1,721,031 research outputs found
Stress regularity for a new quasistatic evolution model of perfectly plastic plates
No full textWe study some properties of solutions to a quasistatic evolution problem for perfectly plastic plates, that has been recently derived from three-dimensional Prandtl-Reuss plasticity. We prove that the stress tensor has locally square-integrable first derivatives with respect to the space variables. We also exhibit an example showing that the model under consideration has in general a genuinely three-dimensional nature and cannot be reduced to a two-dimensional setting
Homogenization of Chiral Magnetic Materials: A Mathematical Evidence of Dzyaloshinskii’s Predictions on Helical Structures
No full textIn this paper, we investigate the influence of the bulk Dzyaloshinskii–Moriya interaction on the magnetic properties of composite ferromagnetic materials with highly oscillating heterogeneities, in the framework of Γ -convergence and 2-scale convergence. The homogeneous energy functional resulting from our analysis provides an effective description of most of the magnetic composites of interest nowadays. Although our study covers more general scenarios than the micromagnetic one, it builds on the phenomenological considerations of Dzyaloshinskii on the existence of helicoidal textures, as a result of possible instabilities of ferromagnetic structures under small relativistic spin–lattice or spin–spin interactions. In particular, we provide the first quantitative counterpart to Dzyaloshinskii’s predictions on helical structures
Analysis of a perturbed Cahn–Hilliard model for Langmuir–Blodgett films
Get PDFAn advective Cahn–Hilliard model motivated by thin film formation is studied in this paper. The one-dimensional evolution equation under consideration includes a transport term, whose presence prevents from identifying a gradient flow structure. Existence and uniqueness of solutions, together with continuous dependence on the initial data and an energy equality are proved by combining a minimizing movement scheme with a fixed point argument. Finally, it is shown that, when the contribution of the transport term is small, the equation possesses a global attractor and converges, as the transport term tends to zero, to a purely diffusive Cahn–Hilliard equation
Derivation of a heteroepitaxial thin-film model
Get PDFA variational model for epitaxially-strained thin films on rigid substrates is derived both by Γ-convergence from a transition-layer setting, and by relaxation from a sharp-interface description available in the literature for regular configurations. The model is characterized by a configurational energy that accounts for both the competing mechanisms responsible for the film shape. On the one hand, the lattice mismatch between the film and the substrate generate large stresses, and corrugations may be present because film atoms move to release the elastic energy. On the other hand, flatter profiles may be preferable to minimize the surface energy. Some first regularity results are presented for energetically-optimal film profiles
L’altalena in Pausania (10,29,3 s.)
No full textAncient people explained the Athenian swing rite as hinting to the hanging suicide of
the mythical Erigone. In effect, Soph. OT 1263 s. demonstrates that the same Greek
term indicates both the rising and the instruments for the rising itself, such as swings
or hanging ropes. This lexical element has made that interpretation easy. On the
contrary, Paus. 10, 29, 3 s. does not indicate that Polygnotos painted swinging Phaidra.
There is no evidence for a swinging Phaidra
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Micromagnetics of thin films in the presence of Dzyaloshinskii-Moriya interaction
Get PDFIn this paper, we study the thin-film limit of the micromagnetic energy functional in the presence of bulk Dzyaloshinskii-Moriya interaction (DMI). Our analysis includes both a stationary Γ-convergence result for the micromagnetic energy, as well as the identification of the asymptotic behavior of the associated Landau-Lifshitz-Gilbert equation. In particular, we prove that, in the limiting model, part of the DMI term behaves like the projection of the magnetic moment onto the normal to the film, contributing this way to an increase in the shape anisotropy arising from the magnetostatic self-energy. Finally, we discuss a convergent finite element approach for the approximation of the time-dependent case and use it to numerically compare the original three-dimensional (3D) model with the 2D thin-film limit
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