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 series of papers is devoted to identifying and explaining the properties of strongly correlating liquids, i.e., liquids with more than 90% correlation between their virial W and potential energy U fluctuations in the NV T ensemble. Paper IV [N. Gnan et al., J. Chem. Phys. 131, 234504 (2009)] showed that strongly correlating liquids have “isomorphs”, which are curves in the phase diagram al...

The Lennard-Jones (LJ) Potential Energy Problem is to construct the most stable form of N atoms of a molecule with the minimal LJ potential energy. This problem has a simple mathematical form

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 series of papers is devoted to identifying and explaining the properties of strongly correlating liquids, i.e., liquids with more than 90% correlation between their virial W and potential energy U fluctuations in the NVT ensemble. Paper IV [N. Gnan et al., J. Chem. Phys. 131, 234504 (2009)] showed that strongly correlating liquids have "isomorphs," which are curves in the phase diagram alo...

We present a systematic study of the thermodynamics of two and three-dimensional generalized Lennard-Jones (LJ) systems focusing on the relationship between the range of the potential, the system density and its dimension. We found that the existence of negative specific heats depends on these three factors and not only on the potential range and the density of the system as stated in recent co...

The Lennard-Jones potential is the most widely-used function for description of non-bonded interactions in transferable force fields condensed phase. This not because it has an optimal...

The Lennard-Jones potential for an atom inside a conducting spherical cavity is derived. The interest is in possible anomalous effects near the focal point of a cavity viewed as a spherical mirror. We find a smooth dependence of the potential on the distance of the atom from the surface of the cavity. 1 Plane Mirror and the C3 coefficient Let us consider first a plane mirror, assumed to lie in ...

We explore a general-purpose heuristic algorithm for finding high-quality solutions to continuous optimization problems. The method, called continuous extremal optimization (CEO), can be considered as an extension of extremal optimization and consists of two components, one which is responsible for global searching and the other which is responsible for local searching. The CEO's performance pr...