The dissipation distance for a 2D single crystal with two symmetric slip systems
| dc.creator | Mittenhuber, Dirk | |
| dc.date | 2002-07-22 | |
| dc.date.accessioned | 2026-07-07T04:49:47Z | |
| dc.date.available | 2026-07-07T04:49:47Z | |
| dc.description | We solve a model problem from single crystal plasticity.We consider 4 slip systems in the plane with orthogonal slip-directions and equal slip rates, forward as well as backwards. We compute the associated dissipation distance by solving an optimal control problem. It turns out that from a computational point of view computing the distance is inexpensive. We put special emphasis on visualization of the metric spheres and the associated length-minimizing curves. As a byproduct we also solve a related problem, optimal path planning for a car driving forwards and backwards with limited turning radius in the hyperbolic plane. This is a hyperbolic version of the Reeds-Shepp-Car-Problem first discussed in (Pac. J. Math. 145:367-393, 1990). | |
| dc.description | 67 pages, 10 figures | |
| dc.identifier | https://arxiv.org/abs/math/0207198 | |
| dc.identifier | http://arxiv.org/abs/math/0207198 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64559 | |
| dc.subject | Optimization and Control | |
| dc.subject | Metric Geometry | |
| dc.subject | 53C22 (Primary) 49Q10 74C15 53A35 (Secondary) | |
| dc.title | The dissipation distance for a 2D single crystal with two symmetric slip systems | |
| dc.type | text |