461,898 research outputs found

    Global and cocycle attractors for non-autonomous reaction-diffusion equations. The case of null upper Lyapunov exponent

    Get PDF
    In this paper we obtain a detailed description of the global and cocycle attractors for the skew-product semiflows induced by the mild solutions of a family of scalar linear-dissipative parabolic problems over a minimal and uniquely ergodic flow. We consider the case of null upper Lyapunov exponent for the linear part of the problem. Then, basically two different types of attractors can appear, depending on whether the linear coefficient in the equations determines a bounded or an unbounded associated real cocycle. In the first case (the one for periodic equations), the structure of the attractor is simple, whereas in the second case (which happens in aperiodic equations), the attractor is a pinched set with a complicated structure. We describe situations in which the attractor is chaotic in measure in the sense of Li-Yorke. Besides, we obtain a non-autonomous discontinuous pitchfork bifurcation scenario for concave equations, applicable for instance to a linear-dissipative version of the Chafee-Infante equation.Ministerio de EconomĂ­a y CompetitividadFondo Europeo de Desarrollo RegionalEuropean CommissionJunta de AndalucĂ­

    Convergence in Comparable Almost Periodic Reaction-Diffusion Systems with Dirichlet Boundary Condition

    Full text link
    The paper is to study the asymptotic dynamics in nonmonotone comparable almost periodic reaction-diffusion system with Dirichlet boundary condition, which is comparable with uniformly stable strongly order-preserving system. By appealing to the theory of skew-product semiflows, we obtain the asymptotic almost periodicity of uniformly stable solutions to the comparable reaction-diffusion system

    Probing nuclear rates with Planck and BICEP2

    Get PDF
    Big Bang Nucleosynthesis (BBN) relates key cosmological parameters to the primordial abundance of light elements. In this paper, we point out that the recent observations of Cosmic Microwave Background anisotropies by the Planck satellite and by the BICEP2 experiment constrain these parameters with such a high level of accuracy that the primordial deuterium abundance can be inferred with remarkable precision. For a given cosmological model, one can obtain independent information on nuclear processes in the energy range relevant for BBN, which determine the eventual ^2H/H yield. In particular, assuming the standard cosmological model, we show that a combined analysis of Planck data and of recent deuterium abundance measurements in metal-poor damped Lyman-alpha systems provides independent information on the cross section of the radiative capture reaction d(p,\gamma)^3He converting deuterium into helium. Interestingly, the result is higher than the values suggested by a fit of present experimental data in the BBN energy range (10 - 300 keV), whereas it is in better agreement with ab initio theoretical calculations, based on models for the nuclear electromagnetic current derived from realistic interactions. Due to the correlation between the rate of the above nuclear process and the effective number of neutrinos Neff, the same analysis points out a Neff>3 as well. We show how this observation changes when assuming a non-minimal cosmological scenario. We conclude that further data on the d(p,\gamma)^3He cross section in the few hundred keV range, that can be collected by experiments like LUNA, may either confirm the low value of this rate, or rather give some hint in favour of next-to-minimal cosmological scenarios.Comment: 10 pages, 9 figure
    • …
    corecore