The energy equation for turbulent flow of fiber suspensions was derived in terms of second order correlation tensors. Fiber motion of turbulent energy including the correlation between pressure fluctuations and velocity fluctuations was discussed at two points of flow field, at which the correlation tensors were the functions of space coordinates, distance between two points, and time.

This work aims at introducing some energy operators linked to the Teager-Kaiser energy operator and expands it from time to space in the real domain. We then show the decomposition of the functions of space and time differentiable at least twice in R using those energy operators. The second part of the work focuses on using the energy operators to redefine the general wave equation. The method ...

We prove the following results: (1) A unique smooth solution exists for short time for the heat equation associated with the MM obius energy of loops in a euclidean space, starting with any simple smooth loop. (2) A critical loop of the energy is smooth if it has cube-integrable curvature. Combining this with an earlier result of M. Freedman, Z. Wang and the author, any local minimizer of the e...

In this work, kinetics and thermodynamics of esterification reaction were studied. This research investigated the esterification reaction between methanol and acidified oil catalyzed by sulfonated cation exchange resin and proposed a new rate equation for consideration of kinetics of this reaction according to the Langmuir-Hinshelwood mechanism. Thermodynamics and kinetics parameters were calcu...

In this paper, a rectangular sandwich plate with a constrained layer and an electrorheological (ER) fluid core is investigated. The rectangular plate is covered an ER fluid core and a constraining layer to improve the stability of the system. The two outer layers of the sandwich structure are elastic. The viscoelastic materials express the middle layer behavior under electric field and small st...

In this paper, we solve numerically a semiconductor device energy balance equation using monotone iterative method. With the proposed solution technique, we prove the solution of ̄nite volume discretized semiconductor device energy balance equation converges monotonically. The method presented here provides an e± cient approach for the numerical solution of energy balance equation in submicron ...

in order to represent the potential energy function over the whole range of r, many potentialenergy functions have been proposed. in the present paper, we employ many potential energyfunctions, to use numerov method for solving the nuclear schrödinger equation for the ifmolecule, as an example of a heteronuclear diatomic molecules. then we determine thespectroscopic constants eω , e e x ω , e b...

the michelsen stability and multiphase flash calculation by direct minimization of gibbs free energy of the system at constant temperature and pressure, was used for systems containing gas hydrates. the solid hydrate phase was treated as a solid solution. the fugacities of all components of the hydrate phase were calculated as a function of compositions by the rearranged model of van der waals ...

In this note, we use an elementary argument to show that the existence and unitarity of radiation fields implies asymptotic partition of energy for the corresponding wave equation. This argument establishes the equipartition of energy for the wave equation on scattering manifolds, asymptotically hyperbolic manifolds, asymptotically complex hyperbolic manifolds, and the Schwarzschild spacetime. ...