Volume 64, Issue 12

This investigation is concerned with the flow and heat transfer analysis between two disks rotating about non-coaxial axes normal to the disks. The constitutive equation of an incompressible Sisko fluid is used. The fluid is electrically conducting and the Hall effect is taken into account. Analytic solutions of the governing nonlinear problem is obtained by homotopy analysis method (HAM). The graphs are presented and discussed. Finally a comparison is made between the results of viscous and Sisko fluids

The variational iteration method is applied to solve the Kawahara equation. This method produces the solutions in terms of convergent series and does not require linearization or small perturbation. Some examples are given. The comparison with the theoretical solution shows that the variational iteration method is an efficient method

The fractional Fokker-Planck equation (FFPE) has been used in many physical transport problems which take place under the influence of an external force field and other important applications in various areas of engineering and physics. In this paper, by means of the homotopy perturbation method (HPM), exact and approximate solutions are obtained for two classes of the FFPE initial value problems. The method gives an analytic solution in the form of a convergent series with easily computed components. The obtained results show that the HPM is easy to implement, accurate and reliable for solving FFPEs. The method introduces a promising tool for solving other types of differential equation with fractional order derivatives

In this paper, a new projective equation (Φ' = σΦ +Φ 2 ) is used to obtain the variable separation solutions with two arbitrary functions of the (2+1)-dimensional Broek-Kaup system with variable coefficients (VCBK). Based on the derived solutions and by selecting appropriate functions, some novel folded solitary wave evolutional behaviours are investigated

The vibrational part of the dihydrogen Hamiltonian obeys a quantized Sommerfeld-Kratzer potential, which takes into account internal H2 symmetries. All constants ω e , k e , and r e needed for the H 2 vibrational system derive from hydrogen mass. Ionic Kratzer bond theory gives covalent bond energy within 0.08% and all levels within 0.02%, which is 30 times better than with a Dunham oscillator and as accurate as early ab initio quantum mechanics

This investigation presents a mathematical model describing the homotopy analysis method (HAM) for systems of linear and nonlinear integro-differential equations. Some examples are analyzed to illustrate the ability of the method for such systems. The results reveal that this method is very effective and highly promising

This paper presents a new approach for solving accurate approximate analytical solutions for nonlinear phenomena governed by pendulum-like differential equations. The new approach couples Taylor series expansion with rational harmonic balancing. An approximate rational solution depending on a small parameter is considered. After substituting the approximate solution into the governing differential equation, this equation is expanded in Taylor series of the parameter prior to harmonic balancing. The approach gives a cubic equation, which must be solved in order to obtain the value of the small parameter. A method for transforming this cubic equation into a linear equation is presented and discussed. Using this approach, accurate approximate analytical expressions for period and periodic solutions are obtained. We also compared the Fourier series expansions of the analytical approximate solution and the exact one. This allowed us to compare the coefficients for the different harmonic terms in these solutions. These analytical approximations may be of interest for those researchers working in nonlinear physical phenomena governed by pendulum-like differential equations in fields such as classical mechanics, vibrations, acoustics, electromagnetism, electronics, superconductivity, optics, gravitation, and others

This work describes the series solution of two-dimensional flow and heat transfer of a second grade fluid in the presence of radiation. The governing partial differential equations are reduced into ordinary differential equations by appropriate similarity tranformation. The series solutions of the resulting ordinary differential equations are obtained by using the homotopy analysis method (HAM). The convergence of the solution is discussed explicitly. The influence of pertinent parameters on the velocity and temperature is graphically displayed and discussed. Numerical values of the skin friction coefficient and the Nusselt number are also tabulated

Introducing the average covalent factor N and considering the interaction of the cubic crystal field, the spin-orbit coupling and Tree’s correction effects, the crystal field parameter Dq was calculated. Also the varying tendency of Dq with the bond length R was investigated. Using the complete diagonalizing method the energy levels of the fine structure of Ga 2 Se 3 :Co 2+ single crystal were calculated and assigned. The calculated and assigned results are consistent with the experimental data

The optical free induction decay (OFID) induced by the transition between 1s and 1p state in a small isolated spherical CdSe/ZnS quantum dot quantum well (QDQW) has been studied numerically under the framework of effective-mass approximation. The size and relaxation time-dependent properties of the OFID have been obtained and analyzed. It shows that the OFID-change mechanisms dependent on shell thickness and core size are different. Moreover, the OFID signal decays sharply in amplitude and life as the transverse relaxation time being reduced while the change is slight to the longitudinal relaxation time. By comparing these two factors, we infer that the size mainly influences the amplitude of the decay signal and the delay time is basically determined by the relaxation time

