59. Al-Hashr/The Encounter
I/We begin by the Blessed Name of Allah
The Immensely Merciful to all, The Infinitely Compassionate to everyone.
59:01
a. Whatever is within the celestial realm and within the terrestrial world is Glorifying Allah
– The One and Only God.
b. And HE is The Almighty, The All-Wise.
59:02
a. It is HE WHO drove out those, who disbelieved, among the Followers of the former
Scriptures from their homes in the very first encounter of the two rival groups.
b. You would have never thought that they may ever leave so easily,
c. just as they thought that their strongholds would protect them from Allah.
d. But then Allah’s seizure came upon them from where they could not even perceive,
e. and HE cast such a terror into their hearts that they destroyed their houses with their own
hands, and with help of hands of the believers.
f. So learn a lesson from this, O People of Insight!
59:03
a. And had Allah not decreed exile for them, HE would have definitely punished them in this
world.
b. As for the Hereafter, they will definitely have the punishment of the Fire.
59:04
a. This is because they had opposed and challenged Allah and HIS Messenger.
b. And whoever challenges and opposes Allah and HIS Messenger should know then that
Allah is certainly severe in punishment.
59:05
a. The palm trees you had cut down of the enemy, or left standing on their stem was by Allah’s Permission,
b. and it was so that HE would disgrace the rebellious.
59:06
a. And whatever Allah bestowed as spoils of war upon HIS...
Stress corrosion cracking (SCC) refers to the damage of mechanical components which are under the combined action of static load and corrosive environment. This phenomenon occurs in various applications including naval and aerospace industry where aluminum and steel alloys experience mechanical loadings in the presence of corrosive environments. In this research work, microstructural and environmental influence on corrosion behavior of Al-6061-T6 at different static loads was investigated. A new test fixture was developed for stress corrosion cracking. Dog-bone shaped tensile specimens of Al-6061-T6 were manufactured using CNC milling machine. Tests were conducted at constant loads of 200 N, 500 N and 800 N, in three different environments: dry ambient conditions, distilled water and 3.5% NaCl solution. Testing continued for different intervals of time i.e. 96 hours, 68 hours and 4.5 hours respectively. After each set of experiments, specimens were observed for cracks using metallurgical microscope. Detailed fractographic investigation of all the tested specimens was carried out using Scanning Electron Microscope (SEM). Excessive corrosion and material degradation was observed in specimens tested in distilled water and 3.5% NaCl environments.
Microstructural analysis depicted pitting corrosion and crack deformation. Some regions clearly showed that grain boundaries were attacked due to oxidation and chemical attack causing weakening of grain boundaries and resulted into intergranular corrosion. Precipitates and grain boundaries in Al-6061-T6 served as a reason of crack initiation due to hydrogen diffusion. Fractographic investigation provided the evidence of trans granular fracture as well as intergranular fracture which was observed as dimples and extensive ductile tearing.
The aim of the thesis is to present iterative reproducing kernel methods, based on reproducing kernel space, for the solution of linear and nonlinear second order to eighth order boundary value problems. The main advantage of reproducing kernel methods is that many boundary values problems which are not simple to solve, can be solved easily in the reproducing kernel spaces. The boundary value problems are solved by combining the properties of reproducing kernel spaces with the computational techniques. The reproducing kernel method is applied directly for the solution of linear BVPs. For the solution of nonlinear boundary value problems, homotopy perturbation - reproducing kernel method, searching least valuereproducing kernel method and two more iterative reproducing kernel methods are proposed. The exact solution is represented in the form of series and the approximate solution converges uniformly to the exact solution. The proposed methods have an advantage that it is possible to pick any point in the interval of integration and the approximate solution will be applicable. The methods proposed reduce the computational cost in solving problems and improve the accuracy of computation by preventing accumulating error of calculation. The performance of the methods proposed is shown to be very encouraging by the numerical results when compared to the results obtained from other existing methods.