Differential forms and Clifford analysis

In this paper we use a calculus of differential forms which is defined using an axiomatic approach. We then define integration of differential forms over chains in a new way and we present a short proof of Stokes' formula using distributional techniques. We also consider differential forms in Clifford analysis, vector differentials and their powers. This framework enables an easy proof for a Cauchy's formula on a k-surface. Finally, we discuss how to compute winding numbers in terms of the monogenic Cauchy kernel and the vector differentials with a new approach which does not involve cohomology of differential forms

Modelling of Elastic Gearboxes Using a Generalized Gear Contact Model

The object of this paper is to present an universal model that describes the gear contact between two gears in a planar environment. The model includes elastic effects between the gear wheels. Using this model it is possible to create arbitrary spur gear connections as well as all kinds of epicyclic gearing configurations by supplying the proper external constraints. The presented model is implementated in the Modelica language and Dymola is used for the simulations

The supersonic fan engine: An advanced concept in supersonic cruise propulsion

Engine performance and mission studies were carried out for turbofan engines equipped with supersonic through-flow fans. The mission was for a commercial supersonic transport with a Mach 2.32 capability. The advantages of the supersonic fan engines are discussed in terms of mission range comparisons with other engine types. The effects of fan efficiency, inlet losses, and engine weight on engine performance and mission range are shown. The range of a supersonic transport with supersonic fan engines could be 10 to 20 percent better than with other types having the same technology core

Turbine bypass engine: A new supersonic cruise propulsion concept

Engine performance and mission studies were carried out for a single-spool Turbine Bypass Engine concept. Comparisons were made between the TBE, a conventional single-spool turbojet, and the Pratt & Whitney Variable Stream Control Engine. The airplane assumed for the study was a Mach 2.32 commercial supersonic transport. The nominal mission was a 4000-nautical miles total range with a 300-nautical miles subsonic cruise leg. The figure of merit was the minimum takeoff gross weight for the mission. Comparisons of the three engines were also made for the 4000-nautical miles total range with longer subsonic cruise legs

Cauchy-Kowalevski extensions and monogenic plane waves using spherical monogenics

Clifford analysis may be regarded as a direct and elegant generalization to higher dimensions of the theory of holomorphic functions in the complex plane, centred around the notion of monogenic function, i.e. a null solution of the Dirac operator. This paper dealswith axial and biaxialmonogenic functions containing sphericalmonogenics. They are constructed bymeans of two fundamentalmethods of Clifford analysis, namely the Cauchy-Kowalevski extension and monogenic plane waves

A discrete Bochner-Martinelli formula

In the even dimensional case the discrete Dirac equation may be reduced to the so-called discrete isotonic Dirac system in which suitable Dirac operators appear from both sides in half the dimension. This is an appropriated framework for the development of a discrete Martinelli-Bochner formula for discrete holomorphic functions on the simplest of all graphs, the rectangular Z(m) one. Two lower-dimensional cases are considered explicitly to illustrate the closed analogy with the theory of continuous variables and the developed discrete scheme