Abstrac. A fast method presented within this paper to find transparent liquid viscosity. An introduced tracking algorithm in image processing used to find a terminal velocity automatically of a falling ball in a tube that filled with a tested liquid. Terminal velocity considered an important parameter to find a liquid viscosity. Therefore, four iron balls, with different diameters and a smartphone camera are used to measure the falling ball terminal velocity. The estimated velocity from the introduced algorithm is compared with the calculated velocity and shows a good matching. The second algorithm used to estimate the viscosity of the tested liquid. The limitation of the ball diameter around 5mm to measure the terminal velocity. The result shows error matching between the fitting data and the estimated data ranging (0.00-0.1%). This method is a faster and easier experiment to use to find any transparent liquid viscosity comparing with a viscometer.

Abstract. We analyze the method of optimal balance which was introduced by Viúdez and Dritschel (J. Fluid Mech. 521, 2004, pp. 343-352) to provide balanced initializations for two-dimensional and three-dimensional geophysical flows, here in the simpler context of a finite dimensional Hamiltonian two-scale system with strong gyroscopic forces. It is well known that when the potential is analytic, such systems have an approximate slow manifold that is defined up to terms that are exponentially small with respect to the scale separation parameter. The method of optimal balance relies on the observation that the approximate slow manifold remains an adiabatic invariant under slow deformations of the nonlinear interactions. The method is formulated as a boundary value problem for a homotopic deformation of the system from a linear regime, where the slow-fast splitting is known exactly, to the full nonlinear regime. We show that, providing the ramp function which defines the homotopy is of Gevrey class 2 and satisfies vanishing conditions to all orders at the temporal end points, the solution of the optimal balance boundary value problem yields a point on the approximate slow manifold that is exponentially close to the approximation to the slow manifold via exponential asymptotics, albeit with a smaller power of the small parameter in the exponent. In general, the order of accuracy of optimal balance is limited by the order of vanishing derivatives of the ramp function at the temporal end points. We also give a numerical demonstration of the efficacy of optimal balance, showing the dependence of accuracy on the ramp time and the ramp function.

We present an algorithm for the efficient numerical evaluation of integrals of the formfor sufficiently smooth but otherwise arbitrary F and ω 1. The method is entirely "black-box", i.e., does not require the explicit computation of moment integrals or other pre-computations involving F . Its performance is uniform in the frequency ω. We prove that the method converges exponentially with respect to its order when F is analytic and give a numerical demonstration of its error characteristics.

No abstract

The technique of spray pyrolysis used to prepare the pure thin films NiO and NiO:Cu. In this study, the nickel chloride salt solution (NiCl2⋅6H2O) was used to fabricate thin films deposited on a glass substrate. The structural, optical, and morphological fabricated properties of the samples were investigated. X‐ray diffraction reveals a polycrystalline nickel oxide layer with a crystalline cubic form, with (111), (200), and (222). Atomic force microscopic studied the surface morphology of the thin‐film samples. The fabrication process of growth was at the specific doping ratio (0%, 0.5%, 1%, 1.5%, and 2%) where all thin films had a cubic structure. The energy difference for the NiO and NiO:Cu reference samples have ranged from 3.25 to 3.5 eV. The mobility, magnetoresistance, resistivity, and conductivity were measured and presented as well as the relationship between current‐voltage and current‐resistivity.