1,721,000 research outputs found
An estimate of the blow-up of Lebesgue norms in the non-tempered case
No full textWe prove that if p>1 and ψ:]0,p−1]→]0,∞[ is just nondecreasing and differentiable (hence not necessarily Δ2), then for every f Lebesgue measurable function on (0,1) sup0<1Sψ(t)‖f⁎‖Ljavax.xml.bind.JAXBElement@5695bc9b(t,1), where f⁎ denotes the decreasing rearrangement of f and Sψ is defined, for ε∈]0,p−1[, through [Formula presented] where cψ is the normalizing constant chosen so that ν((p−1)−)=1. If ψ is in a class of functions satisfying the Δ2 condition, essentially characterized by the so-called ∇′ condition, then inequality (⁎) is sharp, in the sense that both sides are equivalent. Estimate (⁎) generalizes an inequality of the type obtained by the second author with Farroni and Giova in [6] under the growth condition ψ∈Δ2
Micromagnetics of curved thin films
No full textIn this paper, we aim at a reduced 2d-model describing the observable states of the magnetization in curved thin films. Under some technical assumptions on the geometry of the thin-film, it is well-known that the demagnetizing field behaves like the projection of the magnetization on the normal to the thin film. We remove these assumptions and show that the result holds for a broader class of surfaces; in particular, for compact surfaces. We treat both the stationary case, governed by the micromagnetic energy functional, and the time-dependent case driven by the Landau–Lifshitz–Gilbert equation
BMO-type seminorms from Escher-type tessellations
No full textThe paper is about a representation formula introduced by Fusco, Moscariello, and Sbordone in [14]. The formula permits to characterize the gradient norm of a Sobolev function, defined on the whole space [Formula presented], as the limit of non-local energies (BMO-type seminorms) defined on tessellations of [Formula presented] generated by cubic cells with arbitrary orientation. We improve the main result in [14] in three different regards: we give a new concise proof of the representation formula, we analyze the case of a generic open subset [Formula presented], and consider general tessellations of Ω by means of cells more general than cubes, again arbitrarily-oriented, inspired by the creative mind of the graphic artist M.C. Escher
A short proof of local regularity of distributional solutions of Poisson's equation
No full textWe prove a local regularity result for distributional solutions of Poisson's equation with Lp data. We use a very short argument based on Weyl's lemma and the Riesz-Fréchet representation theorem
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
Liouville type results for local minimizers of the micromagnetic energy
No full textWe study local minimizers of the micromagnetic energy in small ferromagnetic 3d convex particles for which we justify the Stoner–Wohlfarth approximation: given a uniformly convex shape Ω⊂R3, there exist δc>0 and C>0 such that for 01, p≠d) is constant
Weak–strong uniqueness for the Landau–Lifshitz–Gilbert equation in micromagnetics
No full textWe consider the time-dependent Landau–Lifshitz–Gilbert equation. We prove that each weak solution coincides with the (unique) strong solution, as long as the latter exists in time. Unlike available results in the literature, our analysis also includes the physically relevant lower-order terms like Zeeman contribution, anisotropy, stray field, and the Dzyaloshinskii–Moriya interaction (which accounts for the emergence of magnetic Skyrmions). Moreover, our proof gives a template on how to approach weak–strong uniqueness for even more complicated problems, where LLG is (nonlinearly) coupled to other (nonlinear) PDE systems
On a sharp Poincare-type inequality on the 2-sphere and its application in micromagnetics
No full textThe main aim of this note is to prove a sharp Poincare-type inequality for vector-valued functions on S2 that naturally emerges in the context of micromagnetics of spherical thin films
La ripartizione delle competenze tra regioni ed enti locali e l'individuazione degli interessi di dimensione regionale nella legislazione statale di settore
No full textOn the possibility of usingModeling and Simulation for environmental footprint in manufacturing. The case of a foundry company involved in the Green Casting Project
No full textThis paper presents a interesting industrial case in which a predicted environmental advantage was found to be ineffectual. To investigate how to address these issues, Environmental performance indicators for the company under consideration are assessed. Carbon and Environmental Footprint calculationmodels are utilized. These indicators domeasure relevant performance tomonitor, but they do not providemeaningful insights into the issues raised in the case under consideration. Modeling and simulation and/or the digital twin, are thus highlighted as potential support tools for guiding the proper decisions for effective environmental management systems. Modeling and simulation tool can then activate virtuos Green Innovation Practices that can lead businesses towards the right steps to improve their environmental performance
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