A DISCRETIZATION SCHEME FOR AN ONE-DIMENSIONAL REACTION-DIFFUSION EQUATION WITH DELAY AND ITS DYNAMICS

The goal of this paper is to present an approximation scheme for a reaction-diffusion equation with finite delay, which has been used as a model to study the evolution of a population with density distribution u, in such a way that the resulting finite dimensional ordinary differential system contains the same asymptotic dynamics as the reaction-diffusion equation.

Global attractor for a model of extensible beam with nonlinear damping and source terms

This paper is concerned with the existence of a global attractor for the nonlinear beam equation, with nonlinear damping and source terms, u(tt) + Delta(2)u -M (integral(Omega)vertical bar del u vertical bar(2)dx) Delta u + f(u) + g(u(t)) = h in Omega x R(+), where Omega is a bounded domain of R(N), M is a nonnegative real function and h is an element of L(2)(Omega). The nonlinearities f(u) and g(u(t)) are essentially vertical bar u vertical bar(rho) u - vertical bar u vertical bar(sigma) u and vertical bar u(t)vertical bar(r) u(t) respectively, with rho, sigma, r > 0 and sigma < rho. This kind of problem models vibrations of extensible beams and plates. (C) 2010 Elsevier Ltd. All rights reserved.

Monotone positive solutions for a fourth order equation with nonlinear boundary conditions

This work is concerned with the existence of monotone positive solutions for a class of beam equations with nonlinear boundary conditions. The results are obtained by using the monotone iteration method and they extend early works on beams with null boundary conditions. Numerical simulations are also presented. (C) 2009 Elsevier Ltd. All rights reserved.

Infrared analysis of ion beam irradiated polymers

Irradiation with heavy ions can produce several modifications in the chain structure of polymers. These modifications can be related to scissioning and cross-linking of chemical bonds. which depend on the ion fluence and the density of energy deposited in the material. Stacked thin film Makrofol-KG (R) samples were irradiated with 350 MeV Au(26+) ions and FTIR absorption spectroscopy was used to determine the bond changes in the samples. Data on the absorption bands as a function of the fluence indicated a higher probability for simple-bonds scissioning than for double-bonds scissioning and no dependence on the number of double bonds breaking with ion fluence. Since sample irradiation was done in a non-track-overlapping regime, a novel process for double bonds formation is suggested: the excitation of a site in the material by only one incident ion followed by a double bond formation during the de-excitation process. (C) 2009 Elsevier B.V. All rights reserved.

Near threshold vibrational excitation of molecules by positron impact: A projection operator approach

We report vibrational excitation (v(i) = 0 -> v(f) = 1) cross-sections for positron scattering by H(2) and model calculations for the (v(i) = 0 -> v(f) = 1) excitation of the C-C symmetric stretch mode of C(2)H(2). The Feshbach projection operator formalism was employed to vibrationally resolve the fixed-nuclei phase shifts obtained with the Schwinger multichannel method. The near threshold behavior of H(2) and C(2)H(2) significantly differ in the sense that no low lying singularity (either virtual or bound state) was found for the former, while a e(+)-acetylene virtual state was found at the equilibrium geometry (this virtual state becomes a bound state upon stretching the molecule). For C(2)H(2), we also performed model calculations comparing excitation cross-sections arising from virtual (-i kappa(0)) and bound (+i kappa(0)) states symmetrically located around the origin of the complex momentum plane (i.e. having the same kappa(0)). The virtual state is seen to significantly couple to vibrations, and similar cross-sections were obtained for shallow bound and virtual states. (c) 2007 Elsevier B.V. All rights reserved.

Cascades of Hopf bifurcations from boundary delay

We consider a 1-dimensional reaction-diffusion equation with nonlinear boundary conditions of logistic type with delay. We deal with non-negative solutions and analyze the stability behavior of its unique positive equilibrium solution, which is given by the constant function u equivalent to 1. We show that if the delay is small, this equilibrium solution is asymptotically stable, similar as in the case without delay. We also show that, as the delay goes to infinity, this equilibrium becomes unstable and undergoes a cascade of Hopf bifurcations. The structure of this cascade will depend on the parameters appearing in the equation. This equation shows some dynamical behavior that differs from the case where the nonlinearity with delay is in the interior of the domain. (C) 2009 Elsevier Inc. All rights reserved.

