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Register a new userSchwarz-Christoffel: piliero en rivero (a pillar on a river)
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La transformoj de Schwarz-Christoffel mapas, konforme, la superan kompleksan duon-ebenon al regiono limigita per rektaj segmentoj. Cxi tie ni priskribas kiel konvene kunigi mapon de la suba duon-ebeno al mapo de la supera duon-ebeno. Ni emfazas la bezonon de klara difino de angulo de kompleksa nombro, por tiu kunigo. Ni diskutas kelkajn ekzemplojn kaj donas interesan aplikon pri movado de fluido. ------- Schwarz-Christoffel transformations map, conformally, the complex upper half plane into a region bounded by right segments. Here we describe how to couple conveniently a map of the lower half plane to the map of the upper half plane. We emphasize the need of a clear definition of angle of a complex, to that coupling. We discuss some examples and give an interesting application for motion of fluid.
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An innovative transformation electromagnetics (TE) paradigm, which leverages on the Schwarz-Christoffel (SC) theorem, is proposed to design effective and realistic field manipulation devices (FMDs). Thanks to the conformal property, such a TE design method allows one to considerably mitigate the anisotropy of the synthesized metalenses (i.e., devices with artificially engineered materials covering an antenna to modify its radiation features) with respect to those yielded by the competitive state-of-the-art TE techniques. Moreover, devices with doubly connected contours, thus including masts with arbitrary sections and lenses with holes/forbidden regions in which the material properties cannot be controlled, can be handled. A set of numerical experiments is presented to assess the features of the proposed method in terms of field-manipulation capabilities and complexity of the lens material in a comparative fashion.
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Within the theory of general relativity gravitational phenomena are usually attributed to the curvature of four-dimensional spacetime. In this context we are often confronted with the question of how the concept of ordinary physical three-dimensional space fits into this picture. In this work we present a simple and intuitive model of space for both the Schwarzschild spacetime and the de Sitter spacetime in which physical space is defined as a specified set of freely moving reference particles. Using a combination of orthonormal basis fields and the usual formalism in a coordinate basis we calculate the physical velocity field of these reference particles. Thus we obtain a vivid description of space in which space behaves like a river flowing radially toward the singularity in the Schwarzschild spacetime and radially toward infinity in the de Sitter spacetime. We also consider the effect of the river of space upon light rays and material particles and show that the river model of space provides an intuitive explanation for the behavior of light and particles at and beyond the event horizons associated with these spacetimes.
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