Following the scheme developed by Engquist and Majda [Math Comp. 31 (1977) 629] for first-order systems, we derive a theoretical perfectly absorbing nonlocal boundary condition for Maxwell's equations at a flat outer boundary.
When a thin melt inclusion having a flat lower boundary to the host mineral is analyzed, reflection from the lower boundary overlaps with the light reflected from the surface.
The theory is presented for a flat plate boundary layer flow, and important parameters such as adiabatic wall temperature and recovery factor are introduced.
Numerical results are presented for a flat plate boundary layer at zero pressure gradient and for a flow with pressure gradient driven separation.
The results of numerical simulation of turbulent compressible flows in a flat plate boundary layer, free mixing layer and free jet provide general statistics of optical distortions by examining the time-averaged intensity pattern and instantaneous flowfield.
For this study, a two-dimensional channel containing two grains separated by a flat grain boundary has been constructed that allows for a channel length on the order of one micrometer.
Several measurement methods are used and compared, namely classical two-dimensional (2D) methods based on metallurgical cross-section analysis and a recently developed 3D stereoscopic method that yields the true three-dimensional angle value for individual inclusions straddling a flat grain boundary.
However, this error does not occur in a geometry with a flat anterior boundary.
This paper develops a novel general matrix method for paraxial skew ray-tracing in systems with non-coplanar optical axes containing spherical and flat boundary surfaces.
We first prove the theorem for the special case of flat boundary, and by using it, we take care of the general cases.
