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- ItemHausdorff metric BV discontinuity of sweeping processes(Bristol : IOP Publ., 2016) Klein, Olaf; Recupero, VincenzoSweeping processes are a class of evolution differential inclusions arising in elastoplasticity and were introduced by J.J. Moreau in the early seventies. The solution operator of the sweeping processes represents a relevant example of rate independent operator. As a particular case we get the so called play operator, which is a typical example of a hysteresis operator. The continuity properties of these operators were studied in several works. In this note we address the continuity with respect to the strict metric in the space of functions of bounded variation with values in the metric space of closed convex subsets of a Hilbert space. We provide counterexamples showing that for all BV-formulations of the sweeping process the corresponding solution operator is not continuous when its domain is endowed with the strict topology of BV and its codomain is endowed with the L1-topology. This is at variance with the play operator which has a BV-extension that is continuous in this case.
- ItemExperimental Observation of Dirac Nodal Links in Centrosymmetric Semimetal TiB2(College Park, MD : American Physical Society, 2018) Liu, Z.; Lou, R.; Guo, P.; Wang, Q.; Sun, S.; Li, C.; Thirupathaiah, S.; Fedorov, A.; Shen, D.; Liu, K.; Lei, H.; Wang, S.The topological nodal-line semimetal state, serving as a fertile ground for various topological quantum phases, where a topological insulator, Dirac semimetal, or Weyl semimetal can be realized when the certain protecting symmetry is broken, has only been experimentally studied in very few materials. In contrast to discrete nodes, nodal lines with rich topological configurations can lead to more unusual transport phenomena. Utilizing angle-resolved photoemission spectroscopy and first-principles calculations, here, we provide compelling evidence of nodal-line fermions in centrosymmetric semimetal TiB2 with a negligible spin-orbit coupling effect. With the band crossings just below the Fermi energy, two groups of Dirac nodal rings are clearly observed without any interference from other bands, one surrounding the Brillouin zone (BZ) corner in the horizontal mirror plane σh and the other surrounding the BZ center in the vertical mirror plane σv. The linear dispersions forming Dirac nodal rings are as wide as 2 eV. We further observe that the two groups of nodal rings link together along the Γ-K direction, composing a nodal-link configuration. The simple electronic structure with Dirac nodal links mainly constituting the Fermi surfaces suggests TiB2 as a remarkable platform for studying and applying the novel physical properties related to nodal-line fermions.