Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 1188.49045
Privat, Yannick
The optimal shape of a dendrite sealed at both ends. (English)
[J] Ann. Inst. Henri Poincaré, Anal. Non Linéaire 26, No. 6, 2317-2333 (2009). ISSN 0294-1449

Summary: We are interested in the geometric structures which appear in nature. We consider the example of a nerve fiber and we suppose that shapes in nature arise in order to optimize some criterion. Then, we try to solve the problem consisting in searching the shape of a nerve fiber for a given criterion. The first considered criterion represents the attenuation in space of the electrical message troughout the fiber and seems to be relevant. Our second criterion represents the attenuation in time of the electrical message and doesn't provide a realistic shape. We prove that the associated optimization problem has no solution.

MSC 2000:: *49Q10 Optimization of the shape other than minimal surfaces
35P05 General spectral theory of PDE
49R05
92C20 Neural biology

Keywords: optimal shape; cable equation; dendrite; eigenvalue problem

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]