Track revelation and optical properties of pentaerythritol tetrakis (allyl carbonate) plastic for application as nuclear track detector: effects of gamma radiations

The etching conditions of an indigenously prepared thin film of pentaerythritol tetrakis(allyl carbonate) (PETAC) were standardised for the use as a nuclear track detector. The optimum etching times in 6?N NaOH at 70°C for the appearance of fission and alpha tracks recorded in this detector from a ²⁵²Cf solid source were found to be 30 min and 1.50?h, respectively. The experimentally determined values for the bulk and track-etch rates for this detector in 6?N NaOH at 70°C were found to be 1.7?±?0.1 and 88.4?±?10.7?µm/h, respectively. From these results, the important track etching properties such as the critical angle of etching, the sensitivity and the fission track registration efficiency were calculated and compared with the commercially available detectors. The activation energy value for bulk etching calculated by applying Arrhenius equation to the bulk etch rates of the detector determined at different etching temperatures was found to be 0.86?±?0.02?eV. This compares very well with the value of about 1.0?eV reported for most commonly used track detectors. The effects of gamma irradiation on this new detector in the dose range of 200–1000?kGy have also been studied using bulk etch rate technique. The activation energy values for bulk etching calculated from bulk etch rates measurements at different temperatures were found to decrease with the increase in gamma dose indicating scission of the detector due to gamma irradiation. The optical band gap of this detector was also determined using UV–visible spectrometry and the value was found to be 4.37?±?0.05?eV.     

Ag implantation-induced modification of Ni–Ti shape memory alloy thin films

Nanocrystalline thin films of Ni–Ti shape memory alloy are deposited on an Si substrate by the DC-magnetron co-sputtering technique and 120?keV Ag ions are implanted at different fluences. The thickness and composition of the pristine films are determined by Rutherford Backscattering Spectrometry (RBS). X-Ray diffraction (XRD), atomic force microscopy (AFM) and four-point probe resistivity methods have been used to study the structural, morphological and electrical transport properties. XRD analysis has revealed the existence of martensitic and austenite phases in the pristine film and also evidenced the structural changes in Ag-implanted Ni–Ti films at different fluences. AFM studies have revealed that surface roughness and grain size of Ni–Ti films have decreased with an increase in ion fluence. The modifications in the mechanical behaviour of implanted Ni–Ti films w.r.t pristine film is determined by using a Nano-indentation tester at room temperature. Higher hardness and the ratio of higher hardness (H) to elastic modulus (E_r) are observed for the film implanted at an optimized fluence of 9?×?10¹⁵ ions/cm². This improvement in mechanical behaviour could be understood in terms of grain refinement and dislocation induced by the Ag ion implantation in the Ni–Ti thin films.     

Asymptotic behavior of solutions for the 1-D isentropic Navier–Stokes–Korteweg equations with free boundary

In this paper, we consider the problem with a gas–gas free boundary for the one dimensional isentropic compressible Navier–Stokes–Korteweg system. For shock wave, asymptotic profile of the problem is shown to be a shifted viscous shock profile, which is suitably away from the boundary, and prove that if the initial data around the shifted viscous shock profile and its strength are sufficiently small, then the problem has a unique global strong solution, which tends to the shifted viscous shock profile as time goes to infinity. Also, we show the asymptotic stability toward rarefaction wave without the smallness on the strength if the initial data around the rarefaction wave are sufficiently small.     

Monotone iterative method of upper and lower solutions applied to a multilayer combustion model in porous media

This paper presents a new nonlinear reaction–diffusion–convection system coupled with a system of ordinary differential equations that models a combustion front in a multilayer porous medium. The model includes heat transfer between the layers and heat loss to the external environment. A few assumptions are made to simplify the model, such as incompressibility; then, the unknowns are determined to be the temperature and fuel concentration in each layer. When the fuel concentration in each layer is a known function, we prove the existence and uniqueness of a classical solution for the initial and boundary value problem for the corresponding system. The proof uses a new approach for combustion problems in porous media. We construct monotone iterations of upper and lower solutions and prove that these iterations converge to a unique solution for the problem, first locally and then, in time, globally.     

Lyapunov criteria for the Feller–Dynkin property of martingale problems

We give necessary and sufficient criteria for the Feller–Dynkin property of solutions to martingale problems in terms of Lyapunov functions. Moreover, we derive a Khasminskii-type integral test for the Feller–Dynkin property of multidimensional diffusions with random switching. For one dimensional switching diffusions with state-independent switching, we provide an integral-test for the Feller–Dynkin property.