The Ljapunov-Schmidt reduction for some critical problems

This is a survey about the application of the Ljapunov-Schmidt reduction for some critical problems

Bubble concentration on spheres for supercritical elliptic problems

We consider the supercritical Lane-Emden problem (P_\eps)\qquad -\Delta v= |v|^{p_\eps-1} v \ \hbox{in}\ \mathcal{A} ,\quad u=0\ \hbox{on}\ \partial\mathcal{A} where $\mathcal A$ is an annulus in \rr^{2m}, $m\ge2$ and p_\eps={(m+1)+2\over(m+1)-2}-\eps, \eps>0. We prove the existence of positive and sign changing solutions of (P_\eps) concentrating and blowing-up, as \eps\to0, on $(m-1)-$dimensional spheres. Using a reduction method (see Ruf-Srikanth (2010) J. Eur. Math. Soc. and Pacella-Srikanth (2012) arXiv:1210.0782)we transform problem (P_\eps) into a nonhomogeneous problem in an annulus \mathcal D\subset \rr^{m+1} which can be solved by a Ljapunov-Schmidt finite dimensional reduction

Gradient flows and instantons at a Lifshitz point

I provide a broad framework to embed gradient flow equations in non-relativistic field theory models that exhibit anisotropic scaling. The prime example is the heat equation arising from a Lifshitz scalar field theory; other examples include the Allen-Cahn equation that models the evolution of phase boundaries. Then, I review recent results reported in arXiv:1002.0062 describing instantons of Horava-Lifshitz gravity as eternal solutions of certain geometric flow equations on 3-manifolds. These instanton solutions are in general chiral when the anisotropic scaling exponent is z=3. Some general connections with the Onsager-Machlup theory of non-equilibrium processes are also briefly discussed in this context. Thus, theories of Lifshitz type in d+1 dimensions can be used as off-shell toy models for dynamical vacuum selection of relativistic field theories in d dimensions.Comment: 19 pages, 1 figure, contribution to conference proceedings (NEB14); minor typos corrected in v

Neurocognitive impact of metal exposure and social stressors among schoolchildren in Taranto, Italy

BACKGROUND: Metal exposure is a public health hazard due to neurocognitive effects starting in early life. Poor socio-economic status, adverse home and family environment can enhance the neurodevelopmental toxicity due to chemical exposure. Disadvantaged socio-economic conditions are generally higher in environmentally impacted areas although the combined effect of these two factors has not been sufficiently studied. METHODS: The effect of co-exposure to neurotoxic metals including arsenic, cadmium, manganese, mercury, lead, selenium, and to socio-economic stressors was assessed in a group of 299 children aged 6-12\u2009years, residing at incremental distance from industrial emissions in Taranto, Italy. Exposure was assessed with biological monitoring and the distance between the home address and the exposure point source. Children's cognitive functions were examined using the Wechsler Intelligence Scale for Children (WISC) and the Cambridge Neuropsychological Test Automated Battery (CANTAB). Linear mixed models were chosen to assess the association between metal exposure, socio-economic status and neurocognitive outcomes. RESULTS: Urinary arsenic, cadmium and hair manganese resulted inversely related to the distance from the industrial emission source (\u3b2 -\u20090.04; 95% CI -0.06, -\u20090.01; \u3b2 -\u20090.02; 95% CI -0.05, -\u20090.001; \u3b2 -\u20090.02 95% CI -0.05, -\u20090.003) while the WISC intellectual quotient and its sub-scores (except processing speed index) showed a positive association with distance. Blood lead and urinary cadmium were negatively associated with the IQ total score and all sub-scores, although not reaching the significance level. Hair manganese and blood lead was positively associated with the CANTAB between errors of spatial working memory (\u3b2 2.2; 95% CI 0.3, 3.9) and the reaction time of stop signal task (\u3b2 0.05; 95% CI 0.02, 0.1) respectively. All the other CANTAB neurocognitive tests did not show to be significantly influenced by metal exposure. The highest socio-economic status showed about five points intellectual quotient more than the lowest level on average (\u3b2 4.8; 95% CI 0.3, 9.6); the interaction term between blood lead and the socio-economic status showed a significant negative impact of lead on working memory at the lowest socio-economic status level (\u3b2 -\u20094.0; 95% CI -6.9, -\u20091.1). CONCLUSIONS: Metal exposure and the distance from industrial emission was associated with negative cognitive impacts in these children. Lead exposure had neurocognitive effect even at very low levels of blood lead concentration when socio-economic status is low, and this should further address the importance and prioritize preventive and regulatory interventions

