Search results for "Isotropy"
showing 10 items of 1099 documents
An overdetermined problem for the anisotropic capacity
2015
We consider an overdetermined problem for the Finsler Laplacian in the exterior of a convex domain in \({\mathbb {R}}^{N}\), establishing a symmetry result for the anisotropic capacitary potential. Our result extends the one of Reichel (Arch Ration Mech Anal 137(4):381–394, 1997), where the usual Newtonian capacity is considered, giving rise to an overdetermined problem for the standard Laplace equation. Here, we replace the usual Euclidean norm of the gradient with an arbitrary norm H. The resulting symmetry of the solution is that of the so-called Wulff shape (a ball in the dual norm \(H_0\)).
Search for First Harmonic Modulation in the Right Ascension Distribution of Cosmic Rays Detected at the Pierre Auger Observatory
2011
We present the results of searches for dipolar-type anisotropies in different energy ranges above 2.5 × 1017 eV with the surface detector array of the Pierre Auger Observatory, reporting on both the phase and the amplitude measurements of the first harmonic modulation in the right-ascension distribution. Upper limits on the amplitudes are obtained, which provide the most stringent bounds at present, being below 2% at 99% C.L. for EeV energies. We also compare our results to those of previous experiments as well as with some theoretical expectations.
Etude theorique de la dynamique du réseau de batio en phase quadratique
1999
Abstract The lattice dynamics of barium titanate BaTiO 3 is discussed quantitatively in the framework of a shell model taking into account the electronic polarizabilities of the constituent ions and including Coulomb and short-range interactions. The results of calculations point out the important role of the anisotropic oxygen polarizability. There is a good agreement between calculated and experimental dispersion curves.
Polar nanoregions in Pb(Mg1/3Nb2/3)O3 (PMN): insights from a supercell approach
2011
Abstract We report construction of a model of polar nanoregions in the PMN relaxor ferroelectric based on first-principles lattice dynamics for chemically ordered supercells [S.A. Prosandeev et al., Phys. Rev. B 70, 134110 (2004)], combined with invariance under permutations and dipole-dipole interaction as a source supporting randomly oriented residual polarization. Representative analytical estimates of polar nanore-gion — supercell mapping reproduce both nonzero local and zero macroscopic polarization of the structure, as well as the temperature change of the supercell anisotropy at cooling and field cooling.
A comparison of numerical surface topography calculations in geodynamic modelling: an evaluation of the ‘sticky air’ method
2012
SUMMARY Calculating surface topography in geodynamic models is a common numerical problem. Besides other approaches, the so-called ‘sticky air’ approach has gained interest as a free-surface proxy at the top boundary. The often used free slip condition is thereby vertically extended by introducing a low density, low viscosityfluid layer. This allows the air/crust interface to behave in a similar manner to a true free surface. We present here a theoretical analysis that provides the physical conditions under which the sticky air approach is a valid approximation of a true free surface. Two cases are evaluated that characterize the evolution of topography on different timescales: (1) isostati…
The cage elasticity and under-field structure of concentrated magnetic colloids probed by small angle X-ray scattering
2013
International audience; In the present study we probe the bulk modulus and the structure of concentrated magnetic fluids by small angle X-ray scattering. The electrostatically stabilized nanoparticles experience a repulsive interparticle potential modulated by dipolar magnetic interactions. On the interparticle distance length scale, we show that nanoparticles are trapped under-field in oblate cages formed by their first neighbours. We propose a theoretical model of magnetostriction for the field-induced deformation of the cage. This model captures the anisotropic features of the experimentally observed scattering pattern on the local scale in these strongly interacting colloidal dispersions
X-ray scattering studies of the structure of aqueous hydroxy-propylcellulose solutions
1991
X-ray diffraction studies have been undertaken on aqueous solutions of hydroxy propylcellulose (HPC) over a wide range of the scattering vector Q. The experiments revealed only modest differences in local structure on a distance scale ca. 5–300 A despite the fact that they covered concentrations generally interpreted as ranging from the isotropic (35.1 wt %) to the anisotropic liquid crystalline (LC) phase (53.5 wt %). Several models were used to interpret the small-angle scattering data, and each gave similar structural parameters and extrapolated intensities (Q → 0) for both solutions. Peaks were observed with d-spacings ca. 12–17 A in both materials. Wide-angle x-ray scattering (WAXS) sh…
Photoelectropoling of azobenzene chromophores in molecular films
1994
The photoinduced reorientation and photoelectropoling processes were investigated in molecular films of aliphatically substituted azobenzenes. While polarized illumination leads to a conversion of isotropic samples into anisotropic ones, upon application of external electric fields even macroscopically polar materials are created. The macroscopic polarity can be reversed under suitable experimental conditions. Order parameters as a function of the poling field were determined by Stark spectroscopy. Using atomic force microscopy it is shown that the structure of the sample is well defined on a microscopic length scale, whereas on a macroscopic length scale it is not.
Validation of buoyancy driven spectral tensor model using HATS data
2016
We present a homogeneous spectral tensor model for wind velocity and temperature fluctuations, driven by mean vertical shear and mean temperature gradient. Results from the model, including one-dimensional velocity and temperature spectra and the associated co-spectra, are shown in this paper. The model also reproduces two-point statistics, such as coherence and phases, via cross-spectra between two points separated in space. Model results are compared with observations from the Horizontal Array Turbulence Study (HATS) field program (Horst et al. 2004). The spectral velocity tensor in the model is described via five parameters: the dissipation rate (), length scale of energy-containing eddi…
Non-London electrodynamics in a multiband London model : anisotropy-induced nonlocalities and multiple magnetic field penetration lengths
2018
The London model describes strongly type-2 superconductors as massive vector field theories, where the magnetic field decays exponentially at the length scale of the London penetration length. This also holds for isotropic multi-band extensions, where the presence of multiple bands merely renormalises the London penetration length. We show that, by contrast, the magnetic properties of anisotropic multi-band London models are not this simple, and the anisotropy leads to the inter-band phase differences becoming coupled to the magnetic field. This results in the magnetic field in such systems having N+1 penetration lengths, where N is the number of field components or bands. That is, in a giv…