Research activity

• bidomain model and nonconvex mean curvature flow
  • slides of the talk
• Apparent contours:
  • appcontour software project; Web interface to the appcontour software (credentials: guest/guest)
  • Slides of my talk at ICNAAM2010, Rhodes
• Kig: interactive geometry software
• 2D automatic triangular mesh generator.
• Stefan problem.
• Polymer crystallization.
• Motion by mean curvature.
• Anisotropic motion by mean curvature.
• Crystalline motion by mean curvature (2D simulations)
• Crystalline motion by mean curvature (3D - facet breaking) october 1999.
  • Pictures presented at the conferences FBP99 (Chiba, Japan, november 1999) and PhTIEE (S. Margherita Ligure, Italy, february 2000).
  • ICIAM 2003. Results of 3D computations starting from a sphere with different choices of crystalline anisotropy, presented in Sydney (july 2003) during the ICIAM 2003 meeting.
• Nonconvex motion by mean curvature, Perona-Malik equation

• Talk presented at OpenMath 2005 (Vicenza, december 14, 2005).
• Talk presented during the LSM/RMLL 2004 meeting (Bordeaux, july 6-10, 2004).
• Official kde web site
• My personal kig site

An example of typical domain divided into subdomains and a zoom of the resulting mesh after flipdiag and pigra regularization. The file protesi.tmg contains the domain description. The mesh in the picture is obtained from the domain description file with the TMG command sequence:
TMG> mesh
TMG> flipdiag
TMG> pigra
TMG> flipdiag



Here is another example...

Related information

Finite element mesh generation : a Web page maintained by Robert Schneiders at Lehrstuhl für angewandte Mathematik insbesondere Informatik.

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Motion by mean curvature.

Click on the icon to view a detailed picture of a torus in the 4D space (a slice of it, actually) flowing by mean curvature. This picture is obtained with the POVRAY package. See also a few variants with different textures.

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Crystalline motion by mean curvature.

We model motion by mean curvature in the particular case of a poligonal Wulff shape (crystalline anisotropy) by means of an Allen-Cahn type regularization, see [GoPa96A]. Simulations include the presence of an $x$ dependent forcing term.

In this picture the solid line represents the Frank diagram of the anisotropy, and the dashed line represents the corresponding Wulff shape.

This is the corresponding evolution starting from a circle (no forcing term).

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Here the anisotropy is nonconvex, and the convexified gives an hexagon. The "ears" in the Wulff shape correspond to the concave parts in the Frank diagram.

Starting from a circle, our Allen-Cahn approach without convexification, gives the following result. Note the formation of wrinklings of the size of the spatial discretization.

More simulations to be inserted here... see pictures here.

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Nonconvex motion by mean curvature, Perona-Malik equation.

Text to be inserted here.....

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MP, Dec 6, 11