Excited States of Proton-bound DNA/RNA Base Homo-dimers: Pyrimidines

We are presenting the electronic photo fragment spectra of the protonated pyrimidine DNA bases homo-dimers. Only the thymine dimer exhibits a well structured vibrational progression, while protonated monomer shows broad vibrational bands. This shows that proton bonding can block some non radiative processes present in the monomer.Comment: We acknowledge the use of the computing facility cluster GMPCS of the LUMAT federation (FR LUMAT 2764

GZK Photons Above 10 EeV

We calculate the flux of "GZK-photons", namely the flux of photons produced by extragalactic nucleons through the resonant photoproduction of pions, the so called GZK effect. This flux depends on the UHECR spectrum on Earth, of the spectrum of nucleons emitted at the sources, which we characterize by its slope and maximum energy, on the distribution of sources and on the intervening cosmological backgrounds, in particular the magnetic field and radio backgrounds. For the first time we calculate the GZK photons produced by nuclei. We calculate the possible range of the GZK photon fraction of the total UHECR flux for the AGASA and the HiRes spectra. We find that for nucleons produced at the sources it could be as large as a few % and as low as 10^{-4} above 10 EeV. For nuclei produced at the sources the maximum photon fraction is a factor of 2 to 3 times smaller above 10 EeV but the minimum could be much smaller than for nucleons. We also comment on cosmogenic neutrino fluxes.Comment: 20 pages, 9 figures (21 panels), iopart.cls and iopart12.clo needed to typese

The Possibility of Thermal Instability in Early-Type Stars Due to Alfven Waves

It was shown by dos Santos et al. the importance of Alfv\'en waves to explain the winds of Wolf-Rayet stars. We investigate here the possible importance of Alfv\'en waves in the creation of inhomogeneities in the winds of early-type stars. The observed infrared emission (at the base of the wind) of early-type stars is often larger than expected. The clumping explains this characteristic in the wind, increasing the mean density and hence the emission measure, making possible to understand the observed infrared, as well as the observed enhancement in the blue wing of the $H_\alpha$ line. In this study, we investigate the formation of these clumps a via thermal instability. The heat-loss function used, $H(T,n)$, includes physical processes such as: emission of (continuous and line) recombination radiation; resonance line emission excited by electron collisions; thermal bremsstrahlung; Compton heating and cooling; and damping of Alfv\'en waves. As a result of this heat-loss function we show the existence of two stable equilibrium regions. The stable equilibrium region at high temperature is the diffuse medium and at low temperature the clumps. Using this reasonable heat-loss function, we show that the two stable equilibrium regions can coexist over a narrow range of pressures describing the diffuse medium and the clumps.Comment: 21 pages (psfig.sty), 5 figures (included), ApJ accepted. Also available at http://www.iagusp.usp.br/preprints/preprint.htm

Formulation of the Dutch Atmospheric Large-Eddy Simulation (DALES) and Overview of Its Applications

The current version of the Dutch Atmospheric Large-Eddy Simulation (DALES) is presented. DALES is a large-eddy simulation code designed for studies of the physics of the atmospheric boundary layer, including convective and stable boundary layers as well as cloudy boundary layers. In addition, DALES can be used for studies of more specific cases, such as flow over sloping or heterogeneous terrain, and dispersion of inert and chemically active species. This paper contains an extensive description of the physical and numerical formulation of the code, and gives an overview of its applications and accomplishments in recent years