Discrete minimal surface algebras.
Discrete thickness
We investigate the relationship between a discrete version of thickness and its smooth counterpart. These discrete energies are deffned on equilateral polygons with n vertices. It will turn out that the smooth ropelength, which is the scale invariant quotient of length divided by thickness, is the Γ-limit of the discrete ropelength for n → ∞, regarding the topology induced by the Sobolev norm ‖ · ‖ W1,∞(S1,ℝd). This result directly implies the convergence of almost minimizers of the discrete energies...
Distance between components in optimal design problems with perimeter penalization
Domain optimization in -axisymmetric elliptic problems by dual finite element method
An axisymmetric second order elliptic problem with mixed boundary conditions is considered. The shape of the domain has to be found so as to minimize a cost functional, which is given in terms of the cogradient of the solution. A new dual finite element method is used for approximate solutions. The existence of an optimal domain is proven and a convergence analysis presented.
Double bubbles minimize.
Dual dynamic approach to shape optimization
Dubins' problem is intrinsically three-dimensional
Dubins' problem is intrinsically three-dimensional
In his 1957 paper [1] L. Dubins considered the problem of finding shortest differentiable arcs in the plane with curvature bounded by a constant and prescribed initial and terminal positions and tangents. One can generalize this problem to non-euclidean manifolds as well as to higher dimensions (cf. [15]). Considering that the boundary data - initial and terminal position and tangents - are genuinely three-dimensional, it seems natural to ask if the n-dimensional problem always reduces to the...
Dynamical shape control in non-cylindrical Navier-Stokes equations.