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    ABSTRACT: We investigate, via the Papkovich-Neuber formulation using prolate spheroidal coordinates, a fully three-dimensional Stokes flow in the exterior of a prolate spheroid driven by its translation or rotation. The Stokes flow is primarily characterized by four parameters: the eccentricity ε of the spheroid, the angle of attack in the case of translation and two rotating angles α and β in the case of rotation. Our mathematical analysis comprises the three parts: (i) derive an analytical three-dimensional solution for the Stokes flow driven by a translating spheroid at an arbitrary angle γ; (ii) derive an analytical three-dimensional solution for the Stokes flow driven by a rotating spheroid with arbitrary angles α and β; and (iii) derive two analytical formulas for the corresponding drag and torque as a function of E, α, β and γ.
    Full-text · Article · Jan 2012 · International Journal of Pure and Applied Mathematics
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    ABSTRACT: A general biotechnological process is modelled by a finite dimensional ordinary differential equation. The stoichiometry is only modelled qualitatively. It is shown that the usual biochemically motivated assumptions are not sufficient to guarantee boundedness of the solution. To overcome this, the concept of non-cyclic biotechnological processes is introduced. Loosely speaking it means that the process does not contain any “reaction loop”. The assumption of non-cyclicity replaces the common assumption of Conservation of Mass. An algorithm is presented so that after finitely many steps it is decided whether a process is non-cyclic or cyclic. Non-cyclicity is also characterised in terms of an echelon matrix derived from the stoichiometric matrix via permutations of columns and rows.
    Full-text · Article · Aug 2010 · Mathematical and Computer Modelling of Dynamical Systems
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    ABSTRACT: ABSTRACTA two-level, s̀-coordinate, β-plane, general circulation model (10,000 km meridional and 30,000 km zonal dimensions) is used to study the effect of planetary scale mountain barriers on vacillation of energy and heat transfer. The results of numerical experiments using models with flat topography (and land-sea heating contrasts) are compared with those using model representations of the Rockies and Himalayas. The mountain barriers were seen to have a crucial effect on the time variation of total eddy kinetic energy, K', meridional temperature gradients, ∇T, and in creating the stationary components of poleward transport of heat and westerly momentum. Preferred regions of high meridional temperature gradients and cyclonic systems formed north-east of the Rockies but north-west of the Himalayas. When K' was partitioned into the values appropriate to the western and eastern halves of the β-plane channel, the time variations of K' associated with each half were frequently out of phase; increasing K'(t) in one half and decreasing K'(t) in the other half was related to eastward moving peaks of baroclinic activity (created downstream of a barrier). A similar process was found in an analysis of atmospheric data for 1961–63, the orientation of the polar vortex being closely related to the west-east oscillation of K'; the model results suggest that the mountain barrier system has a large influence. Time variations in regional weather characteristics are likely to be closely related to this process; it is clearly an important factor to be represented in climatic change modelling.
    Preview · Article · Mar 2010
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