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This paper aims to focus on an assessment of the electrochemical corrosion performance of bulk NC copper in a variety of corrosion environments.

The electrochemical corrosion behavior of bulk nanocrystalline (NC) copper prepared by inert gas condensation and in situ warm compress technique was studied by using potentiodynamic polarization and electrochemical impedance spectroscopy tests in de-aerated 0.1 M NaOH solution.

NC copper exhibited a typical active-passive-transpassive behavior with the formation of duplex passive films, which was qualitatively similar to coarse-grain (CG) copper. Although a compact passive film formed on NC copper surface, the corrosion resistance of NC copper was lower in comparison with CG copper. The increase in corrosion rate for NC copper was mainly attributed to the high activity of surface atoms and intergranular atoms. These atoms led to an enhancement of passive ability and an increase of dissolution rate of passive film in oxygen-deficiency solution. For NC copper, the corrosion resistance decreased as grain size increased in NC range.

The difference in corrosion resistance between bulk NC copper and its CG counterpart is dependent upon the corrosion solution. In a previous work, the potentiodynamic polarization tests revealed that NC copper bulks (grain size 48, 68, 92 nm) had identical corrosion resistance to CG copper bulk in naturally aerated 0.1 M NaOH solution. The results might be related to the dissolved oxygen in the medium.

The purpose of this paper is to develop two meshfree algorithms based on multiquadric radial basis functions (RBFs) and differential quadrature (DQ) technique for numerical simulation and to capture the shocks behavior of Burgers’ type problems.

The algorithms convert the problems into a system of ordinary differential equations which are solved by the Runge–Kutta method.

Two meshfree algorithms are developed and their stability is discussed. Numerical experiment is done to check the efficiency of the algorithms, and some shock behaviors of the problems are presented. The proposed algorithms are found to be accurate, simple and fast.

The present algorithms LRBF-DQM and GRBF-DQM are based on radial basis functions, which are new for Burgers’ type problems. It is concluded from the numerical experiments that LRBF-DQM is better than GRBF-DQM. The algorithms give better results than available literature.

This paper aims to find the numerical solution of planar and non-planar Burgers’ equation and analysis of the shock behave.

First, the authors discritize the time-dependent term using Crank–Nicholson finite difference approximation and use quasilinearization to linearize the nonlinear term then apply Scale-2 Haar wavelets for space integration. After applying this scheme on partial differential, the equation transforms into a system of algebraic equation. Then, the system of equation is solved using Gauss elimination method.

Present method is the extension of the method (Jiwari, 2012). The numerical solutions using Scale-2 Haar wavelets prove that the proposed method is reliable for planar and non-planar nonlinear Burgers’ equation and yields results better than other methods and compatible with the exact solutions.

The numerical results for non-planar Burgers’ equation are very sparse. In the present paper, the authors identify where the shock wave and discontinuity occur in planar and non-planar Burgers’' equation.