We prove that the scattering matrix at a fixed quasi–energy determines uniquely a time–periodic potential that belongs to L and that decays exponentially at infinity. Our result is new even in the time–independent case, where it was only proven for bounded exponentially decreasing potentials.

We improve the best known lower bounds on the distance between two points of a Morse cluster in R, with ρ ∈ [4.967, 15]. Our method is a generalization of the one applied to the Lennard-Jones potential in [2], and it also leads to improvements of lower bounds for the energy of a Morse cluster. Some of the numerical results have been announced in [1].

Holly E Holmes, Frances Wiseman, James M O'Callaghan, Jack A Wells, Victor LJ Tybulewicz, Elizabeth MC Fisher, and Mark F Lythgoe Centre for Advanced Biomedical Imaging, University College London, London, Greater London, United Kingdom, Department of Neurodegenerative Disease, Institute of Neurology, London, Greater London, United Kingdom, MRC National Institute for Medical Research, London, Gr...

In this paper we derive a lower bound, independent from the number of atoms N , for the minimal interatomic distances between atoms in a cluster whose total energy is modelled by means of the so called Morse potential. A similar result was previously proven for Lennard-Jones clusters but the proof can not be extended to Morse clusters. Besides the theoretical interest, the derivation of this lo...

We have designed several schemes to reduce the number of parameters in the problem of minimizing the total energy of Lennard Jones clusters We will discuss our schemes development in three dimensions The value of our work lies in the simplicity with which it provides a new approach to problems involving huge Lennard Jones clusters

Model calculations of Langmuir monolayers: Pressure effects on tilting behavior of idealized amphiphiles" (1996). Model amphiphiles consisting of lines of Lennard-Jones ͑LJ͒ centers are investigated to determine the effect of pressure and molecular geometry on ground-state tilting behavior. Both the amphiphile length and the intramolecular distance between LJ centers is varied. The results give g...

Physically motivated expressions for the transport cross sections describing classical scattering in the Lennard-Jones potential are proposed. These expressions, which agree with the numerical results better than to within ±1%, can be easy implemented in practical situations. Some relevant examples are provided.

As r e s e a r c h i n n a t u r a l l a n g u a g e p r o c e s s i n g spawns c o m m e r c i a l p r o d u c t s , a s i t now b e g i n s Co, o u r r e s e a r c h communi ty a c q u i r e s new e t h i c a l and p r a c t i c a l r e s p o n s i b i l i t i e s . All software packages have limitations, and research progress consists in d e v i s i n g t e c h n i q u e s t h a t l e a d t ...

This paper investigates a non-commutative first-order sequent calculus NCLK. For that, this paper extends a non-commutative positive fragment to a full first-order sequent calculus LK− having antecedent-grouping and no right exchange rule. This paper shows (1) NCLK is equivalent to LJ, (2) NCLK with the exchange rule is equivalent to LK, (3) LK− is equivalent to LJ, and (4) translations between...

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 ...