The complex Stuart}Landau equation models a prototypical Hopf bifurcation in which, when the control parameter exceeds a critical value, the null solution bifurcates into a "nite amplitude time-periodic solution. We study the response of this equation to time-harmonic forcing in the subcritical regime (i.e., before the bifurcation). We show that when a second parameter in the Stuart}Landau equa...

The computational simulation of the Bray-Liebhafsky (BL) oscillating chemical reaction by differential kinetic methodology is carried out in this work. According to the mechanism of Treindl and Noyes involving 10 reaction steps, the changes of the concentrations of I2 and O2 in solution are simulated. When the control parameters are α = 0.55, β = 0.2882 and δ < 0.6, the differential equations p...

Using singular spectral theory, a boundary-initial value problem is solved for the interfacial concentration of a surfactant on a liquid droplet oscillating in a surrounding second immiscible liquid phase. Besides being of value to the specific application the methodology of this paper is useful for a variety of boundary-initial value problems of interest to chemical engineers in which material...

A high-order spectral difference (SD) method for solving the Navier-Stokes equations on moving, deformable unstructured grids has been developed [1]. In this paper, the SD method and the artificial compressibility method (ACM) are integrated with a dual time-stepping scheme to model unsteady incompressible viscous flow past an inline tube bundle of cylinders equally sized (diameter = d) and spa...

A new sub-optimal subset search method for feature selection is introduced. As opposed to other till now known subset selection methods the oscillating search is not dependent on pre-specified direction of search (forward or backward). The generality of oscillating search concept allowed us to define several different algorithms suitable for different purposes. We can specify the need to obtain...

The manufacture of miniature Stirling cycle cryocoolers, using standard micro-machining techniques and materials has been pursued by the authors [1]. A MEMS based cryocooler would allow integration of a cryogenic cooling system directly into a cryoelectronic device. Resonant bossed diaphragms were proposed as the means to sweep the working gas in the Stirling cooler, replacing the pistons and d...

We give general mathematical results concerning oscillating singularities and we study examples of functions composed only of oscillating singularities. These functions are deened by explicit coeecients on an orthonormal wavelet basis. We compute their HH older regularity and oscillation at every point and we deduce their spectrum of oscillating singularities.

We study the asymptotic behavior of the solution of the Laplace equation in a domain, a part of which boundary is highly oscillating. The motivation comes from the study of a longitudinal flow in an infinite horizontal domain bounded at the bottom by a wall and at the top by a rugose wall. The latter is a plane covered with periodic asperities which size depends on a small parameter ε > 0. The ...

In this paper we present two new methods based on an implicit Runge-Kutta method Gauss which is of algebraic order fourth and has two stages: the first one has zero dispersion and the second one has zero dispersion and zero dissipation. The efficiency of these methods is measured while integrating the radial Schrödinger equation and other well known initial value problems.