Dinesh Khattar

A new coupled approach high accuracy numerical method for the solution of 3D non-linear biharmonic equations

In this paper, we derive a new fourth order finite difference approximation based on arithmetic average discretization for the solution of three-dimensional non-linear biharmonic partial differential equations on a 19-point compact stencil using coupled approach. The numerical solutions of unknown variable u(x,y,z) and its Laplacian @?^2u are obtained at each internal grid point. The resulting stencil algorithm is presented which can be used to solve many physical problems. The proposed method allows us to use the Dirichlet boundary conditions directly and there is no need to discretize the derivative boundary conditions near the boundary. We also show that special treatment is required to handle the boundary conditions. The new method is tested on three problems and the results are compared with the corresponding second order approximation, which we also discuss using coupled approach.

Dual combination combination multi switching synchronization of eight chaotic systems

Abstract In this paper, a novel scheme for synchronizing four drive and four response systems is proposed by the authors. The idea of multi switching and dual combination synchronization is extended to dual combination-combination multi switching synchronization involving eight chaotic systems and is a first of its kind. Due to the multiple combination of chaotic systems and multi switching the resultant dynamic behaviour is so complex that, in communication theory, transmission and security of the resultant signal is more effective. Using Lyapunov stability theory, sufficient conditions are achieved and suitable controllers are designed to realise the desired synchronization. Corresponding theoretical analysis is presented and numerical simulations performed to demonstrate the effectiveness of the proposed scheme.

Stability of an expanding bubble in the Rayleigh model

A bubble expands adiabatically in an incompressible, inviscid liquid. The variation of its radiusR with time is given by the Rayleigh’s equation. We find that the bubble is stable at the equilibrium point in this model.

Effect of rotation on stability of suspended sediments

In this paper we consider the steady sedimentation of a uniform distribution of particles in a uniformly rotating liquid, and examine its stability by solving the set of conservation equations for a two-phase flow. The sixth order algebraic equation in the frequency which results from the perturbation equations is solved numerically. The effects of the variation of the rotation rate, sediment concentration, and vertical wave numbers of small disturbances are discussed and presented graphically.

Bifurcation in a bubble translating and expanding in a sound field

We study the interaction of the motion of an expanding and translating bubble with a sound field, using the method of effective potential adopted by Landau and Lifshitz. We work under the assumption that the amplitude of the sound is small, while the frequency of the sound is large compared to the characteristic oscillation frequency of the bubble. We find that the equilibrium value of the mean radius R of the bubble exhibits a bifurcation as the amplitude of the high frequency sound field increases in a neighbourhood of the value zero.

On integrals and invariants for inviscid, compressible, two-dimensional flows under gravity

Conservation laws for two-dimensional, irrotational flows under gravity of a perfect fluid obtained earlier by Longuet-Higgins (J. Fluid Mech. 134 (1983) 155–159) are extended to the case of a compressible fluid flow.