On Generalized Compressible Fluid Systems on an Evolving Surface with a Boundary

We consider compressible fluid flow on an evolving surface with a piecewise Lipschitz-continuous boundary from an energetic point of view. We employ both an energetic variational approach and the first law of thermodynamics to make a mathematical model for compressible fluid flow on the evolving surface. Moreover, we investigate the boundary conditions in co-normal direction for our fluid system to study the conservation and energy laws of the system.Comment: arXiv admin note: text overlap with arXiv:1705.0718

Local and Global Solvability for Advection-Diffusion Equation on an Evolving Surface with a Boundary

This paper considers the existence of local and global-in-time strong solutions to the advection-diffusion equation with variable coefficients on an evolving surface with a boundary. We apply both the maximal $L^p$-in-time regularity for Hilbert space-valued functions and the semigroup theory to construct local and global-in-time strong solutions to an evolution equation. Using the approach and our function spaces on the evolving surface, we show the existence of local and global-in-time strong solutions to the advection-diffusion equation. Moreover, we derive the asymptotic stability of the global-in-time strong solution

Angle Dependence of Photonic Enhancement of Magneto-Optical Kerr Effect in DMS Layers

We investigate theoretically an angle dependence of enhancement of polar magneto-optical Kerr effect (MOKE) obtained thanks to a deposition of a paramagnetic Diluted Magnetic Semiconductor (DMS) layer on one-dimensional photonic crystal layer. Our transfer matrix method based calculations conducted for TE and TM polarizations of the incident light predict up to an order of magnitude stronger MOKE for a (Ga,Fe)N DMS layer when implementing the proposed design. The maximum enhancement for TE and TM polarization occurs for the light incidence at the normal and at the Brewster angle, respectively. This indicates a possibility of tuning of the MOKE enhancement by adjustment of the polarization and the incidence angle of the light.Comment: 6 figure

Truncation Error Analysis of Approximate Operators for a Moving Particle Semi-Implicit Method

This paper considers several approximate operators used in a particle method based on a Voronoi diagram. Under some assumptions on a weight function, we derive truncation error estimates for our approximate gradient and Laplace operators. Our results show that our approximate gradient and Laplace operators tend to the usual gradient and Laplace operators when the ratio (the radius of the interaction area/the radius of a Voronoi cell) is sufficiently large. The key idea of our approach is to divide the integration region into two ring-shaped areas.Comment: 2 figure