A direct formulation of electromagnetic scattering based only on scalar Helmholtz equations is given. The solution, expressed as coupled non-singular boundary integral equations for the field components, provides the benefits of the reduction of dimensionality. For perfect conductors, consideration of induced surface current densities, central to standard methods, is not required. This approach has utility in high aspect ratio electromagnetic problems, surface plasmon spectra and dis- persion force calculations of complex nano structures as near and far field values are given with equal precision. Extension to dielectric scatterers and elastic wave propagation in solids is immediate.
J. Oshitani, S. Hahashi, D. Y. C. Chan
Order from Chaos: Dynamics of density segregation in continuously aerated granular systems
Physical Review Letters [Submitted 6 Feb 2017]. pdf, supp
Under continual disturbance such as vibration, tumbling, flow or aeration, granular or powder systems can display solid or fluid like behavior. Using a well-mixed system of same size (0.2 mm) non-cohesive glass beads and iron powder, we show that gentle aeration can completely segregate the components thereby reducing the entropy of mixing to create near total order from an initially chaotic mixture. We quantify the time dependence of the segregation process and identify two dynamic pathways that dominate depending on the intensity of the aeration. Such findings can facilitate the search for energy efficient methods to process granular systems in pharmaceutical, mining and waste recovery industries.
D. Y. C. Chan, E. Klaseboer, Q. Sun
A stable zero frequency surface integral formulation for E and H
Progress in Electromagnetics Research Letters [17120307 Submitted 03 Dec 2017]. pdf
The frequency domain Maxwell's equations in linear homogeneous media are re-cast as 4 scalar Helmholtz equations: 3 for the Cartesian components of the electric field, E and 1 for the scalar function (r · E), with identical equations for the magnetic field, H. Their surface integral equation solution involves only the Green’s function, G(r, r') = exp(ik|r − r'|)/(4π|r − r'|) but can be written in a form with bounded integrands. Solving with the Nyström quadrature method with quadratic area elements gives a linear system for E and H on the boundary directly. Hypersingular dyadic Green's function and surface currents do not feature. This simpler direct approach is stable in the long wavelength limit, unaffected by the zero frequency catastrophe in the EFIE and MFIE formulations.