On the mixed problem for quasilinear pseudoparabolic equation

In this paper the multidimensional mixed problem for the quasilinear pseudoparabolic equation u_t-L_xu-εL_xu_t=f(t,x,u) is considered. L_x is a differential operator, which composes (with boundary operator) a self adjoint operator. An existence, uniqueness and also continuous dependense on the small parameter ε>0 of generalized solution is proved. The estimation of the difference of exact and approximate solutions is obtained     

Numerical study of the asymptotics of the second Painlevé equation by a functional fitting method

The Painlevé equations arise as reductions of the soliton equations such as the Korteweg–de Vries equation, the nonlinear Schrödinger equation and so on. In this study, we are concerned with numerical approximation of the asymptotics of solutions of the second Painlevé equation on pole‐free intervals along the real axis. Classical integrators such as high order Runge–Kutta schemes might be expensive to simulate oscillation, decay and blow‐up behaviours depending on initial conditions. However, a lower order functional fitting method catches all kinds of solutions even for relatively large step sizes. Copyright © 2013 John Wiley & Sons, Ltd.     

Injection-seeded, gain-switched tunable Cr:ZnSe laser

We report a narrow-linewidth, tunable, gain-switched Cr:ZnSe laser operating between 2255 and 2455 nm. The spectral width of the laser was reduced from 125 nm to 0.3 nm by using injection seeding. Seeding was achieved with a second tunable CW Cr:ZnSe laser. The output wavelength was varied by tuning the wavelength of the seed laser. The seeded oscillator produced as high as 157 μJ pulses with 598 μJ incident pump pulse energy at a repetition rate of 1 kHz. The slope efficiency was determined to be 26%.     

Flow around a cylinder surrounded by a permeable cylinder in shallow water

The change in flow characteristics downstream of a circular cylinder (inner cylinder) surrounded by an outer permeable cylinder was investigated in shallow water using particle image velocimetry technique. The diameter of the inner cylinder and the water height were kept constant during the experiments as d?=?50?mm and h _w ?=?25?mm, respectively. The depth-averaged free-stream velocity was also kept constant as U?=?170?mm/s which corresponded to a Reynolds number of Re_d?=?8,500 based on the inner cylinder diameter. In order to examine the effect of diameter and porosity of the outer cylinder on flow characteristics of the inner cylinder, five different outer cylinder diameters (D?=?60, 70, 80, 90 and 100?mm) and four different porosities (???=?0.4, 0.5, 0.6 and 0.7) were used. It was shown that both porosity and outer cylinder diameter had a substantial effect on the flow characteristics downstream of the circular cylinder. Turbulent statistics clearly demonstrated that in comparison with the bare cylinder (natural case), turbulent kinetic energy and Reynolds stresses decreased remarkably when an outer cylinder was placed around the inner cylinder. Thereby, the interaction of shear layers of the inner cylinder has been successfully prevented by the presence of outer cylinder. It was suggested by referring to the results that the outer cylinder having 1.6????D/d????2.0 and 0.4????D/d????0.6 should be preferred to have a better flow control in the near wake since the peak magnitude of turbulent kinetic energy was considerably low in comparison with the natural case and it was nearly constant for these mentioned porosities ??, and outer cylinder to inner cylinder diameter ratios D/d.     

Theoretical modelling of surface phonons

We present a mini review of progress made towards theoretical modelling of surface phonons. We outline the essential ingredients of two theoretical methods, viz. an adiabatic bond charge method for semiconductor surfaces and the ab-initio density-functional perturbation method for solid surfaces in general. From the results of theoretical calculations we establish trends and criteria for the existence of localized phonon modes on group-IV(001) and III-V(110) semiconductor surfaces. We further obtain signatures of characteristic vibrational modes which develop during dissociative molecular adsorption on Si(001) surfaces. The results are compared with available experimental measurements. Some remarks are forwarded regarding manipulation of surface phonon modes for scientific advances and technological applications.      

Effects of Permeable Cylinder on the Flow Structure in Deep Water

Flow behaviors around permeable cylinders were investigated using Particle Image Velocimetry technique in deep water. The height of deep water and free stream velocity were kept constant as h_w = 340 mm and U = 156 mm/s. To find out the effect of the permeable cylinders on the flow structure, eight different porosities (β = 0.4, 0.5, 0.6, 0.65, 0.7, 0.75, 0.8, and 0.85) were used. The results have indicated that the permeable cylinders are effective on the control of large-scale vortical structures downstream of the permeable cylinder. As the porosity increases, turbulent kinetic energy and Reynolds shear stress decrease. This means that the fluctuations in the wake region are significantly weakened by permeable cylinders. The permeable cylinders having the porosity higher than 0.6 do not pose an obstacle in the flow. Furthermore, for all diameter values of permeable cylinders, it can be concluded that the flow structures downstream of the permeable cylinder show similar trend with each other.     

Nonlinear optical properties of asymmetric n-type double <Emphasis Type="Italic">δ</Emphasis>-doped GaAs quantum well under intense laser field

The effect of non-resonant intense laser field on the intersubband-related optical absorption coefficient and refractive index change in the asymmetric n-type double δ-doped GaAs quantum well is theoretically investigated. The confined energy levels and corresponding wave functions of this structure are calculated by solving the Schrödinger equation in the laser-dressed confinement potential within the framework of effective mass approximation. The optical responses are reported as a function of the δ-doped impurities density and the applied non-resonant intense laser field. Additionally, the calculated results also reveal that the non-resonant intense laser field can be used as a way to control the electronic and optical properties of the low dimensional semiconductor nano-structures.     

Relativistic Hydrogen-Like Atom on a Noncommutative Phase Space

The energy levels of hydrogen-like atom on a noncommutative phase space were studied in the framework of relativistic quantum mechanics. The leading order corrections to energy levels 2S _1/2, 2P _1/2 and 2P _3/2 were obtained by using the ?? and the \(\bar \theta \) modified Dirac Hamiltonian of hydrogen-like atom on a noncommutative phase space. The degeneracy of the energy levels 2P _1/2 and 2P _3/2 were removed completely by ??-correction. And the \(\bar \theta \)-correction shifts these energy levels.     

Isolation and identification of a new neo-clerodane diterpenoid from Teucrium chamaedrys L.

Teucrium chamaedrys L. is an aromatic and medicinal plant used as traditional medicine. Aerial parts of the plant material were dried and extracted with hexane–dichloromethane (extract 1), ethyl acetate–dichloromethane (extract 2) and methanol–dichloromethane (extract 3) in a ratio of 1:1 at rt successively. The solvents were evaporated to give crude extracts. Extract 1 was suspended in water at 60°C then partitioned successively with hexane and ethyl acetate to give hexane and ethyl acetate portions. After the column chromatography (silica gel) of ethyl acetate extract, one new and four known compounds were isolated. The new compound was named as 1(12S,18R)-15,16-epoxy-2β,6β-dihydroxy-neo-cleroda-13(16),14-dien-20,l2-olide-l8,l9-hemiacetal (teuchamaedryn D) (4). The known compounds were teucrin A (1), dihydroteugin (2), teucroxide (3), syspirensin A (5). The chromatographic methods were also applied for extract 3 to isolate verbascoside (6) and teucrioside (7). The structure of isolated compounds was elucidated by spectroscopic methods including LC-TOF/MS, 1D NMR and 2D NMR.