \) to…
We develop an analogue for sphere packing of the linear programming bounds for error-correcting codes, and use it to prove upper bounds for the density of sphere packings, which are the best bounds known at least for dimensions 4 through…