Nonclassical Symmetries for Nonlinear Partial Differential Equations via Compatibility

The determining equations for the nonclassical symmetry reductions of nonlinear partial differential equations with arbitrary order can be obtained by requiring the compatibility between the original equations and the invariant surface conditions. The (2+1)-dimensional shallow water wave equation,
Boussinesq equation, and the dispersive wave equations in shallow water serve as examples illustrating how compatibility leads quickly and easily to the determining equations for their nonclassical symmetries.     

On the accuracy of bore reconstruction from input impedance measurements: application to bassoon crook measurements

The determination of a pipe bore from the measured reflection function is a technique that has reached a certain maturity. However, the measurement of the reflection function in the time domain (pulse reflectometry) requires equipment that is rather difficult to operate. On the other hand, the techniques for measuring the input impedance have reached an unquestionable maturity with respect to measurement setup and to calibration. It is thus likely that impedance measurements might be able to give the same information. By doing simulations, it is first shown that the reflection function deduced from the input impedance gives access to the bore with a precision comparable with that obtained with pulse reflectometry. It is then shown that the accuracy obtained with measurements is of the same order as that obtained from simulations. The technique is then used for the dimensional inspection of bassoon crooks.     

Preparation and properties of semiconductor CuO nanoparticles via a simple precipitation method at different reaction temperatures

Preparation and properties of CuO nanoparticles as an important p-type semiconductor via a simple precipitation method at different reaction temperatures varying from 10 to 115°C using copper acetate as a starting material have been reported. In addition, we investigated the influence of the ultrasonic irradiation through synthesizing the nanosized CuO at 60°C. Samples were characterized by XRD, FT-IR, SEM, TEM and UV-Vis techniques. XRD patterns of samples were identical to the single-phase pure CuO with a monoclinic structure. FT-IR spectra exhibited sharp peaks at around 519 and 598?cm^?1 which can be assigned to vibrations of the Cu-O bond. Results indicated that properties of samples had great dependence on the temperature and ultrasonic irradiation. The crystallite size and crystallization increased with increasing the temperature from 10 to 115°C. The band gap of samples was estimated to be in the range of 1.9–2.9?eV that is larger than the reported value for the bulk CuO (1.85?eV). This study provides a simple method for the preparation of nanosized CuO with a better surface uniformity and a narrow size distribution. Synthesized CuO samples with adjustable and controllable optical properties make the applicability of copper oxide even more versatile.     

Physiological Flow of Jeffrey Six Constant Fluid Model due to Ciliary Motion

The main purpose of this article is to present a mathematical model of ciliary motion in an annulus. In this analysis, the peristaltic motion of non-Newtonian Jeffrey six constant fluid is observed in an annulus with ciliated tips in the presence of heat and mass transfer. The effects of viscous dissipation are also considered. The flow equations of non-Newtonian fluid for the two-dimensional tube in cylindrical coordinates are simplified using the low Reynolds number and long wave-length approximations. The main equations for Jeffrey six constant fluid are considered in cylindrical coordinates system. The resulting nonlinear problem is solved using the regular perturbation technique in terms of a variant of small dimensionless parameter α. The results of the solutions for velocity, temperature and concentration field are presented graphically. B_k is Brinkman number, ST is soret number, and SH is the Schmidth number. Outcome for the longitudinal velocity, pressure rise, pressure gradient and stream lines are represented through graphs. In the history, the viscous-dissipation effect is usually represented by the Brinkman number.     

用纳米压痕法分析溶剂对聚醚醚酮(PEEK)力学性能的影响

Poly (ether ether ketone)(PEEK) is a high-performance semi-crystalline thermoplastic polymer.Exposure of the polymeric surface to solvents can have a strong effect like softening/swelling of polymeric network or dissolution.In this study,nano-indentation analysis was performed to study the effect of acetone on the surface mechanical properties of PEEK using different exposure time.The experiments were performed with a constant loading rate (10 nm/s) to a maximum indentation displacement (1000 nm).A 30-second hold segment was included at the maximum load to account for any creep effects followed by an unloading segment to 80% unloading.The indentation hardness and the elastic modulus were computed as a continuous function of the penetration displacement in the continuous stiffness mode (CSM) indentation.The experimental data showed that the peak load decreased from ~5.2 mN to ~1.7 mN as exposure time in solvent environment increased from 0 to 18 days.The elastic modulus and the hardness of PEEK samples also displayed a decreasing trend as a function of exposure time in the solvent environment.Two empirical models were used to fit the experimental data of hardness as a function of exposure time which showed a good agreement with the experimental values.     

