Application of Hyperelastic Nodal Force Method to Evaluation of Aortic Valve Cusps Coaptation: Thin Shell vs. Membrane Formulations

Coaptation characteristics are crucial in an assessment of the competence of reconstructed aortic valves. Shell or membrane formulations can be used to model the valve cusps coaptation. In this paper we compare both formulations in terms of their coaptation characteristics for the first time. Our numerical thin shell model is based on a combination of the hyperelastic nodal forces method and the rotation-free finite elements. The shell model is verified on several popular benchmarks for thin-shell analysis. The relative error with respect to reference solutions does not exceed 1–2%. We apply our numerical shell and membrane formulations to model the closure of an idealized aortic valve varying hyperelasticity models and their shear moduli. The coaptation characteristics become almost insensitive to elastic potentials and sensitive to bending stiffness, which reduces the coaptation zone.

Higher-spin Cotton tensors and massive gauge-invariant actions in AdS3

In a conformally flat three-dimensional spacetime, the linearised higher-spin Cotton tensor ℭα(n)(h) is the unique conserved conformal current which is a gauge-invariant descendant of the conformal gauge prepotential hα(n). The explicit form of ℭα(n)(h) is well known in Minkowski space. Here we solve the problem of extending the Minkowskian result to the case of anti-de Sitter (AdS) space and derive a closed-form expression for ℭα(n)(h) in terms of the AdS Lorentz covariant derivatives. It is shown that every conformal higher-spin action $$ {S}_{\mathrm{CS}}^{(n)}\left[h\right]\propto \int {\mathrm{d}}^3{xeh}^{\alpha (n)}{\mathrm{\mathfrak{C}}}_{\alpha (n)}(h) $$ S CS n h ∝ ∫ d 3 xeh α n ℭ α n h factorises into a product of (n − 1) first-order operators that are associated with the spin-n/2 partially massless AdS values. Our findings greatly facilitate the on-shell analysis of massive higher-spin gauge-invariant actions in AdS3. The main results are extended to the case of $$ \mathcal{N} $$ N = 1 AdS supersymmetry. In particular, we derive simple expressions for the higher-spin super-Cotton tensors in AdS3.

On the acquisition of potential verbs and conjugation types of verbs in Japanese

It is well-known that children whose native language is Japanese first begin vocalizing potential verbs at about the age of 2 years and continue to utter ungrammatical forms which are not used in adults’ speech as well as correct ones until approximately at the age of 5 years when their acquisition of potential verbs completes, with virtually no erroneous uses observed. Interestingly enough, the process of the acquisition of potential verbs proceeds in a manner parallel with that of causative/inchoative alternation. In this study, based on children’s natural speech data reported in previous research, we argue that the approach put forth in Fuji, Hashimoto, and Murasugi (2008a. “A VP-shell analysis for the undergeneration and the overgeneration in the acquisition of Japanese causatives and potentials.” Nanzan Linguistics 4: 21–41; 2008b. “VP-shell analysis for the acquisition of Japanese potentials.” Nanzan Linguistics: Special Issue 3(2): 65–102) is not empirically valid in that it cannot correctly predict changes in morphological patterns of potential verbs uttered by children along the period of language acquisition. Moreover, in the course of our discussion, it is shown that the acquisition process of the potential morpheme e by children can be identified as that of (in)transitive morpheme e which forms the class of mono-grade vowel-ending verbs.

A $$C^1$$-continuous Trace-Finite-Cell-Method for linear thin shell analysis on implicitly defined surfaces

A Trace-Finite-Cell-Method for the numerical analysis of thin shells is presented combining concepts of the TraceFEM and the Finite-Cell-Method. As an underlying shell model we use the Koiter model, which we re-derive in strong form based on first principles of continuum mechanics by recasting well-known relations formulated in local coordinates to a formulation independent of a parametrization. The field approximation is constructed by restricting shape functions defined on a structured background grid on the shell surface. As shape functions we use on a background grid the tensor product of cubic splines. This yields $$C^1$$ C 1 -continuous approximation spaces, which are required by the governing equations of fourth order. The parametrization-free formulation allows a natural implementation of the proposed method and manufactured solutions on arbitrary geometries for code verification. Thus, the implementation is verified by a convergence analysis where the error is computed with an exact manufactured solution. Furthermore, benchmark tests are investigated.