this paper investigates the lateral vibration of single-layered graphene sheets based on a new theory called doublet mechanics with a length scale parameter. after a brief reviewing of doublet mechanics fundamentals, a sixth order partial differential equation that governs the lateral vibration of single-layered graphene sheets is derived. using doublet mechanics, the relation between natural f...

The space P of pure states of any physical system, classical or quantum, is identified as a Poisson space with a transition probability. The latter is a function p : P × P → [0, 1]; in addition, a Poisson bracket is defined for functions on P . These two structures are connected through unitarity. Classical and quantum mechanics are each characterized by a simple axiom on the transition probabi...

Carbon can form numerous allotropes because of its valency. Graphene, carbon nanotubes,capped carbon nanotubes, buckyballs, and nanocones are well-known polymorphs of carbon.Remarkable mechanical properties of these carbon atoms have made them the subject of intenseresearch. Several studies have been conducted on carbon nanotubes or graphene. In the presentstudy, the molecular mechanics method ...

This review describes the theory and implementation of implicit solvation models based on continuum electrostatics. Within quantum chemistry this formalism is sometimes synonymous with polarizable model, a particular boundary-element approach to problem defined by Poisson or Poisson–Boltzmann equation, but that moniker belies diversity available methods. work reviews current state-of-the art, e...

This work extends our earlier two-domain formulation of a differential geometry based multiscale paradigm into a multidomain theory, which endows us the ability to simultaneously accommodate multiphysical descriptions of aqueous chemical, physical and biological systems, such as fuel cells, solar cells, nanofluidics, ion channels, viruses, RNA polymerases, molecular motors and large macromolecu...

The common structure of the space of pure states P of a classical and a quantum mechanical system is that of a Poisson space with a transition probability. This is a uniform space equipped with a Poisson structure, as well as with a function p : P × P → [0, 1], with certain properties. The Poisson structure is connected with the transition probabilities through unitarity: each point ρ ∈ P defin...

The Molecular Mechanics Poisson-Boltzmann Surface Area (MMPBSA) approach has been widely applied as an efficient and reliable free energy simulation method to model molecular recognition, such as for protein-ligand binding interactions. In this review, we focus on recent developments and applications of the MMPBSA method. The methodology review covers solvation terms, the entropy term, extensio...

Molecular dynamics simulations of a keratin/peptide complex have been conducted to predict the binding affinity of four different peptides toward human hair. Free energy calculations on the peptides' interaction with the keratin model demonstrated that electrostatic interactions are believed to be the main driving force stabilizing the complex. The molecular mechanics-Poisson-Boltzmann surface ...

An easy implementation of molecular mechanics and molecular dynamics simulation using a continuum solvent model is presented that is particularly suitable for biomolecular simulations. The computation of solvation forces is made using the linear Poisson-Boltzmann equation (polar contribution) and the solvent-accessible surface area approach (nonpolar contribution). The feasibility of the method...

The common structure of the space of pure states P of a classical or a quantum mechanical system is that of a Poisson space with a transition probability. This is a topological space equipped with a Poisson structure, as well as with a function p : P×P → [0, 1], with certain properties. The Poisson structure is connected with the transition probabilities through unitarity (in a specific formula...