The third order Melnikov function of a quadratic center under quadratic perturbation

We study quadratic perturbations of the integrable system (1+x)dH; where H =(x²+y²)=2: We prove that the first three Melnikov functions associated to the perturbed system give rise at most to three limit cycles

Effective in Vitro Photokilling by Cell-Adhesive Gold Nanorods

Upon excitation of their localized surface plasmon resonance (LSPR) band, gold nanorods (AuNRs) show a characteristic light-to-heat transduction, a useful and versatile property for a range of biomedical applications such as photothermal therapy, drug delivery, optoacoustic imaging and biosensing, among others. Nanoparticle (NP)-mediated photothermal therapy (PTT) rests on the ability of nanomaterials to convert light energy into heat and can currently be considered as a promising method for selectively destroying tumor cells by (photo)-thermoablation. One inherent limitation to NP-mediated PTT is that the nanoparticles must arrive at the site of action to exert their function and this typically involves cellular internalization. Here we report the use of the Keggin-type polyoxometalate (POM) phosphotungstic acid (PTA) as an inorganic gelling agent for the encapsulation of plasmonic gold nanorods (AuNRs) inside a biocompatible and cell-adhesive chitosan hydrogel matrix. These functional sub-micrometric containers are non-cytotoxic and present the ability to adhere to the cytoplasmic membranes of cells avoiding any need for cellular internalization, rendering them as highly efficient thermoablating agents of eukaryotic cells in vitro

Homogenization and enhancement for the G-equation

We consider the so-called G-equation, a level set Hamilton-Jacobi equation, used as a sharp interface model for flame propagation, perturbed by an oscillatory advection in a spatio-temporal periodic environment. Assuming that the advection has suitably small spatial divergence, we prove that, as the size of the oscillations diminishes, the solutions homogenize (average out) and converge to the solution of an effective anisotropic first-order (spatio-temporal homogeneous) level set equation. Moreover we obtain a rate of convergence and show that, under certain conditions, the averaging enhances the velocity of the underlying front. We also prove that, at scale one, the level sets of the solutions of the oscillatory problem converge, at long times, to the Wulff shape associated with the effective Hamiltonian. Finally we also consider advection depending on position at the integral scale

Asymptotics for turbulent flame speeds of the viscous G-equation enhanced by cellular and shear flows

G-equations are well-known front propagation models in turbulent combustion and describe the front motion law in the form of local normal velocity equal to a constant (laminar speed) plus the normal projection of fluid velocity. In level set formulation, G-equations are Hamilton-Jacobi equations with convex ($L^1$ type) but non-coercive Hamiltonians. Viscous G-equations arise from either numerical approximations or regularizations by small diffusion. The nonlinear eigenvalue $\bar H$ from the cell problem of the viscous G-equation can be viewed as an approximation of the inviscid turbulent flame speed $s_T$. An important problem in turbulent combustion theory is to study properties of $s_T$, in particular how $s_T$ depends on the flow amplitude $A$. In this paper, we will study the behavior of $\bar H=\bar H(A,d)$ as $A\to +\infty$ at any fixed diffusion constant $d > 0$. For the cellular flow, we show that $$\bar H(A,d)\leq O(\sqrt {\mathrm {log}A}) \quad \text{for all $d>0$}.$$ Compared with the inviscid G-equation ($d=0$), the diffusion dramatically slows down the front propagation. For the shear flow, the limit \nit $\lim_{A\to +\infty}{\bar H(A,d)\over A} = \lambda (d) >0$ where $\lambda (d)$ is strictly decreasing in $d$, and has zero derivative at $d=0$. The linear growth law is also valid for $s_T$ of the curvature dependent G-equation in shear flows.Comment: 27 pages. We improve the upper bound from no power growth to square root of log growt

Out-of-equilibrium states as statistical equilibria of an effective dynamics

We study the formation of coherent structures in a system with long-range interactions where particles moving on a circle interact through a repulsive cosine potential. Non equilibrium structures are shown to correspond to statistical equilibria of an effective dynamics, which is derived using averaging techniques. This simple behavior might be a prototype of others observed in more complicated systems with long-range interactions, like two-dimensional incompressible fluids or self-gravitating systems.Comment: 4 figure

