Maximal Function Characterizations of Hardy Spaces on Rn with Pointwise Variable Anisotropy

In 2011, Dekel et al. developed highly geometric Hardy spaces Hp(Θ), for the full range 0<p≤1, which were constructed by continuous multi-level ellipsoid covers Θ of Rn with high anisotropy in the sense that the ellipsoids can rapidly change shape from point to point and from level to level. In this article, when the ellipsoids in Θ rapidly change shape from level to level, the authors further obtain some real-variable characterizations of Hp(Θ) in terms of the radial, the non-tangential, and the tangential maximal functions, which generalize the known results on the anisotropic Hardy spaces of Bownik.

Effect of nonuniform perpendicular anisotropy in ferromagnetic resonance spectra in magnetic nanorings

The high frequency dynamic behaviors of magnetic nanorings with variable anisotropy along their radius have been studied using micromagnetic simulations. The dynamic susceptibility spectrum and spatial localization of the ferromagnetic resonance modes are investigated by varying anisotropy gradients in nanorings of 200 nm of external radius, with different internal radii. Both the resonant frequencies and the number of peaks depend on the lower energy magnetization configuration which in turn is a function of anisotropy gradients. Besides, it is shown that the effects of the anisotropy gradient are relevant even for the narrowest ring of 10 nm wide. The idea of controlling frequencies by modifying the anisotropy gradients of the system suggests the possibility of using these nanostructures in potential magnetic controllable frequency devices.

Variable Anisotropic Hardy Spaces with Variable Exponents

Let p(·) : ℝ n → (0, ∞] be a variable exponent function satisfying the globally log-Hölder continuous and let Θ be a continuous multi-level ellipsoid cover of ℝ n introduced by Dekel et al. [12]. In this article, we introduce highly geometric Hardy spaces Hp (·)(Θ) via the radial grand maximal function and then obtain its atomic decomposition, which generalizes that of Hardy spaces Hp (Θ) on ℝ n with pointwise variable anisotropy of Dekel et al. [16] and variable anisotropic Hardy spaces of Liu et al. [24]. As an application, we establish the boundedness of variable anisotropic singular integral operators from Hp (·)(Θ) to Lp (·)(ℝ n ) in general and from Hp (·)(Θ) to itself under the moment condition, which generalizes the previous work of Bownik et al. [6] on Hp (Θ).

Physical explanation for the galaxy distribution on the (λR, ε) and (V/σ, ε) diagrams or for the limit on orbital anisotropy

ABSTRACT In the (λR, ε) and (V/σ, ε) diagrams for characterizing dynamical states, the fast-rotator galaxies (both early type and spirals) are distributed within a well-defined leaf-shaped envelope. This was explained as due to an upper limit to the orbital anisotropy increasing with galaxy intrinsic flattening. However, a physical explanation for this empirical trend was missing. Here, we construct Jeans Anisotropic Models (JAM), with either cylindrically or spherically aligned velocity ellipsoid (two extreme assumptions), and each with either spatially constant or variable anisotropy. We use JAM to build mock samples of axisymmetric galaxies, assuming on average an oblate shape for the velocity ellipsoid (as required to reproduce the rotation of real galaxies), and limiting the radial anisotropy β to the range allowed by physical solutions. We find that all four mock samples naturally predict the observed galaxy distribution on the (λR, ε) and (V/σ, ε) diagrams, without further assumptions. Given the similarity of the results from quite different models, we conclude that the empirical anisotropy upper limit in real galaxies, and the corresponding observed distributions in the (λR, ε) and (V/σ, ε) diagrams, are due to the lack of physical axisymmetric equilibrium solutions at high β anisotropy when the velocity ellipsoid is close to oblate.

Variable anisotropy of small-scale stratospheric irregularities retrieved from stellar scintillation measurements by GOMOS/Envisat

In this paper, we consider possibilities for studying the anisotropy of small-scale air density irregularities using satellite observations of bi-chromatic stellar scintillations during tangential occultations. Estimation of the anisotropy coefficient (the ratio of the characteristic horizontal to vertical scales) and other atmospheric parameters is based on the comparison of simulated/theoretical and experimental auto-spectra and coherency spectra of scintillation. Our analyses exploit a 3-D model of the spectrum of atmospheric inhomogeneities, which consists of anisotropic and isotropic components. For the anisotropic component, a spectral model with variable anisotropy is used. Using stellar scintillation measurements by GOMOS (Global Ozone Monitoring by Occultation of Stars) fast photometers, estimates of the anisotropy coefficient are obtained for atmospheric irregularities with vertical scales of 8–55 m at altitudes of 43–30 km. It is shown that the anisotropy increases from about 10 to 50 with increasing vertical scales.