Nonlinear absorption properties correlated with the surface and structural changes of ultra short pulse laser irradiated CR-39

We have investigated femtosecond laser irradiation effects on the surface topography, structural changes and nonlinear absorption properties of CR-39. For this purpose, a CR-39 target was exposed in air to 25 fs, 800 nm Ti: sapphire laser radiation at fluences ranging from 0.25 J cm⁻² to 3.6 J cm⁻². The surface of irradiated CR-39 probed by an Atomic Force Microscope (AFM) exhibits the formation of several topographical structures, like bumps, explosions and nano cavities. Raman spectroscopy is performed to explore chemical and structural modification of the irradiated target. The spectroscopy reveals changes such as cross linking, bond breaking, formation of new bonds etc. in the fundamental structure of the polymer after irradiation. In order to establish a correlation between morphological and structural changes with the changes in the nonlinear absorption of the irradiated CR-39, a Z-scan technique was employed. A comparison of experimentally obtained data from Z-scan measurements with our calculations predicts the dominance of three-photon absorption in the case of pristine CR-39, whereas for irradiated targets concurrence of three- and two-photon absorption is probable. Nonlinear absorption increases with increasing laser fluences and is well correlated by surface and structural changes revealed by AFM and Raman spectroscopy.     

Dynamical behavior of a stochastic predator-prey model with stage structure for prey

Abstract

In the present paper, we focus on a stochastic predator-prey model with stage structure for prey. Firstly, by using the stochastic Lyapunov function method, we obtain sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model. Then we establish sufficient conditions for extinction of the predator population in two cases. Some examples and numerical simulations are carried out to validate our analytical findings.     

Fractional order nonlinear mixed coupled systems with coupled integro-differential boundary conditions

We study the existence and uniqueness of solutions for a class of coupled fractional differential equations involving both Riemann-Liouville and Caputo fractional derivatives, and coupled integro-differential boundary conditions. We derive the desired results with the aid of modern methods of functional analysis. An example illustrating the abstract results is also presented.     

Dynamical behavior of a stochastic food chain chemostat model with Monod response functions

This paper studies a food chain chemostat model with Monod response functions, which is perturbed by white noise. Firstly, we prove the existence and uniqueness of the global positive solution. Then sufficient conditions for the existence of a unique ergodic stationary distribution are established by constructing suitable Lyapunov functions. Moreover, we consider the extinction of microbes in two cases. In the first case, both the predator and prey species are extinct. In the second case, only the predator species is extinct, and the prey species survives. Finally, numerical simulations are carried out to illustrate the theoretical results.     

Existence and approximation of solutions of forced duffing type integro-differential equations with three-point nonlinear boundary conditions

A generalized quasilinearization technique is developed to obtain an analytic approximation of the solutions of the forced Duffing type integro-differential equation with nonlinear three-point boundary conditions. Monotone sequences of approximate solutions converging uniformly and quadratically to a unique solution of the problem are presented.     

A facile synthesis of novel unsymmetrical N-(4-oxo-2-phenyl-3(4H)-quinazolinoyl)-N-(aryl)acetamidines

<正>A series of novel unsymmetrical N-(4-oxo-2-phenyl-3(4H)-quinazolinoyl)-N-(aryl) acetamidines was synthesized by reacting ethyl(1H)-N-(4-oxo-2-phenylquinazolin-3(4H)-y1)ethanimidoate(2) and suitable reactive aromatic amines.Structures' determination of the synthesized compounds was carried out using spectroscopic techniques including IR,~1H NMR,and mass spectrometry. Structural effects on reactivity were also studied.     

Reliable fabrication method of transferable micron scale metal pattern for poly(dimethylsiloxane) metallization

We have developed a reliable fabrication method of forming micron scale metal patterns on poly(dimethylsiloxane) (PDMS) using a pattern transfer process. A metal stack layer consisting of Au-Ti-Au layers, providing a weak but reliable adhesion, was deposited on a silicon wafer. The metal stack layer was then transferred to a PDMS substrate using serial and selective etching. We demonstrate that features as small as 2 microm were reliably transferred on to the PDMS substrate for use as interconnects and electrodes for biosensors and flexible electronics application.     

Existence and approximation of solutions for a class of nonlinear impulsive functional differential equations with anti-periodic boundary conditions

This paper describes the method of quasilinearization for first-order nonlinear impulsive functional differential equations with anti-periodic boundary conditions. A monotone iterative technique coupled with lower and upper solutions is employed to obtain sequences of approximate solutions converging monotonically and quadratically to the unique solution of the problem at hand.