Geological influence on the activity concentration of terrestrial radionuclides 226Ra, 232Th and 40K in the Jos Plateau,Nigeria

The Jos Plateau has been reported to have elevated levels of natural background radiation. A few earlier studies have measured the levels of natural radioactivity for specific locations in the area. Our interest is to investigate how geology of the study area influences the activity concentrations of natural radionuclides. Thus, the activity concentrations of terrestrial radionuclides in soil samples collected across the geological formations of the Jos Plateau were determined by gamma spectrometry technique. The mean activity concentrations of ²²⁶Ra, ²³²Th and ⁴⁰K were found to exceed their corresponding world reference values of 35, 40 and 400?Bq?kg^?1, respectively. Data were compared using statistical methods, analysis of variance (ANOVA) and post hoc tests. The results revealed in some instances significant influences of geological types on the activity concentrations in the area. The spatial distribution maps of activity concentrations of ²²⁶Ra, ²³²Th and ⁴⁰K were geostatistically interpolated by ordinary Kriging method using ArcGIS software.     

One-dimensional backreacting holographic <Emphasis Type="Italic">p</Emphasis>-wave superconductors

We analytically and numerically study the properties of one-dimensional holographic p-wave superconductors in the presence of backreaction. We employ the Sturm–Liouville eigenvalue problem for the analytical calculation and the shooting method for the numerical investigations. We apply the \(\hbox {AdS}_{{3}}\)/\(\hbox {CFT}_{{2}}\) correspondence and determine the relation between the critical temperature \(T_{c}\) and the chemical potential \(\mu \) for different values of the mass m of a charged spin-1 field \(\rho _{\mu }\) and backreacting parameters. We observe that the data of both analytical and numerical studies are in good agreement. We find that increasing the backreaction and the mass parameter causes the greater values for \({T_{c}}/{\mu }\). Thus, it makes the condensation harder to form. In addition, the analytical and numerical approaches show that the value of the critical exponent \( \beta \) is 1 / 2, which is the same as in the mean field theory. Moreover, both methods confirm the existence of a second order phase transition.     

Numerical simulation of unsteady 3D magneto-Sisko fluid flow with nonlinear thermal radiation and homogeneous–heterogeneous chemical reactions

In this paper, we study the qualitative behaviour of satellite systems using bifurcation diagrams, Poincaré section, Lyapunov exponents, dissipation, equilibrium points, Kaplan–Yorke dimension etc. Bifurcation diagrams with respect to the known parameters of satellite systems are analysed. Poincaré sections with different sowing axes of the satellite are drawn. Eigenvalues of Jacobian matrices for the satellite system at different equilibrium points are calculated to justify the unstable regions. Lyapunov exponents are estimated. From these studies, chaos in satellite system has been established. Solution of equations of motion of the satellite system are drawn in the form of three-dimensional, two-dimensional and time series phase portraits. Phase portraits and time series display the chaotic nature of the considered system.     

Electron Acceleration by Beating of Two Intense Cross-Focused Hollow Gaussian Laser Beams in Plasma

This paper presents propagation of two cross-focused intense hollow Gaussian laser beams(HGBs) in collisionless plasma and its effect on the generation of electron plasma wave(EPW) and electron acceleration process,when relativistic and ponderomotive nonlinearities are simultaneously operative. Nonlinear differential equations have been set up for beamwidth of laser beams, power of generated EPW, and energy gain by electrons using WKB and paraxial approximations. Numerical simulations have been carried out to investigate the effect of typical laser-plasma parameters on the focusing of laser beams in plasmas and further its effect on power of excited EPW and acceleration of electrons. It is observed that focusing of two laser beams in plasma increases for higher order of hollow Gaussian beams,which significantly enhanced the power of generated EPW and energy gain. The amplitude of EPW and energy gain by electrons is found to enhance with an increase in the intensity of laser beams and plasma density. This study will be useful to plasma beat wave accelerator and in other applications requiring multiple laser beams.