A Lindenstrauss theorem for some classes of multilinear mappings

Under some natural hypotheses, we show that if a multilinear mapping belongs to some Banach multlinear ideal, then it can be approximated by multilinear mappings belonging to the same ideal whose Arens extensions simultaneously attain their norms. We also consider the class of symmetric multilinear mappings.Comment: 11 page

Probing structures in channel flow through SO(3) and SO(2) decomposition

SO(3) and SO(2) decompositions of numerical channel flow turbulence are performed. The decompositions are used to probe, characterize, and quantify anisotropic structures in the flow. Close to the wall the anisotropic modes are dominant and reveal the flow structures. The SO(3) decomposition does not converge for large scales as expected. However, in the shear buffer layer it also does not converge for small scales, reflecting the lack of small scales isotropization in that part of the channel flow.Comment: 25 pages, 22 figure

An accurate and efficient Lagrangian sub-grid model

A computationally efficient model is introduced to account for the sub-grid scale velocities of tracer particles dispersed in statistically homogeneous and isotropic turbulent flows. The model embeds the multi-scale nature of turbulent temporal and spatial correlations, that are essential to reproduce multi-particle dispersion. It is capable to describe the Lagrangian diffusion and dispersion of temporally and spatially correlated clouds of particles. Although the model neglects intermittent corrections, we show that pair and tetrad dispersion results nicely compare with Direct Numerical Simulations of statistically isotropic and homogeneous $3D$ turbulence. This is in agreement with recent observations that deviations from self-similar pair dispersion statistics are rare events

Quantum dissipative effects in graphene-like mirrors

We study quantum dissipative effects due to the accelerated motion of a single, imperfect, zero-width mirror. It is assumed that the microscopic degrees of freedom on the mirror are confined to it, like in plasma or graphene sheets. Therefore, the mirror is described by a vacuum polarization tensor $\Pi_{\alpha\beta}$ concentrated on a time-dependent surface. Under certain assumptions about the microscopic model for the mirror, we obtain a rather general expression for the Euclidean effective action, a functional of the time-dependent mirror's position, in terms of two invariants that characterize the tensor $\Pi_{\alpha\beta}$. The final result can be written in terms of the TE and TM reflection coefficients of the mirror, with qualitatively different contributions coming from them. We apply that general expression to derive the imaginary part of the `in-out' effective action, which measures dissipative effects induced by the mirror's motion, in different models, in particular for an accelerated graphene sheet.Comment: 8 pages, 2 figures. Minor changes, version to be published in Phys. Rev.

Cosmological Magnetic Fields from Gauge-Mediated Supersymmetry-Breaking Models

We study the generation of primordial magnetic fields, coherent over cosmologically interesting scales, by gravitational creation of charged scalar particles during the reheating period. We show that magnetic fields consistent with those detected by observation may obtained if the particle mean life \tau_s is in the range 10^{-14} sec \leq \tau_s \leq 10{-7} sec. We apply this mechanism to minimal gauge mediated supersymmetry-breaking models, in the case in which the lightest stau \tilde\tau_1 is the next-to-lightest supersymmetric particle. We show that, for a large range of phenomenologically acceptable values of the supersymmetry-breaking scale \sqrt{F}, the generated primordial magnetic field can be strong enough to seed the galactic dynamo.Comment: 12 pages, Latex. Final version accepted for publication in Phys. Lett.

Casimir interaction between two concentric cylinders at nonzero temperature

We study the finite temperature Casimir interaction between two concentric cylinders. When the separation between the cylinders is much smaller than the radii of the cylinders, the asymptotic expansions of the Casimir interaction are derived. Both the low temperature and the high temperature regions are considered. The leading terms are found to agree with the proximity force approximations. The low temperature leading term of the temperature correction is also computed and it is found to be independent of the boundary conditions imposed on the larger cylinder.Comment: 6 pages, 1 figur

Scalar Turbulence in Convective Boundary Layers by Changing the Entrainment Flux

Abstract A large-eddy simulation model is adopted to investigate the evolution of scalars transported by atmospheric cloud-free convective boundary layer flows. Temperature fluctuations due to the ground release of sensible heat and concentration fluctuations of a trace gas emitted at the homogeneous surface are mixed by turbulence within the unstable boundary layer. On the top, the entrainment zone is varied to obtain two distinct situations: (i) the temperature inversion is strong and the trace gas increment across the entrainment region is small, yielding to a small top flux with respect to the surface emission; (ii) the temperature inversion at the top of the convective boundary layer is weak, and the scalar increment large enough to achieve a concentration flux toward the free atmosphere that overwhelms the surface flux. In both cases, an estimation of the entrainment flux is obtained within a simple model, and it is tested against numerical data. The evolution of the scalar profiles is discussed in terms of the different entrainment–surface flux ratios. Results show that, when entrainment at the top of the boundary layer is weak, temperature and trace gas scalar fields are strongly correlated, particularly in the lower part of the boundary layer. This means that they exhibit similar behavior from the largest down to the smallest spatial scales. However, when entrainment is strong, as moving from the surface, differences in the transport of the two scalars arise. Finally, it is shown that, independently of the scalar regime, the temperature field exhibits more intermittent fluctuations than the trace gas