On the Global Regularity of a Helical-decimated Version of the 3D Navier-Stokes Equations

We study the global regularity, for all time and all initial data in $H^{1/2}$, of a recently introduced decimated version of the incompressible 3D Navier-Stokes (dNS) equations. The model is based on a projection of the dynamical evolution of Navier-Stokes (NS) equations into the subspace where helicity (the $L^2-$scalar product of velocity and vorticity) is sign-definite. The presence of a second (beside energy) sign-definite inviscid conserved quadratic quantity, which is equivalent to the $H^{1/2}-$Sobolev norm, allows us to demonstrate global existence and uniqueness, of space-periodic solutions, together with continuity with respect to the initial conditions, for this decimated 3D model. This is achieved thanks to the establishment of two new estimates, for this 3D model, which show that the $H^{1/2}$ and the time average of the square of the $H^{3/2}$ norms of the velocity field remain finite. Such two additional bounds are known, in the spirit of the work of H. Fujita and T. Kato \cite{kato1,kato2}, to be sufficient for showing well-posedness for the 3D NS equations. Furthermore, they are directly linked to the helicity evolution for the dNS model, and therefore with a clear physical meaning and consequences

Superfluid Bose-Fermi mixture from weak-coupling to unitarity

We investigate the zero-temperature properties of a superfluid Bose-Fermi mixture by introducing a set of coupled Galilei-invariant nonlinear Schr\"odinger equations valid from weak-coupling to unitarity. The Bose dynamics is described by a Gross-Pitaevskii-type equation including beyond-mean-field corrections possessing the correct weak-coupling and unitarity limits. The dynamics of the two-component Fermi superfluid is described by a density-functional equation including beyond-mean-field terms with correct weak-coupling and unitarity limits. The present set of equations is equivalent to the equations of generalized superfluid hydrodynamics, which take into account also surface effects. The equations describe the mixture properly as the Bose-Bose repulsive (positive) and Fermi-Fermi attractive (negative) scattering lengths are varied from zero to infinity in the presence of a Bose-Fermi interaction. The present model is tested numerically as the Bose-Bose and Fermi-Fermi scattering lengths are varied over wide ranges covering the weak-coupling to unitarity transition.Comment: 11 page

Medical use of cannabis: italian and european legislation

This review illustrates some brief considerations of the medical use of cannabis recently issued in Italy. History and uses of cannabis throughout centuries and different countries are illustrated together with a description of botany and active phytocannabinoids. Then, medical use of cannabis anti-pain treatment for patients resistant to conventional therapies is described in case of chronic neuropathic pain, spasticity, for anticinetosic and antiemetic effect in nausea and vomiting caused by chemotherapy, for appetite stimulating effect in cachexia, anorexia, loss of appetite in cancer patients or patients with AIDS and in anorexia nervosa, hypotensive effect in glaucoma resistant to conventional therapies and for reduction of involuntary body and facial movements in Gilles de la Tourette syndrome. Italian most recent legislation on medical cannabis is detailed with some law proposals, also showing the inconsistent legislation within European Union. Some final considerations of future studies are also reported

Aspects of symmetry breaking in SO(10) GUTs

I review some recent results on the Higgs sector of minimal SO(10) grand unified theories both with and without supersymmetry. It is shown that nonsupersymmetric SO(10) with just one adjoint triggering the first stage of the symmetry breaking does provide a successful gauge unification when radiative corrections are taken into account in the scalar potential, while in the supersymmetric case it is argued that the troubles in achieving a phenomenologically viable breaking with representations up to the adjoint are overcome by considering the flipped SO(10) embedding of the hypercharge.Comment: 8 pages, 1 figure; prepared for the proceedings of DISCRETE'10 - Symposium on Prospects in the Physics of Discrete Symmetrie

Contributions of cortical feedback to sensory processing in primary visual cortex

Closing the structure-function divide is more challenging in the brain than in any other organ (Lichtman and Denk, 2011). For example, in early visual cortex, feedback projections to V1 can be quantified (e.g., Budd, 1998) but the understanding of feedback function is comparatively rudimentary (Muckli and Petro, 2013). Focusing on the function of feedback, we discuss how textbook descriptions mask the complexity of V1 responses, and how feedback and local activity reflects not only sensory processing but internal brain states

A Parallel Hamiltonian Eigensolver for Passivity Characterization and Enforcement of Large Interconnect Macromodels

Best Paper Award Nominatio

Finite times to equipartition in the thermodynamic limit

We study the time scale T to equipartition in a 1D lattice of N masses coupled by quartic nonlinear (hard) springs (the Fermi-Pasta-Ulam beta model). We take the initial energy to be either in a single mode gamma or in a package of low frequency modes centered at gamma and of width delta-gamma, with both gamma and delta-gamma proportional to N. These initial conditions both give, for finite energy densities E/N, a scaling in the thermodynamic limit (large N), of a finite time to equipartition which is inversely proportional to the central mode frequency times a power of the energy density E/N. A theory of the scaling with E/N is presented and compared to the numerical results in the range 0.03 <= E/N <= 0.8.Comment: Plain TeX, 5 `eps' figures, submitted to Phys. Rev.