In this paper, we derive analytically the dynamical laws of the coupled GrossPitaevskii equations (CGPEs) without/with an angular momentum rotation term and an external magnetic field for modelling nonrotating/rotating spin-1 Bose-Eintein condensates. We prove the conservation of the angular momentum expectation when the external trapping potential is radially symmetric in two dimensions and cy...

in this paper, the dynamical behavior of an axially moving string modeled by fractional derivative is investigated. the governing equation represented motion is solved by the method of multiple scales. considering principal parametric resonance, the stability boundaries for string with simple supports are obtained. numerical results indicate the effects of fractional damping on stability.

A novel semi analytical method is developed for transient analysis of single-lap adhesive joints with laminated composite adherends subjected to dynamical loads. The presented approach has the capability of choosing arbitrary loadings and boundary conditions. In this model, adherends are assumed to be orthotropic plates that pursuant to the classical lamination theory. Stacking sequences can be...

simulation of turbulence boiling, generation of vapour and predication of its behaviour are still subject to debate in the two-phase flow area and they receive a high level of worldwide attention. in this study, a new arrangement of the three dimensional governing equations for turbulence two-phase flow with heat and mass transfer are derived by using ensemble averaging two-fluid model and util...

This paper reports on the results of combining the Maple packages Dynaflex and RifSimp. The Dynaflex package has been developed to generate the governing dynamical equations for mechanical systems; the RifSimp package has been developed for the symbolic analysis of differential equations. We show that the output equations from Dynaflex can be converted into a form which can be analyzed by RifSi...

Numerical modelling of geological processes, such as mantle convection, flow in porous media, and geothermal heat transfer, has become quite common with the increase in computing and the availability of usable software. Today modelling these dynamical processes entails the solving of the governing equations involving the mass, momentum, energy and chemical transport. These equations represent p...

By the nonstandard analysis theory of turbulence, the governing equations of compressible turbulence are given. The equations can hold at non-uniform points, in fact, are new kind of equations. There are three choices. In the choice one, the second-order infinitesimal quantities are neglected, the closed equations about the point(monad)-average quantities are obtained. In other two choices, the...

(1) Because all of CFD is based on these equations, it is important for each student to feel very comfortable with these equations before continuing further with his or her studies, and certainly before embarking on any application of CFD to a particular problem. (2) This author assumes that the attendees of the present VKI short course come from varied background and experience. Some of you ma...

flood routing has many applications in engineering projects and helps designers in understanding the flood flow characteristics in river flows. floods are taken unsteady flows that vary by time and location. equations governing unsteady flows in waterways are continuity and momentum equations which in case of one-dimensional flow the saint-venant hypothesis is considered. dynamic wave model as ...