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 ...

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 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...

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...

We characterize the circular periodic solutions of the generalized Lennard–Jones Hamiltonian system with two particles in Rn, and we analyze what of these periodic solutions can be continued to periodic solutions of the anisotropic generalized Lennard–Jones Hamiltonian system. We also characterize the periods of antiperiodic solutions of the generalized Lennard–Jones Hamiltonian system on R2n, ...

It is a deep fact that the homotopy classification of topological manifolds is convariantly functorial. In other words, a map M → N of topological manifolds naturally induces a map S(M) → S(N) of their structure sets. We extend the fact to the isovariant structure set SG(M, rel Ms) of G-equivariant topological manifolds isovariantly homotopy equivalent to M and restricts to homormorphism on the...

Smit and Frenkel’ have shown that the phase diagram of the two-dimensional Lennard-Jones fluid depends largely on the details of the truncation of the potential. In this Note, Gibbs-ensemble calculations are reported for the three-dimensional Lennard-Jones fluid. As expected, the phase diagram for this system also depends significantly on the details of the truncation. The Lennard-Jones potenti...

Abstract We study the transition pathways of a Lennard-Jones cluster of seven particles in three dimensions. Low lying saddle points of the LJ cluster, which can be reached directly from a minimum without passing through another minimum, are identified without any presumption of their characteristics, nor of the product states they lead to. The probabilities are computed for paths going from a ...