Critical Point Theorems and Applications to Differential Equations

This paper contains a generalization of the well-known Palais-Smale and Cerami compactness conditions. The compactness condition introduced is used to prove some general existence theorems for critical points. Some applications are given to differential equations.     

The single-valued extension property for bilateral operator weighted shifts

In this paper, we give necessary and sufficient conditions for a bilateral operator weighted shift to enjoy the single-valued extension property.

     

Synthesis of highly condensed heterocycles using radical reactions

Using radical chemistry novel highly condensed heterocycles have been synthesized. The mechanism for their formation is discussed.     

Principles and Synthesis of Hydractive CRONE Suspension

Mechatronic subsystems have been extensively developed in automotive applications as they increase performance compared to passive components. The Hydractive CRONE suspension based on fractional differentiation is presented as a hybrid system undergoing an infinite sequence of autonomous switchings. The modelling and operation of Hydractive CRONE suspension as a hybrid system are presented. The stability of Hydractive CRONE suspension is demonstrated using the maximum principle extended to hybrid systems. Finally, comfort mode synthesis is proposed using the third generation CRONE control system design.     

LES of turbulent heat transfer: proper convection numerical schemes for temperature transport

Large eddy simulations of two basic configurations (decay of isotropic turbulence, and the academic plane channel flow) with heat transfer have been performed comparing several convection numerical schemes, in order to discuss their ability to evaluate temperature fluctuations properly. Results are compared with the available incompressible heat transfer direct numerical simulation data. It is shown that the use of regularizing schemes (such as high order upwind type schemes) for the temperature transport equation in combination with centered schemes for momentum transport equation gives better results than the use of centred schemes for both equations. Copyright © 2004 John Wiley & Sons, Ltd.     

High‐order accurate numerical solutions of incompressible flows with the artificial compressibility method

A high‐order accurate, finite‐difference method for the numerical solution of incompressible flows is presented. This method is based on the artificial compressibility formulation of the incompressible Navier–Stokes equations. Fourth‐ or sixth‐order accurate discretizations of the metric terms and the convective fluxes are obtained using compact, centred schemes. The viscous terms are also discretized using fourth‐order accurate, centred finite differences. Implicit time marching is performed for both steady‐state and time‐accurate numerical solutions. High‐order, spectral‐type, low‐pass, compact filters are used to regularize the numerical solution and remove spurious modes arising from unresolved scales, non‐linearities, and inaccuracies in the application of boundary conditions. The accuracy and efficiency of the proposed method is demonstrated for test problems. Copyright © 2004 John Wiley & Sons, Ltd.     

Effect of decoupled fluid loading on nonlinear vibration of a flat plate

Numerical simulations of nonlinear responses of a flat plate subject to decoupled fluid loading are carried out. Under clamped boundary conditions and subject to forced vibration at its natural frequency corresponding to the (5,1) mode, the various response modes of the plate are determined. It is found that increasing the excitation amplitude, the response changed from periodic to chaotic. In addition, the fluid-wall shear stresses are found to change the response from linear to nonlinear and vice versa depending on their magnitudes. When a static pressure load is combined with fluid-wall shear stresses and low excitation amplitude, the resulting response was chaotic.