@article{9376,
  abstract     = {This paper presents a method for designing planar multistable compliant structures. Given a sequence of desired stable states and the corresponding poses of the structure, we identify the topology and geometric realization of a mechanism—consisting of bars and joints—that is able to physically reproduce the desired multistable behavior. In order to solve this problem efficiently, we build on insights from minimally rigid graph theory to identify simple but effective topologies for the mechanism. We then optimize its geometric parameters, such as joint positions and bar lengths, to obtain correct transitions between the given poses. Simultaneously, we ensure adequate stability of each pose based on an effective approximate error metric related to the elastic energy Hessian of the bars in the mechanism. As demonstrated by our results, we obtain functional multistable mechanisms of manageable complexity that can be fabricated using 3D printing. Further, we evaluated the effectiveness of our method on a large number of examples in the simulation and fabricated several physical prototypes.},
  author       = {Zhang, Ran and Auzinger, Thomas and Bickel, Bernd},
  issn         = {1557-7368},
  journal      = {ACM Transactions on Graphics},
  keywords     = {multistability, mechanism, computational design, rigidity},
  number       = {5},
  publisher    = {Association for Computing Machinery},
  title        = {{Computational design of planar multistable compliant structures}},
  doi          = {10.1145/3453477},
  volume       = {40},
  year         = {2021},
}

@article{7389,
  abstract     = {Recently Kloeckner described the structure of the isometry group of the quadratic Wasserstein space W_2(R^n). It turned out that the case of the real line is exceptional in the sense that there exists an exotic isometry flow. Following this line of investigation, we compute Isom(W_p(R)), the isometry group of the Wasserstein space
W_p(R) for all p \in [1,\infty) \setminus {2}. We show that W_2(R) is also exceptional regarding the
parameter p: W_p(R) is isometrically rigid if and only if p is not equal to 2. Regarding the underlying
space, we prove that the exceptionality of p = 2 disappears if we replace R by the compact
interval [0,1]. Surprisingly, in that case, W_p([0,1]) is isometrically rigid if and only if
p is not equal to 1. Moreover, W_1([0,1]) admits isometries that split mass, and Isom(W_1([0,1]))
cannot be embedded into Isom(W_1(R)).},
  author       = {Geher, Gyorgy Pal and Titkos, Tamas and Virosztek, Daniel},
  issn         = {10886850},
  journal      = {Transactions of the American Mathematical Society},
  keywords     = {Wasserstein space, isometric embeddings, isometric rigidity, exotic isometry flow},
  number       = {8},
  pages        = {5855--5883},
  publisher    = {American Mathematical Society},
  title        = {{Isometric study of Wasserstein spaces - the real line}},
  doi          = {10.1090/tran/8113},
  volume       = {373},
  year         = {2020},
}