Computation of synthetic seismogram in real earth model by eigen function expansion

The method of eigen function expansion has been used in the present study to compute synthetic or theoretical seismogram in layered elastic half-space of real earth model. Simple dislocation source model has been considered. The transverse (SH) or radial and vertical (P-SV) components of displacement field have been computed as summed modes and compared by using both exact and numerical techniques. The methods used in the study, include exact evaluation by propagator matrix approach using Reflection-Transmission coefficients as well as numerical computations using Runge-Kutta method of order 4. The specialty of the present study is to evaluate approximate displacement field for the earth models with homogeneous and / or inhomogeneous layers. The normalization technique has been used in the study to control the overflow errors. The study has an advantage to get an idea of earth structure or source model by an inverse iterative technique.

POSSIBLE ENERGY SPECTRUM OF THE TWO DIMENSIONAL SPATIAL KLEIN-GORDON OSCILLATOR EQUATION

In the present article, one had found a complete energy spectrum and eigen-function of the solution of two dimensional (2D) spatial Klein-Gordon oscillator equation which shows that its relativistic degeneracy energy is related to the eigen-function.

Numerical Assessment of Rectangular Straight/Reverse Mufflers at High-Order-Modes

There has been wide-spread use of plane wave theory in muffler design in industry. However, This has led to an underestimation of acoustical performances at higher frequencies. To overcome the above drawback, the finite element and boundary element methods have been developed. Nevertheless, the time consumed in calculating the noise level is unacceptable. Moreover, considering the acoustical effect and necessity of space-constrained situation in industry, a compact design of reverse mufflers which may improve the acoustical efficiency is then proposed.In this paper, a numerical assessment of rectangular mufflers hybridized with straight/reverse chambers using eigen function, four-pole matrix, and genetic algorithm under limited space is developed. Before the optimization is performed, an accuracy check of the mathematical models for the muffler will be carried out. Results reveal that the noise reduction will increase when the number of chambers increases. In addition, the acoustical performance of the mufflers is reversely proportional to the diameter of the inlet/outlet tubes. Also, the TL of the mufflers will be improved when using more number of target tones in the objective function. Consequently, a successful approach in searching optimal shaped rectangular straight/reverse mufflers using an eigen function and a genetic algorithm method within a constrained space has been demonstrated.

Calculation of Wave Forces Acting on a Cylinder With a Porous Plate Fixed Inside

To evaluate wave forces and to estimate the motion of breakwater, a circular cylinder is investigated based on the linear wave theory in the present work. The cylinder possesses a porous sidewall, an impermeable bottom and a horizontal porous plate inside that is fixed in the cylinder to work as obstruct and make wave dissipation more effectively. To simplify the problem, the Darcy’s fine-pore model is applied to the boundary condition on the porous body surface. The boundary value problem is solved by means of the eigen-function expansion approach. The fluid domain is divided into three regions and different eigen-function series are used. The so-called dispersion relation for the region inside the cylinder is quite different from a conventional one due to the existence of the porous plate. It leads to eigen values of complex number. To obtain solutions for the radiation problems, particular solution should be constructed to take account of the normal velocity appearing on the porous boundary. The wave loads are evaluated by integrating the pressure difference on two sides of the wetted body surface. The theoretical works are in good consistence with the experimental results. The Haskind relations are examined for the porous body. It is found that the damping coefficient consists of two parts. In addition to the component of conventional wave-radiating damping, exists a second component caused by the porous effects.