Descripción: In this paper, we introduce a dispersion equation for 3D photonic crystals made of parallel layers of non-overlapping spheres, valid when both wavelength and separation between layers are much larger than the distance between neighbouring spheres. This equation is based on the Korringa-Kohn-Rostoker (KKR) wave calculation method developed by Stefanou et al. and can be used to predict the spectral positions of bandgaps in structures made of dispersive spheres. Perfect agreement between the spectral positions of bandgaps predicted with our simplified equation and those obtained with the numerical code MULTEM2 was observed. We find that this simplified relation allows us to identify two types of bandgaps: those related to the constitutive parameters of the spheres and those related to the three dimensional periodicity (distance between layers). Bandgaps of the first type are independent of the frequency and the distance between layers, while those of the second type depend only on these two quantities. We then analyze the influence of the constitutive parameters of the spheres on the spectral position of bandgaps for spheres immersed in dielectric or magnetic homogeneous media. The number and positions of the bandgaps are affected by the permitivity (permeability) of the host medium if the spheres have dispersive permitivity (permeability).

Descripción: A theoretical study of the relation between the relativistic formulation of the nuclear magnetic shielding and spin-rotation tensors is presented. To this end a theoretical expression of the relativistic spin-rotation tensor is formulated, considering a molecular Hamiltonian of relativistic electrons and non-relativistic nuclei. Molecular rotation effects are introduced considering the terms of the Born-Oppenheimer decomposition, which couple the electrons and nuclei dynamics. The loss of the simple relation linking both spectral parameters in the non-relativistic formulation is further analyzed carrying out a perturbative expansion of relativistic effects by means of the linear response within the elimination of the small component approach. It is concluded that relativistic effects on the spin-rotation tensor are less important than those of the nuclear magnetic shielding tensor. © 2012 American Institute of Physics.

Descripción: We present numerical evidence on how three-dimensionalization is recovered at small scale in rotating turbulence with helical forcing provided by a Beltrami flow. The relevant ranges (large-scale inverse cascade of energy, anisotropic and isotropic direct cascades of energy and helicity, dissipative) are each moderately resolved. These results stem from large direct numerical simulations on grids of either 15363 or 30723 points. In the latter case, the scale at which the inertial wave time and the eddy turn-over time are equal is found to be more than one order of magnitude larger than the dissipation scale. We also examine how the presence of such an intermediate scale could affect truncation due to the use of a helical spectral Large Eddy Simulation procedure which can allow for extending the analysis to a wider range of parameters. Finally, the self-similarity of the direct cascade of energy to small scales for rotating flows, observed recently in numerical simulations as well as in several laboratory experiments, will be discussed briefly for its scaling properties and its conformal invariance.