No abstract

The existence of cold patches at the base of a glacier suggests that the sliding law will depend on these patches, which will essentially affect the viscosity constant. In a poly thermal glacier, such as a glacier which is cold in its lower part and temperate in its upper part, basal boundary conditions change from no-slip to viscous sliding. It is anticipated that the viscosity constant of this sliding law will depend on the distance from the transition line between cold and temperate ice.The mixed boundary conditions, namely no-slip where the ice is cold and viscous sliding where it is temperate, induce large stresses and velocity changes close to the transition line. In fact, it is shown that, for a Newtonian fluid and all investigated discontinuities of boundary data, square-root singularities of the stresses will develop at the transition line. Asymptotic expressions for the basal stresses are derived. The explicit forms of these asymptotic expansions depend on the form of the spatial dependence of the sliding law and, furthermore, on the numerical values of the viscosity coefficient. It is, moreover, argued that the stress concentrations are sufficiently pronounced to account for the removal of basal rock especially in regions of high cleavage concentrations, the details again depending upon the sliding coefficients.No mathematical details of the problem solved are presented as attention is focused on the physical processes.

Natural convection in triangular enclosures is an important problem. It displays well the generic attributes of this class of convection, with its dependence on enclosure geometry, orientation and thermal boundary conditions. It is particularly rich in its variety of flow regimes and thermal fields as well as having significant practical application. In this paper, a comprehensive view of the research area is sought by critically examining the experimental and numerical approaches adopted in studies of this problem in the literature. Different thermal boundary conditions for the evolution of the flow regimes and thermal fields are considered. Effects of changes in pitch angle and the Rayleigh number on the flow and thermal fields are examined in detail. Although most of the past studies are in the laminar regime, the review extends up to the recent studies of the low turbulent regime. Finally, areas of further research are highlighted

In recent years, the use of Fuzzy set theory has been popularised for handling overlap domains in control engineering but this has mostly been within the context of triangular membership functions. In actual practice however, such domains are hardly triangular and in fact for most engineering applications the membership functions are usually Gaussian and sometimes cosine. In an earlier paper, we derived explicit Fourier series expressions for systematic and dynamic computation of grade of membership in the overlap and non-overlap regions of triangular Fuzzy sets. In another paper, we extended the methodology to cover cases of cosine, exponential and Gaussian Fuzzy sets by presenting explicit Fourier series representation for encoding fuzziness in the overlap and non-overlap domains of Fuzzy sets. This current paper presents the development of a “Fuzzy Controller” device, which incorporates the formal mathematical representation for computing grade of membership of Gaussian and triangular Fuzzy sets. It is shown that triangular approximation of Gaussian membership function in Fuzzy control can lead to wrong linguistic classification which may have adverse effects on operational and control decisions. The development of the Fuzzy controller demonstrates that the proposed technique can indeed be incorporated in engineering systems for dynamic and systematic computation of grade of membership in the overlap and non-overlap regions of Fuzzy sets; and thus provides a basis for the design of embedded Fuzzy controller for mission critical applications

Vibration and noise reduction in structures can significantly enhance dynamic stability. In fact, exploitation of such mechanisms can lead to an improvement of aerodynamic performance in flight motions by aircrafts, hydrodynamic performance in ocean water navigation by ships or floating structures, as well as dynamic behavior of machine structures in production processes and systems. In this paper slip damping with layered viscoelastic beam-plate structures for dissipation of vibration energy in aircraft, hydrodynamic, and machine structures is investigated analytically. For this problem, a boundary value partial differential equation is formulated via contact mechanics. In particular, the effect of interfacial pressure distribution variation at the interface of the layered structures on the energy dissipation and logarithmic damping decrement with such layered structures is analyzed and presented for design applications. This allows for a better understanding of the selection process of viscoelastic damping materials for such structures.