Topology and geometry of caustics in relation with experiments

Alain Joets

Displaying similar documents to “Topology and geometry of caustics in relation with experiments”

Singularities in drawings of singular surfaces

Alain Joets (2008)

Banach Center Publications

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When drawing regular surfaces, one creates a concrete and visual example of a projection between two spaces of dimension 2. The singularities of the projection define the apparent contour of the surface. As a result there are two types of generic singularities: fold and cusp (Whitney singularities). The case of singular surfaces is much more complex. A priori, it is expected that new singularities may appear, resulting from the "interaction" between the singularities of the surface and...

A stable class of spacetimes with naked singularities

Marcus Kriele (1997)

Banach Center Publications

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We present a stable class of spacetimes which satisfy the conditions of the singularity theorem of Hawking & Penrose (1970), and which contain naked singularities. This offers counterexamples to a geometric version of the strong cosmic censorship hypothesis.

Examples of string-theoretic Euler numbers.

Roczen, Marko (2001)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

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Singularities of relativistic membranes

J. Eggers, J. Hoppe, M. Hynek, N. Suramlishvili (2015)

Geometric Flows

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Pointing out a crucial relation with caustics of the eikonal equation we discuss the singularity formation of 2-dimensional surfaces that sweep out 3-manifolds of zero mean curvature in R3,1.

A septic with 99 real nodes

Oliver Labs (2006)

Rendiconti del Seminario Matematico della Università di Padova

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Stanisław Janeczko, Vladimir Zakalyukin, Vladimir Arnol'd (1999)

Banach Center Publications

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Differential spaces and singularities of space-time.

Buchner, Klaus (1997)

General Mathematics

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Singularities of eddy current problems

Martin Costabel, Monique Dauge, Serge Nicaise (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We consider the time-harmonic eddy current problem in its electric formulation where the conductor is a polyhedral domain. By proving the convergence in energy, we justify in what sense this problem is the limit of a family of Maxwell transmission problems: Rather than a low frequency limit, this limit has to be understood in the sense of Bossavit [11]. We describe the singularities of the solutions. They are related to edge and corner singularities of certain problems for the scalar Laplace...