Energy decay for the elastic wave equation with a local time-dependent nonlinear damping

In this paper, we shall investigate the decay property of the solutions to the initial-boundary value problem for the elastic wave equation with a local time-dependent nonlinear damping. We give some decay rate of the energy when the damping term is effective only in a neighborhood of a suitable subset of the boundary. The results obtained in this paper extend, in particular, the known results for the scalar wave equation.     

Acid-catalyzed N-alkylation of tosylhydrazones using benzylic alcohols

N-Alkylation of tosylhydrazones in the presence of an acid catalyst is described for the first time. Tris(pentafluorophenyl) borane was found to be a mild and efficient catalyst when benzylic alcohols were used as the alkylating agents.     

Elaboration and characterisation of a plasticized cellulose triacetate membrane containing trioctylphosphine oxyde (TOPO): Application to the transport of uranium and molybdenum ions

A cellulose triacetate (CTA) membrane containing trioctylphosphine oxyde (TOPO) as carrier and 2-nitrophenyloctyl ether (NPOE) as a plasticizer was prepared. The membrane CTA + NPOE + TOPO was characterised using chemical techniques as well as Fourier Transform InfraRed (FTIR) spectroscopy, X-ray diffraction and Scanning Electron Microscopy (SEM). The CTA membrane is characterised by well-defined pores; these pores are completely filled with the NPOE and carrier. Surfaces of membranes with TOPO are smooth. The systems constituted by the mixture of CTA + NPOE, CTA + NPOE + TOPO do not give any diffraction. This can be due to the absence of crystallization within the membrane. On the other hand, this result should be attributable to the amorphous state of the structure, which permits us to eliminate the mechanism of transfer of the ions by electron jump. A comparative study of transport across a polymer inclusion membrane (PIM) and a supported liquid membrane (SLM) containing the same carrier in chloroform has shown that uranium or molybdenum transport efficiency was increased using PIM instead of SLM. PIM showed higher stability than SLM, the flux of transport remain constant in the former case after 2 weeks.     

Wideband chaos generation using a delayed oscillator and a two-dimensional nonlinearity induced by a quadrature phase-shift-keying electro-optic modulator

We present a new optoelectronic architecture intended for chaotic optical intensity generation. The principle relies on an electro-optic nonlinear delay dynamics, where the nonlinearity originates from an integrated four-wave optical interferometer, involving two independent electro-optic modulation inputs. Consequently, the setup involves both two-dimensional nonlinearity and dual-delay feedback dynamics, which results in enhanced chaos complexity of particular interest in chaos encryption schemes. The generated chaos observed with large feedback gains has a bandwidth ranging from 30 kHz to 13 GHz and is confirmed by numerical simulations of the proposed dynamical model and bifurcation diagram calculation.     

Plancherel–Rotach Asymptotic Expansion for Some Polynomials from Indeterminate Moment Problems

We study the Plancherel–Rotach asymptotics of four families of orthogonal polynomials: the Chen–Ismail polynomials, the Berg–Letessier–Valent polynomials, and the Conrad–Flajolet polynomials I and II. All these polynomials arise in indeterminate moment problems, and three of them are birth and death process polynomials with cubic or quartic rates. We employ a difference equation asymptotic technique due to Z. Wang and R. Wong. Our analysis leads to a conjecture about large degree behavior of polynomials orthogonal with respect to solutions of indeterminate moment problems.     

An Explicit Solution with Correctors for the Green–Naghdi Equations

In this paper, the water waves problem for uneven bottoms in a highly nonlinear regime is studied. It is well known that, for such regimes, a generalization of the Boussinesq equations called the Green–Naghdi equations can be derived and justified when the bottom is variable (Lannes and Bonneton in Phys Fluids 21, 2009). Moreover, the Green–Naghdi and Boussinesq equations are fully nonlinear and dispersive systems. We derive here new linear asymptotic models of the Green–Naghdi and Boussinesq equations so that they have the same accuracy as the standard equations. We solve explicitly the new linear models and numerically validate the results.     

A one-dimensional plume plasma expansion: Self-similar approach

The expansion of a plasma induced by laser ablation is investigated using a single-fluid model combined with Saha?s equation. The space coordinates x and time t are combined to a one self-similar variable ξ=x/(ct). To obtain ordinary differential equations, two different transformations for the density are used. The density profiles during the expansion are found to be completely different, one corresponds to the common results i.e., the density decreases monotonically with ξ, while with the second transformation, the profile shows a density increasing for certain interval of the self-similar variable. This effect is enhanced with higher initial ionization fraction. The role of the initial velocity which corresponds to the start of the expansion from an unperturbed plasma or from an expansion already going on is pointed out.     

DSC study of the kinetic parameters of the metastable phases formation during non-isothermal annealing of an Al–Si–Mg alloy

Kinetics of β″ and β′ precipitations in an AlSiMg have been studied under non-isothermal conditions using differential scanning calorimetry (DSC) technique. The variation of the activation energy as a function of transformed fraction is determined using two isoconversional methods of Kissinger–Akahira–Sunose (KAS) and Friedman. The results obtained using the two methods show a change in the activation energy for both metastable phases precipitations as a function of transformed fraction. The results obtained from KAS method as compared with those obtained from Friedman method, show some major disagreements between the two methods. The growth exponent, determined by Ozawa method, decreases as a function of temperature for both phases.     

Radii of Redox Components from Absolute Redox Potentials Compared with Covalent and Aqueous Ionic Radii

Aqueous standard potentials, referred to that of the SHE as zero, were recently shown to vary linearly with gaseous ionization potentials, with the absolute potential of SHE as the intercept. This enabled arriving at the absolute redox potentials of elements. Here, the distances between the oxidized and reduced forms in aqueous solutions have been evaluated. From the linear dependence of these distances on the covalent radii of atoms, the radii of the redox components have been obtained. The latter also vary linearly with the aqueous ionic radii estimated earlier from ion‐water distances, and indicate the presence of aqueous molecular anions.