Browsing by Subject "RIGIDITY"

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  • Lai, Ru-Yu; Shankar, Ravi; Spirn, Daniel; Uhlmann, Gunther (2017)
    We consider the problem of reconstructing the features of a weak anisotropic background potential by the trajectories of vortex dipoles in a nonlinear Gross-Pitaevskii equation. At leading order, the dynamics of vortex dipoles are given by a Hamiltonian system. If the background potential is sufficiently smooth and flat, the background can be reconstructed using ideas from the boundary and the lens rigidity problems. We prove that reconstructions are unique, derive an approximate reconstruction formula, and present numerical examples.
  • Hyttinen, Tapani; Paolini, Gianluca (2019)
    We study classes of right-angled Coxeter groups with respect to the strong submodel relation of a parabolic subgroup. We show that the class of all right-angled Coxeter groups is not smooth and establish some general combinatorial criteria for such classes to be abstract elementary classes (AECs), for them to be finitary, and for them to be tame. We further prove two combinatorial conditions ensuring the strong rigidity of a right-angled Coxeter group of arbitrary rank. The combination of these results translates into a machinery to build concrete examples of AECs satisfying given model-theoretic properties. We exhibit the power of our method by constructing three concrete examples of finitary classes. We show that the first and third classes are nonhomogeneous and that the last two are tame, uncountably categorical, and axiomatizable by a single L-omega 1,L- omega-sentence. We also observe that the isomorphism relation of any countable complete first-order theory is kappa-Borel reducible (in the sense of generalized descriptive set theory) to the isomorphism relation of the theory of right-angled Coxeter groups whose Coxeter graph is an infinite random graph.
  • Hytonen, Tuomas; Naor, Assaf (2019)
    For every Banach space (Y, parallel to . parallel to(Y)) that admits an equivalent uniformly convex norm we prove that there exists c = c(Y) is an element of(0, infinity) with the following property. Suppose that n is an element of N and that X is an n-dimensional normed space with unit ball B-X. Then for every 1-Lipschitz function f : B-X -> Y and for every epsilon is an element of(0, 1/2] there exists a radius r >= exp (1/epsilon(cn)), a point x is an element of B-X with x + r B-X subset of B-X, and an affine mapping Lambda : X -> Y such that parallel to f (y) - Lambda (y)parallel to(Y)
  • Lassas, Matti; Saksala, Teemu; Zhou, Hanming (2018)
    Given a smooth non-trapping compact manifold with strictly convex boundary, we consider an inverse problem of reconstructing the manifold from the scattering data initiated from internal sources. These data consist of the exit directions of geodesics that are emaneted from interior points of the manifold. We show that under certain generic assumption of the metric, the scattering data measured on the boundary determine the Riemannian manifold up to isometry.
  • Forte, Giancarlo; Pagliari, Stefania; Ebara, Mitsuhiro; Uto, Koichiro; Van Tam, Janice Kal; Romanazzo, Sara; Escobedo-Lucea, Carmen; Romano, Elena; Di Nardo, Paolo; Traversa, Enrico; Aoyagi, Takao (2012)
    Biomaterials to be used as cell delivery systems for cardiac tissue engineering should be able to comply with cardiac muscle contractile activity, while favoring cell survival and neo-angiogenesis in a hostile environment. Biocompatible synthetic materials can be tailored to mimic cardiac tissue three-dimensional organization in the micro- and nanoscales. Nonetheless, they usually display mechanical properties that are far from those of the native myocardium and thus could affect host cell survival and activity. In the present investigation, inert poly-ɛ-caprolactone planar layers were manufactured to change the surface stiffness (with Young's modulus ranging from 1 to 133 MPa) without changing matrix chemistry. These substrates were challenged with neonatal murine cardiomyocytes to study the possible effect of substrate stiffness on such cell behavior without changing biological cues. Interestingly, softer substrates (0.91±0.08 and 1.53±0.16 MPa) were found to harbor mostly mature cardiomyocytes having assembled sarcomeres, as shown by the expression of alpha actinin and myosin heavy chain in typical striations and the upregulation of sarcomeric actin mRNA. On the other hand, a preferential expression of immature cardiac cell genes (Nkx-2.5) and proteins (GATA-4) in cardiac cells grown onto stiffer materials (49.67±2.56 and 133.23±8.67 MPa) was detected. This result could not be ascribed to significant differences in cell adhesion or proliferation induced by the substrates, but to the stabilization of cardiomyocyte differentiated phenotype induced by softer layers. In fact, cardiac cell electromechanical coupling was shown to be more organized on softer surfaces, as highlighted by connexin 43 distribution. Moreover, a differential regulation of genes involved in extracellular matrix remodeling was detected on soft films (0.91±0.08 MPa) as compared with the stiffest (133.23±8.67 MPa). Finally, the upregulation of a number of genes involved in inflammatory processes was detected when the stiffest polymer is used. These events highlight the differences in cell mechanosensitivity in a heterogeneous cell preparation and are likely to contribute to the differences encountered in cardiac cell phenotype induced by substrate stiffness.