منابع مشابه
Optimal filling of shapes.
We present filling as a type of spatial subdivision problem similar to covering and packing. Filling addresses the optimal placement of overlapping objects lying entirely inside an arbitrary shape so as to cover the most interior volume. In n-dimensional space, if the objects are polydisperse n-balls, we show that solutions correspond to sets of maximal n-balls. For polygons, we provide a heuri...
متن کاملON OPTIMAL NOZZLE SHAPES OF GAS-DYNAMIC LASERS
Pontryagin's principle is used to study the shape of the supersonic part of the nozzle of a carbon dioxide gas-dynamic laser whose gain is maximal. The exact shape is obtained for the uncoupled approximation of Anderson's bimodal model. In this case, if sharp corners are allowed, the ceiling of the supersonic part consists of a slant rectangular sheet followed by a horizontal one; otherwise...
متن کاملOPTIMAL NOZZLE SHAPES OF CO2-N2-H2O GASDYNAMIC LASERS
In an axisymmetric CO2-N2-H2O gas dynamic laser, let ? denote the intersection of the vertical plane of symmetry with the upper part of the (supersonic) nozzle. To obtain a maximal small signal gain, some authors have tested several families of curves for ?. To find the most general solution for ?, an application of Pontryagin’s principle led to the conjuncture that the optimal ? must consist o...
متن کاملDo optimal shapes exist?
This paper surveys the talk given by the author at ”Seminario Matematico e Fisico di Milano” in November 2006. It deals with the existence question for shape optimization problems associated to the Dirichlet Laplacian. Existence of solutions is seen from both geometrical and functional (γ-convergence) point of view and is discussed in relationship with the optimality conditions and numerical al...
متن کاملOptimal Shapes for Gears
| Gear theory is reexamined and we nd optimal shapes for gears. As optimality criteria, we allow: (1) minimal frictional losses (highest eeciency) assuming linear law of friction or (2) uniform maximum stress (it will wear out slowly and last the longest) assuming Hertzian contacts or (3) uniform maximal temperature, assuming we are in a high power limit in which all heat is removed by the lubr...
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ژورنال
عنوان ژورنال: Physical Review Letters
سال: 2012
ISSN: 0031-9007,1079-7114
DOI: 10.1103/physrevlett.108.198304