We present a numerical scheme for viscoelastic flow based on a second-order central differencing method recently introduced in the context of incompressible newtonian flow; the incompressibility constraint is treated with the projection method. The result is a simple and efficient scheme that is readily adaptable to a wide class of differential constitutive equations and flow geometries. We imp...

In this paper, the nonlinear dynamic system of equations, a type of nuclear ssion reactor is solved analytically and numerically. Considering that the direct solution of three-dimensional dynamical systems analysis and more in order to determine the stability and instability, in terms of algebraicsystems is dicult. Using certain situations in mathematics called Hurwitz criterion, Necessary and ...

It is well known that time delays exist widely in biology, neural network, automatic control engineering and so on. Since the existence of delays is frequently a source of instability, bifurcation and chaos, it is important to study the dynamical behaviors of the differential equations with delays. Recently, the periodic problem of Rayleigh equations with a deviating argument x′′ + f(x′(t)) + g...

Low order moments of the alpha dynamo equations in a geophysical regime are related to the dependent variables in a reversing disk dynamo. The link suggests that nonperiodic reversal is an intrinsic feature of the alpha dynamo equations provided the forcing is vigorous and the toroidal and poloidal magnetic fields are sufficiently out of phase. The nonuniformities in reversal frequency are then...

The magnetorotational instability(MRI) in the Kerr spacetime is studied on a 3+1 viewpoint. The Maxwell's equations are expressed in a circularly orbiting observer's frame that co-rotates with matter in Keplerian orbits. The hydromag-netic equations are represented in a locally nonrotating frame(LNRF). There exist large proper growth rates in MRI around a rapidly rotating black hole. The large ...

This paper presents the Adjoint Parabolized Stability Equations (APSE) which are used to predict the receptivity of shear layers to a variety of disturbances. Results from the APSE are first carefully validated against solutions of the Adjoint Navier–Stokes (ANS) equations which demonstrates that APSE is an accurate and effecient means of predicting receptivity. Then APSE is used to document th...

The effect of the magnetic field on the Jeans instability of self-gravitating strongly coupled dusty plasma is investigated. The medium consists of extremely massive, negatively charged strongly correlated dust grains and weakly correlated Boltzmann distributed electrons and ions. The basic equations of the problem are constructed using generalized hydrodynamic model. In deriving dispersion rel...

Dit proefscrift werd mede mogelijk gemaakt met financï ele steun van de Koninklijke Nederlandse Akademie van Wetenschappen (KNAW). " Allah will exalt those who believe among you and those who have knowledge to high ranks. " (QS Al-Mujaadalah 58:11) for: my beloved ones Contents 1 Josephson junctions and sine-Gordon equations: an Introduction 3 1.1 Josephson junctions with phase shift 5 1.2 Sine...

The nonlinear evolution of a helical wiggler free electron laser is investigated within the framework of a macroclump model for the trapped electrons. The model describes the nonlinear evolution of a right-circularly polarized electromagnetic wave with frequency w, and wavenumber k,, and slowly varying amplitude &,(z, t) and phase 8 ,(z, t) (eikonal approximation). The model further assumes tha...

We consider the mean eld theory of optimally pruned per-ceptrons. Using the cavity method, microscopic equations for the weights and the examples are derived. Their statistical properties agree with previous results using the replica method. There is a gap in the weight distribution, causing an instability in the ground state. A rough energy landscape better describes the learning problem. Solu...