Forced Stratified Turbulence: Successive Transitions with Reynolds Number

Numerical simulations are made for forced turbulence at a sequence of increasing values of Reynolds number, R, keeping fixed a strongly stable, volume-mean density stratification. At smaller values of R, the turbulent velocity is mainly horizontal, and the momentum balance is approximately cyclostrophic and hydrostatic. This is a regime dominated by so-called pancake vortices, with only a weak excitation of internal gravity waves and large values of the local Richardson number, Ri, everywhere. At higher values of R there are successive transitions to (a) overturning motions with local reversals in the density stratification and small or negative values of Ri; (b) growth of a horizontally uniform vertical shear flow component; and (c) growth of a large-scale vertical flow component. Throughout these transitions, pancake vortices continue to dominate the large-scale part of the turbulence, and the gravity wave component remains weak except at small scales.Comment: 8 pages, 5 figures (submitted to Phys. Rev. E

Aproximaciones y perspectivas de derecho ambiental

Texto de autoria de ministro do Superior Tribunal de Justiça

Academic freedom in Europe: time for a Magna Charta?

This paper is a preliminary attempt to establish a working definition of academic freedom for the European Union states. The paper details why such a definition is required for the European Union and then examines some of the difficulties of defining academic freedom. By drawing upon experience of the legal difficulties beset by the concept in the USA and building on previous analyses of constitutional and legislative protection for academic freedom, and of legal regulations concerning institutional governance and academic tenure, a working definition of academic freedom is then derived. The resultant definition which, it is suggested, could form the basis for a European Magna Charta Libertatis Academicae, goes beyond traditional discussions of academic freedom by specifying not only the rights inherent in the concept but also its accompanying duties, necessary limitations and safeguards. The paper concludes with proposals for how the definition might be tested and carried forward

New measurement of neutron capture resonances of 209Bi

The neutron capture cross section of Bi209 has been measured at the CERN n TOF facility by employing the pulse-height-weighting technique. Improvements over previous measurements are mainly because of an optimized detection system, which led to a practically negligible neutron sensitivity. Additional experimental sources of systematic error, such as the electronic threshold in the detectors, summing of gamma-rays, internal electron conversion, and the isomeric state in bismuth, have been taken into account. Gamma-ray absorption effects inside the sample have been corrected by employing a nonpolynomial weighting function. Because Bi209 is the last stable isotope in the reaction path of the stellar s-process, the Maxwellian averaged capture cross section is important for the recycling of the reaction flow by alpha-decays. In the relevant stellar range of thermal energies between kT=5 and 8 keV our new capture rate is about 16% higher than the presently accepted value used for nucleosynthesis calculations. At this low temperature an important part of the heavy Pb-Bi isotopes are supposed to be synthesized by the s-process in the He shells of low mass, thermally pulsing asymptotic giant branch stars. With the improved set of cross sections we obtain an s-process fraction of 19(3)% of the solar bismuth abundance, resulting in an r-process residual of 81(3)%. The present (n,gamma) cross-section measurement is also of relevance for the design of accelerator driven systems based on a liquid metal Pb/Bi spallation target.Comment: 10 pages, 5figures, recently published in Phys. Rev.

Measurement of the (90,91,92,93,94,96)Zr(n,gamma) and (139)La(n,gamma) cross sections at n_TOF

Open AccessNeutron capture cross sections of Zr and La isotopes have important implications in the field of nuclear astrophysics as well as in the nuclear technology. In particular the Zr isotopes play a key role for the determination of the neutron density in the He burning zone of the Red Giant star, while the (139)La is important to monitor the s-process abundances from Ba up to Ph. Zr is also largely used as structural materials of traditional and advanced nuclear reactors. The nuclear resonance parameters and the cross section of (90,91,92,93,94,96)Zr and (139)La have been measured at the n_TOF facility at CERN. Based on these data the capture resonance strength and the Maxwellian-averaged cross section were calculated