In this paper we give an introduction to the volume conjecture and its generalizations. Especially we discuss relations of the asymptotic behaviors of the colored Jones polynomials of a knot with different parameters to representations of the fundamental group of the knot complement at the special linear group over complex numbers by taking the figure-eight knot and torus knots as examples. Aft...

A general method for obtaining minimal interatomic distance in molecule conformation problems is introduced. The method can be applied to a wide family of potential energy functions having reasonable properties. Using this method new lower bounds for the minimal inter-particle distance for the optimal Lennard-Jones and Morse potential functions are derived which are independent from the number ...

This paper introduces a general method for obtaining lower bounds for the total energy and the minimal inter-particle distance in optimal atom cluster problems with pair potential functions under weak general conditions on the pair potential. The bounds obtained are sharper than those previously known for both the Lennard-Jones potential and various Morse potentials. Statistics on the putative ...

1 DOI: 10.1002/smll.201102350 The Removal of Single Layers from Multi-Layer Graphene by Low Energy Electron Stimulation Jason D. Jones, Rakesh K. Shah, Guido F. Verbeck, and Jose M. Perez* [*] Prof. J. M. Perez Department of Physics University of North Texas Denton, TX 76203 (USA) E-mail: [email protected] J. D. Jones, R. K. Shah Department of Physics University of North Texas Denton, TX 76203 (US...

Cover page: The fth frequency breakdown (2562 particles) of a spherical icosahedron projected onto a hyperbolic surface. The shown Voronoi polygons of the particles are coloured according to the Lennard-Jones potential energy: bright is high energy, dark is low energy.