Gas transport through nanochannels is ubiquitous in nature and also plays an important role industry. The gas flow this regime can be described by the Knudsen theory, which assumes that molecules diffusely reflect on confining walls [1]. However, with emergence of low dimensional carbon-based materials such as graphene carbon nanotubes, it has been evidenced assumption might not hold for some a...

In standard treatments of atomic multipole models, interaction energies, total molecular forces, and total molecular torques are given for multipolar interactions between rigid molecules. However, if the molecules are assumed to be flexible, two additional multipolar atomic forces arise because of (1) the transfer of torque between neighboring atoms and (2) the dependence of multipole moment on...

Let G = (V,E) be a simple graph with n = |V | vertices and m = |E| edges; let d1, d2, . . . , dn denote the degrees of the vertices of G. If ∆ = max i di ≤ 4, G is a chemical graph. The first and second Zagreb indices are defined as M1 = ∑

The Distance Geometry Problem (DGP) seeks to find positions for a set of points in geometric space when some distances between pairs these are known. so-called discretization assumptions allow us discretize the search DGP instances. In this paper, we focus on key subclass DGP, namely Discretizable Molecular and study its associated graph vertex ordering problem, Contiguous Trilateration Orderin...