In this paper we present a new theory of exterior calculus over k-dimensional domains in a smooth n-manifold, unifying the discrete and continuum theories. The discrete theory carries a full set of classical operators, products, and relations of calculus and geometry and is free from the standard problems encountered in other theories of discrete exterior calculus. It is based on the Koszul com...

topological analysis has been performed on the total electron density of the two forms of ozonemolecule,c2v and d3h ,to investigate the nature of chemical bonds ,molecular structure , atomiccharges and electrical properties. while these concepts have been completely discussed usingclassical models the emphasize in this work is based on quantum theory of atoms in molecules(qtaim). because the d3...

This paper describes a preliminary investigation into the use of normal form theory for modelling large non-linear dynamical systems. Limit cycle oscillations are determined for simple two-degree-of-freedom double pendulum systems. The double pendulum system is reduced into its centre manifold before computing normal forms. Normal forms are obtained using a period averaging method which is appl...

Deflection analysis of a simply supported microbeam subjected to a concentrated load at the middle is investigated on the basis of a shear deformable beam theory and non-classical theory. Effects of shear deformation and small size are taken into consideration by hyperbolic shear deformable beam theory and modified strain gradient theory, respectively. The governing differential equations and c...

In the present study, the dynamic buckling of the graphene sheet coupled by a viscoelastic matrix was studied. In light of the simplicity of Eringen's non-local continuum theory to considering the nanoscale influences, this theory was employed. Equations of motion and boundary conditions were obtained using Mindlin plate theory by taking nonlinear strains of von Kármán and Hamilton's principle ...

A dielectric continuum theory for the solvation of a polar molecule in a polar, polarizable solvent is tested using computer simulations of formaldehyde in water. Many classes of experiments, for example those which measure solvent-shifted vertical transition energies or electron transfer rates, require an explicit consideration of the solvent electronic polarization. Due to the computational c...

Microcontinuum field theories, including Micromorphic theory, Microstructure theory, Micropolar theory, Cosserat theory, nonlocal theory and couple stress theory, are the extensions of the classical field theories for the applications in microscopic space and time scales. They have been expected to overlap atomic model at microscale and encompass classical continuum mechanics at macroscale. Thi...

The purpose of this research is to study the mechanical behavior of a micropump with clamped circular diaphragm which is the main component of drug delivery systems. In this paper, the non-linear governing equations of the circular microplate using Kirchhoff thin plate theory was been extracted based on the modified couple stress (MCST) and classical (CT) theories. Then, the non-linear equation...

Due to high surface-to-volume ratio of nanoscale structures, surface stress effects have a significant influence on their behavior. In this paper, a two-dimensional problem for an elastic layer that is bonded to a rigid substrate and subjected to an inclined concentrated line load acting on the surface of the layer is investigated based on Gurtin-Murdoch continuum model to consider surface stre...

a classical theory is developed which calculates the momentum transfer rate constant between an ion and a non-polar molecule. the model takes into consideration the effect of diffraction outside the capture limit on the rate constants. the theory is used to calculate momentum transfer rate constant for cl- with trans-dichloroethylene and para-difluorobenzene. theoretical results are compared to...