The scalar theory of the self-focusing of an optical beam is not valid for a very narrow beam, and a correct description of the beam behavior requires a vector analysis in this case. A vector nonparaxial theory is developed from the vector Maxwell equations by application of an order-of-magnitude analysis method. For the same input beam, the numerical results of self-focusing from both scalar a...

In the presented paper, the governing equations of a vibratory beam with moderately large deflection are derived using the first order shear deformation theory. The beam is homogenous, isotropic and it is subjected to the dynamic transverse and axial loads. The kinematic of the problem is according to the Von-Karman strain-displacement relations and the Hook's law is used as the constitutive eq...

When a specimen surface carrying a high-frequency line grating is examined under a scanning electron microscope (SEM), moiré fringes are observed at several different magnifications. The fringes are characterized by their spatial frequency, orientation, and contrast. These features of the moiré pattern depend on the spatial frequency mismatch between the specimen grating and the raster scan lin...

background edible salt is the most commonly used food additive worldwide. therefore, any contamination of table salt could be a health hazard. objectives the present study aimed to determine the levels of heavy metals in table and bakery refined salts. materials and methods eighty-one table refined salt samples and the same number of bakery refined salt samples were purchased from retail market...

Neutralization of external stimuli in dynamic systems has the major role in health, life, and function of the system. Today, dynamic systems are exposed to unpredicted factors. If the factors are not considered, it will lead to irreparable damages in energy consumption and manufacturing systems. Continuous systems such as beams, plates, shells, and panels that have many applications in differen...

A new electron beam smelting technology was employed to prepare the Inconel 718 alloy, and microstructure evolution nucleation coarsening mechanisms of γ', γ″ δ phase this alloy investigated. The microstructures can be refined by means smelting, good stability is observed at 700 °C, which least 20 °C beyond limiting temperature that sustain for prolonged periods. γ' precipitates could formed in...