By L. Boi, D. Flament, Jean-Michel Salanskis

Within the first 1/2 the nineteenth century geometry replaced greatly, and withina century it helped to revolutionize either arithmetic and physics. It additionally positioned the epistemology and the philosophy of technological know-how on a brand new footing. In this quantity a valid assessment of this improvement is given by means of major mathematicians, physicists, philosophers, and historians of technological know-how. This interdisciplinary procedure provides this assortment a distinct personality. it may be utilized by scientists and scholars, however it additionally addresses a common readership.

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Fig. 4. Extracted interior (blue) and boundary (red) critical points. Periodic orbit (magenta). (Colorplate on p. ) Fig. 5. Streamlines seeded near the boundary critical point (black) and the interior critical point (white). (Colorplate on p. ) Topology-guided Visualization of Constrained Vector Fields 29 Consistent with the situation sketched in Fig. 1, the stable manifold of the interior critical point encloses the recirculation zone (Fig. 6). The recirculation zone contains a single periodic orbit which is of twisted saddle type (Fig.

Inspecting the nearby critical points reveals that there is a pair of spiral saddles in this region, one of them is on the no-slip boundary (upper right in Fig. 4). A quick exploration by integrating a streamline forward and backward from seed points near the critical points gives an idea of the stable and unstable manifolds of the two spiral saddles (Fig. 5). Fig. 4. Extracted interior (blue) and boundary (red) critical points. Periodic orbit (magenta). (Colorplate on p. ) Fig. 5. Streamlines seeded near the boundary critical point (black) and the interior critical point (white).

IEEE Computer, 22(8):27–36, 1989. 8. J. L. Helman and L. Hesselink. Visualizing Vector Field Topology in Fluid Flows. IEEE Comput. Graph. , 11(3):36–46, 1991. 9. T. Iijima. Basic theory on normalization of a pattern (in case of typical onedimensional pattern). Bulletin of Electrical Laboratory, 26:368–388, 1962. 10. J. J. Koenderink. The Structure of Images. Biological Cybernetics, 50:363–370, 1984. 11. A. Kuijper. The Deep Structure of Gaussian Scale Space Images. PhD thesis, Utrecht University, 2002.

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