Dynamic modeling of α in the isotropic lagrangian averaged navier-stokes-α equations

A dynamic procedure for the Lagrangian Averaged Navier- Stokes-α (LANS-α) equations is developed where the variation in the parameter α in the direction of anisotropy is determined in a self-consistent way from data contained in the simulation itself. In order to derive this model, the incompressible Navier-Stokes equations are Helmholtz-filtered at the grid and a test filter levels. A Germano type identity is derived by comparing the filtered subgrid scale stress terms with those given in the LANS-α equations. Assuming constant α in homogenous directions of the flow and averaging in these directions, results in a nonlinear equation for the parameter α, which determines the variation of α in the non-homogeneous directions or in time. Consequently, the parameter α is calculated during the simulation instead of a pre-defined value. As an initial test, the dynamic LANS-α model is used to compute isotropic homogenous forced and decaying turbulence, where α is constant over the computational domain, but is allowed to vary in time. The resulting simulations are compared with direct numerical simulations and with the LANS-α simulations using fixed value of α. As expected, α is found to change rapidly during the first eddy turn-over time during the simulations. It is also observed that by using the dynamic LANS-α procedure a more accurate simulation of the isotropic homogeneous turbulence is achieved. The energy spectra and the total kinetic energy decay are captured more accurately as compared with the LANS-α simulations using a fixed α. The current results suggest some promising applications of this dynamic LANS-α model, such as to a spatially varying turbulent flow, which we hope to undertake in future research

Attractor solutions for general hessence dark energy

As a candidate for the dark energy, the hessence model has been recently introduced. We discuss the critical points of this model in almost general case, that is for arbitrary hessence potential and almost arbitrary hessence-background matter interaction. It is shown that in all models, there always exist some stable late-time attractors. It is shown that our general results coincide with those solutions obtained earlier for special cases, but some of them are new. These new solutions have two unique characteristics. First the hessence field has finite value in these solutions and second, their stabilities depend on the second derivative of the hessence potential.Comment: 11 pages. Add some explanations about the autonomousity of the equations, and also a conclusion section was added. To appear in Phys. Rev. D (2006

A Note on Gravitational Baryogenesis

The coupling between Ricci scalar curvature and the baryon number current dynamically breaks CPT in an expanding universe and leads to baryon asymmetry. We study the effect of time dependence of equation of state parameter of the FRW universe on this asymmetry.Comment: 10 pages, accepted for publication in Physical Review

Multicomponent solution in modified theory of gravity in the early universe

We study the modified theory of gravity in Friedmann Robertson Walker universe composed of several perfect fluids. We consider the power law inflation and determine the equation of state parameters in terms of the parameters of modified gravity's Lagrangian in the early universe. We also discuss briefly the gravitational baryogenesis in this model.Comment: 9 pages, accepted for publication in Physical Review

Numerical Simulations of the Lagrangian Averaged Navier-Stokes (Lans-α) Equations for Forced Homogeneous Isotropic Turbulence

The modeling capabilities of the Lagrangian Averaged Navier-Stokes-α equations (LANS-α) is investigated in statistically stationary three-dimensional homogeneous and isotropic turbulence. The predictive abilities of the LANS-α equations are analyzed by comparison with DNS data. Two different forcing techniques were implemented to model the energetics of the energy containing scales. The resolved flow is examined by comparison of the energy spectra of the LANS-α and the DNS computations; furthermore, the correlation between the vorticity and the eigenvectors of the rate of the resolved strain tensor is studied. We find that the LANS-α equations captures the gross features of the flow while the wave activity below a given scale α is filtered by the non- linear dispersion

Application of He's variational iteration method to nonlinear Jaulent–Miodek equations and comparing it with ADM

AbstractInstead of finding a small parameter for solving nonlinear problems through perturbation method, a new analytical method called He's variational iteration method (VIM) is introduced to be applied to solve nonlinear Jaulent–Miodek, coupled KdV and coupled MKdV equations in this article. In this method, general Lagrange multipliers are introduced to construct correction functionals for the problems. The multipliers can be identified optimally via the variational theory. The results are compared with exact solutions