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 ...

an analytical equation of state was applied to calculate the thermodynamic properties for argon.the equation of state is that of song and mason. it is based on a statistical-mechanical perturbationtheory of the hard convex bodies and can be written as fifth-order polynomial in the density. thereexist three temperature-dependent parameters: the second virial coefficient, an effective molecularvo...

A cluster is a group of identical molecules or atoms loosely bound by inter-atomic forces. The optimal geometry minimizes the potential energy — usually modelled as the Lennard-Jones potential — of the cluster. The minimization of the Lennard-Jones potential is a very difficult global optimization problem with extremely many local minima. In addition to cluster problems, the Lennard-Jones poten...

In Bartels–Lück [1] we introduced the concept of transfer reducible groups with respect to a family of subgroups. This definition is somewhat technical and recalled as Definition 0.4 below. We showed that groups that are transfer reducible over the family of virtually cyclic subgroups satisfy the Farrell–Jones Conjecture with coefficients in an additive category. For further explanations about ...

We reanalyse the cell theory of Lennard-Jones and Devonshire and find that in addition to the critical point originally reported for the 12−6 potential (and widely quoted in standard textbooks), the model exhibits a further critical point. We show that the latter is actually a more appropriate candidate for liquid-gas criticality than the original critical point. Typeset using REVTEX

Accurate prediction of alkane phase transitions involving solids is needed to prevent catastrophic pipeline blockages, improve lubrication formulations, smart insulation, and energy storage, as well bring fundamental understanding processes such artificial morphogenesis. However, simulation these challenging therefore often omitted in force field development. Here, we perform a series benchmark...

in this paper, the radial breathing mode (rbm) frequencies of multi-walled carbon nanotubes (mwcnts) are  obtained based on the multiple-elastic thin shell model. for this purpose, mwcnt is considered as a multiple concentric elastic thin cylindrical shells, which are coupled through van der waals (vdw) forces between two adjacent tubes. lennard-jones potential is used to calculate the vdw forc...

The operator Lry = / + Py, whose domain is determined in part by the Stieltjes integral boundary condition Jo dv{i)y{f) = 0, is studied in Xj¡($>, 1), 1 < p < oo. It is shown that Lp has a dense domain; hence there exists a dual operator L* operating on .£¡¡(0,1). After finding LJ we show that both L, and L¡¡ are Fredholm operators. This implies some elementary results concerning the spectrum a...

We use density functional theory to investigate adsorption of liquid mixtures on solid surfaces modified with end-grafted chains. The chains are modelled as freely joined spheres. The fluid molecules are spherical. All spherical species interact via the Lennard-Jones (12-6) potential. The Lennard-Jones (9-3) potential describes interactions of solvent molecules with the substrate. We study the ...

We apply conformal solution theory and extend to mixtures a recently derived equation of state for glass-forming liquids. The equation of state is based on the statistical properties of the multidimensional potential energy surface as a function of a macroscopic system’s degrees of freedom (energy landscape), and allows the calculation of an ideal glass transition locus, along which the configu...