ON THE SUPERCRITICALITY OF THE FIRST HOPF BIFURCATION IN A DELAY BOUNDARY PROBLEM

The goal of this paper is to analyze the character of the first Hopf bifurcation (subcritical versus supercritical) that appears in a one-dimensional reaction-diffusion equation with nonlinear boundary conditions of logistic type with delay. We showed in the previous work [Arrieta et al., 2010] that if the delay is small, the unique non-negative equilibrium solution is asymptotically stable. We also showed that, as the delay increases and crosses certain critical value, this equilibrium becomes unstable and undergoes a Hopf bifurcation. This bifurcation is the first one of a cascade occurring as the delay goes to infinity. The structure of this cascade will depend on the parameters appearing in the equation. In this paper, we show that the first bifurcation that occurs is supercritical, that is, when the parameter is bigger than the delay bifurcation value, stable periodic orbits branch off from the constant equilibrium.

Direct Observation of Tetragonal Distortion in Epitaxial Structures through Secondary Peak Split in a Synchrotron Radiation Renninger Scan

This paper reports a direct observation of an interesting split of the (022)(022) four-beam secondary peak into two (022) and (022) three-beam peaks, in a synchrotron radiation Renninger scan (phi-scan), as an evidence of the layer tetragonal distortion in two InGaP/GaAs (001) epitaxial structures with different thicknesses. The thickness, composition, (a perpendicular to) perpendicular lattice parameter, and (01) in-plane lattice parameter of the two epitaxial ternary layers were obtained from rocking curves (omega-scan) as well as from the simulation of the (022)(022) split, and then, it allowed for the determination of the perpendicular and parallel (in-plane) strains. Furthermore, (022)(022) omega:phi mappings were measured in order to exhibit the multiple diffraction condition of this four-beam case with their split measurement.

Metal location and thickness in a multilayered sheet by measuring K alpha/K beta, L alpha/L beta and L alpha/L gamma X-ray ratios

When a multilayered material is analyzed by means of energy-dispersive X-ray fluorescence analysis, then the X-ray ratios of K alpha/K beta, or L alpha/L beta and L alpha/L gamma, for an element in the multilayered material, depend on the composition and thickness of the layer in which the element is situated, and on the composition and thickness of the superimposed layer (or layers). Multilayered samples are common in archaeometry, for example, in the case of pigment layers in paintings, or in the case of gilded or silvered alloys. The latter situation is examined in detail in the present paper, with a specific reference to pre-Columbian alloys from various museums in the north of Peru. (C) 2009 Elsevier B.V. All rights reserved.

PIXE analysis of chromium phytoaccumulation by the aquatic macrophytes Eicchornia crassipes

The uptake of hexavalent chromium in free living floating aquatic macrophytes Eicchornia crassipes cultivated in non-toxic chromium-doped hydroponic solutions is presented. A Cr-uptake bioaccumulation experiment was carried out using healthy macrophytes grown in a temperature controlled greenhouse. Six samples of nutrient media and plants were collected during the 23 day experiment. Roots and leaves were acid digested with the addition of an internal Gallium standard, for thin film sample preparation and quantitative Cr analysis by PIXE method. The Cr(6+) mass uptake by the macrophytes reached up to 70% of the initial concentration, comparable to former results and literature data. The Cr-uptake data were described using a non-structural first order kinetic model. Due to low cost and high removal efficiency, living aquatic macrophytes E. crassipes are a viable biosorbent in an artificial wetland of a water effluent treatment plant. (c) 2009 Elsevier B.V. All rights reserved.

Dosimetric properties of UV irradiated calcium co-doped borate glass-ceramic

The thermoluminescence (TL) response of Dy and Li doped 20CaB(4)O(7)-80CaB(2)O(4) (Wt%) glass-ceramic irradiated with ultraviolet (UV) radiation was studied. In order to act as TL activator ions, the Dy and Li ions were included in the matrix during the melting process to increase its TL efficiency. A single crystalline CaB2O4 phase was present in the glass-ceramic as determined by X-ray diffraction (XRD). The glass-ceramic 20CaB(4)O(7)-80CaB(2)O(4):Dy,Li wt% (named 20CBO7:Dy,Li) is a newly prepared TL material. Its thermoluminescent dosimetric characteristics have shown a linear response under UV radiation exposure and a good TL signal reproducibility, thus proving to be a promising material for using as an ultraviolet radiation dosimeter. (C) 2007 Elsevier B.V. All rights reserved.