Abstract: Photonic Crystal Fiber (PCF) uses are no longer limited to telecommunication only rather it is now used for many sensors-based fiber optics application, medical science, space application and so on. In this paper, the authors have proposed a microstructure PCF that is designed by using Finite Element Method (FEM) based software. Besides designing, authors have discussed the necessity of the characteristics that it poses for some specified applications because it is not possible to have all good characteristics from a single PCF. Proposed PCF shows the property of ultra-high birefringence (0.0262 at 1550 nm) which is more useful for sensor based on fiber optics. The non-linearity of this fiber is 50.86 w-1km-1 at 1550 nm wavelength which is very high to guide the light through the core tightly. For Perfectly Matched Boundary Layer (PML), 0.6 μm diameter is taken. This design will offer the characteristics of Nonzero-Dispersion-Shifted Fiber (NZ-DSF) for 450 nm waveband. Since it is a software-based design and no practical evaluation has made, 2% tolerance is checked and the authors have found very small variation of the characteristics.
Abstract: Discretization of spatial derivatives is an important
issue in meshfree methods especially when the derivative terms
contain non-linear coefficients. In this paper, various methods used
for discretization of second-order spatial derivatives are investigated
in the context of Smoothed Particle Hydrodynamics. Three popular
forms (i.e. "double summation", "second-order kernel derivation",
and "difference scheme") are studied using one-dimensional unsteady
heat conduction equation. To assess these schemes, transient response
to a step function initial condition is considered. Due to parabolic
nature of the heat equation, one can expect smooth and monotone
solutions. It is shown, however in this paper, that regardless of
the type of kernel function used and the size of smoothing radius,
the double summation discretization form leads to non-physical
oscillations which persist in the solution. Also, results show that when
a second-order kernel derivative is used, a high-order kernel function
shall be employed in such a way that the distance of inflection
point from origin in the kernel function be less than the nearest
particle distance. Otherwise, solutions may exhibit oscillations near
discontinuities unlike the "difference scheme" which unconditionally
produces monotone results.