Shape transitions in non-Euclidean ribbons
Monday, 23.5.22, 09:30-10:30, Raum 226, Hermann-Herder-Str. 10
Mechanical properties of plants: structural background and what can be learnt for biomimetic applications
Monday, 23.5.22, 14:00-15:00, Raum 226, Hermann-Herder-Str. 10
Numerical Approximations of Thin Structures Undergoing Large Deformations
Monday, 23.5.22, 15:50-16:50, Raum 226, Hermann-Herder-Str. 10
Wrinkles in nature and technology
Tuesday, 24.5.22, 09:30-10:30, Raum 226, Hermann-Herder-Str. 10
Understanding the mechanical interaction of plants with their environment
Tuesday, 24.5.22, 14:00-15:00, Raum 226, Hermann-Herder-Str. 10
Design of origami structures with curved tiles between the creases
Tuesday, 24.5.22, 15:50-16:50, Raum 226, Hermann-Herder-Str. 10
Fractional total variation denoising model with L^1 fidelity
Thursday, 2.6.22, 11:15-12:15, Raum 226, Hermann-Herder-Str. 10
We study a nonlocal version of the total variation-based model with \(L^1\) fidelity for image denoising,\nwhere the regularizing term is replaced with the fractional s-total variation.\nWe discuss regularity of the level sets and uniqueness of solutions, both for high and low values of the fidelity parameter.\nWe analyse in detail the case of binary data given by the characteristic functions of convex sets.\n
On the existence of isoperimetric sets on nonnegatively curved spaces
Thursday, 2.6.22, 12:15-13:15, Raum 226, Hermann-Herder-Str. 10
We consider the isoperimetric problem on Riemannian manifolds with nonnegative\nRicci curvature and Euclidean volume growth, i.e., such that the volume of balls grows\nlike the one of Euclidean ones as the radius diverges. The problem aims at minimizing the\nperimeter among sets having a fixed volume. Under an additional natural assumption on\nasymptotic cones to the manifold, we prove existence of minimizers, called isoperimetric\nsets, for any sufficiently large volume. The existence result holds without additional\nassumptions on manifolds with nonnegative sectional curvature.\nThe proof builds on an asymptotic mass decomposition result for minimizing sequences, on a sharp isoperimetric inequality, and on concavity properties of the isoperimetric profile.\nMore generally, the results hold on N-dimensional RCD(0, N) metric measure spaces,\nwhich are spaces having Ricci curvature bounded from below by zero in a generalized\nsense.\nThe results mentioned are contained in works in collaboration with G. Antonelli, E.\nBru`e, M. Fogagnolo, S. Nardulli, E. Pasqualetto, and D. Semola.
Theory and Implementation of Bowed Strings using Cosserat Rod theory and the Null Space method
Tuesday, 21.6.22, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
\n\nStarting point is the so called Helmholtz Motion discovered by Helmholtz in 1877 for bowed string instruments. We aimed to simulate the same motion.\nFirst we adapt the existence theory for struts designed as Cosserat Rod (Paper of S. Antman and T. Seidman [2005]) to a clamped violin string. The existence theory is still in progress.\nFocus is set on the implementation of a bowed string including bowing and torsional constraints that also can appear in bowed strings. We are able to show the same energy behavior as in the theoretical part.\nMoreover we present the Null Space method for Cosserat rods (Paper by P. Betsch [2005]) and how to apply it in this setting.\nThe second main aspect is the inclusion of a two-step algorithm to realize mechanical damping in order to get the desired energy decay and get more realistic simulations.\nFinally, numerous simulations are shown produced with C++ and MatLab.
Numerical Optimal Control for Differential Equations with State Dependent Switches and Jumps
Tuesday, 5.7.22, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
Optimal control problems for dynamical systems with state dependent switches are inherently non-smooth and non-convex and therefore difficult to treat numerically. Systems with state dependent jumps are even more difficult to treat than systems with switches, as they lead to discontinuous state trajectories. We present two recently developed ideas: First, the method of Finite Elements with Switch Detection (FESD) to numerically solve optimal control problems of switched systems with high order of accuracy. Second, the time-freezing idea for optimal control problems with state jumps, which allows one to reformulate these problems into the easier class of problems with switches, which can then be treated by the FESD method. Both methods are illustrated with numerical examples including the challenging optimal control problem of a hopping robot with ground contact and friction that should detect an optimal jump sequence to a final position in the presence of holes.
Numerical Optimal Control of a Rotary Crane - From Modeling to Real-world Experiments
Tuesday, 19.7.22, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
Numerical optimal control methods were investigated and applied to perform point-to-point motions of a small scale woodyard crane on a pilot plant from Psiori GmbH in Freiburg. Suitable dynamical models were derived and their parameters identified, focusing on the actuator dynamics and the pendulum movements introduced from the actuator motions. An optimal control problem formulation for the given task was derived; its parameterization led to a numerically solvable nonlinear programming problem. Numerical simulation experiments were conducted to explore the solution set of the problem and possible design choices during the implementation process of the online optimization algorithm. A numerical error analysis was done for the parameters arising from the direct multiple shooting approach which led to insights in how to choose the parameters appropriately.
TBA
Tuesday, 26.7.22, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
TBA