Four structurally related Schiff’s base compounds are synthesized and their mesogenic properties are characterized by using Thermal Microscopy (TM) and Differential Scanning Calorimetry (DSC). The position of oxygen is varied from either sides of the bridging site, oxygen introduced on both sides and the oxygen is removed from the bridging site for the values of n = 8 and m = 5. The influence of oxygen atom to the extent of increase in thermal range, depression in melting temperature, elevation of clearing temperature is observed for all four compounds, viz. N (p-n-Octyloxy benzylidene) p-n-Pentyl aniline (8O.5), N (p-n-Octyl benzylidene) p-n-Pentyloxy aniline (8.O5), N (p-n-Octyloxy benzylidene) p-n-Pentyloxy aniline (8O.O5), and N (p-n-Octyl benzylidene) p-n- Pentyl aniline (8.5). The shift in the position of oxygen from the aldehyde to the aniline side and the removal of oxygen has a greater effect as they become room temperature liquids, whereas the oxygen on the aldehyde side and the oxygen on both sides of the rigid core moiety effect only the clearing temperatures. The results obtained are discussed in the light of the earlier data available on Schiff’s base nO.m compounds

The two-dimensional Ising model with nearest-neighbour pair interactions is simulated on the Creutz cellular automaton by using the finite-size lattices with the linear dimensions L = 80, 120, 160, and 200. The temperature variations and the finite-size scaling plots of the specific heat and the Binder parameter verify the theoretically predicted expression near the infinite lattice critical temperature. The approximate values for the critical temperature of the infinite lattice Tc = 2.287(6), Tc = 2.269(3), and Tc =2.271(1) are obtained from the intersection points of specific heat curves, Binder parameter curves, and the straight line fit of specific heat maxima, respectively. These results are in agreement with the theoretical value (Tc =2.269) within the error limits. The values obtained for the critical exponent of the specific heat, α = 0.04(25) and α = 0.03(1), are in agreement with α = 0 predicted by the theory. The values for the Binder parameter by using the finite-size lattices with the linear dimension L = 80, 120, 160, and 200 at Tc = 2.269(3) are calculated as gL(Tc) = −1.833(5), gL(Tc) = −1.834(3), gL(Tc) = −1.832(2), and gL(Tc) = −1.833(2), respectively. The value of the infinite lattice for the Binder parameter, gL(Tc) = −1.834(11), is obtained from the straight line fit of gL(Tc) = −1.833(5), gL(Tc) = −1.834(3), gL(Tc) = −1.832(2), and gL(Tc) = −1.833(2) versus L = 80, 120, 160, and 200, respectively

The first UV-absorption band of the polar molecules trans-4-dimethylamino-4'-nitrostilbene (DMANS), 5-dimethylamino-5'-nitro-2,2'-bithiophene (DMANBT), and 4-nitroanisole (NA), and of the slightly polar pesticide diclofop-methyl in the nonpolar supercritical solvent carbon dioxide (CO 2 ) and in the slightly polar supercritical solvent trifluoromethane (CHF 3 ) was measured in the pressure range from 1.5 to 30 MPa and the temperature range from 298 to 353 K with the purpose of studying the solvent-solute interactions in these molecules. The theory of Liptay for the effect of the solvent on the wave number of the electronic absorption of the solute molecule was applied. In this theory the solvent is represented by an isotropic and homogeneous dielectric continuum characterized by a pressure and temperature dependent dielectric constant ε (P,T), and an optical refraction index n. For the isotherms which approach the critical point in both solvents there is a change in the slope of the plot of the wave number maximum against the solvent parameter g=(ε−1)/(2ε+1) which is reminiscent of complex formation. A possible mechanism for this phenomenon is the arrangement of the solvent molecules around the dilute solute in the intermediate region at the (continuous) transition of the solvent from the dense vapour to the supercritical fluid

In this work, the unitarity of the Cabibbo-Kobayashi-Maskawa (CKM) mixing matrix has been investigated by studying the eleven well-known superallowed Fermi Beta decays; their parent nuclei are 10 C, 14 O, 26 Al, 34 Cl, 38 K, 42 Sc, 46 V, 50 Mn, 54 Co, 62 Ga, and 74 Rb. The numerical value of the Vud element of the CKM mixing matrix has been calculated following the standart procedure. Using a different method from those of the previous studies, the effect of the isospin breaking due to the Coulomb forces has been evaluated more accurately. Here, the shell model has been modified by Pyatov’s restoration because of the isospin breaking and the transition matrix elements have been found by means of the random phase approximation (RPA)

The results by S. Devasia seem to miss the invariance properties of special relativity and of relativistic electromagnetism. Incorrect conclusions are pointed out and the correct ones as well as the physical consequences are presented. These include the covariant formulation of the laws of physics, the correct formulation of the Doppler effect, and of the invariance of light propagation

Responses to the comments in A. Georges, Z. Naturforsch. 64a, 872 (2009) on the author’s paper are given

A recent technique, known as He’s frequency-amplitude formulation approach, is proposed in this letter to obtain an analytical approximate periodic solution to a nonlinear oscillator equation with potential of arbitrary fractional order. The solution procedure of the present approach is very simple and more convenient in comparison with the harmonic balance method

In this paper results are presented on the development of a device demonstrating the uptake and release of L-glutamate in solutions with neutral pH. A device which selectively regulates the concentration of biomolecules, such as the primary neural transmitter L-glutamate, could be useful for many biological and medical applications. In the literature it has been demonstrated that polypyrrole (PPy) is a promising material for the recognition basis of molecularly selective devices [1, 2]. In this study we investigated the feasibility of the PPy based “glutamate switch” for the voltage dependent uptake and release of L-glutamate for physiological applications