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.
E. Klaseboer, Q. Sun, D. Y. C. Chan
Dynamic linear elasticity using a Helmholtz decomposition and boundary elements
Journal of Elasticity [ELAS-D-18-00071 Submitted 6 Jun 2018]. pdf
The displacement field for three-dimensional (3D) dynamic elasticity problems in the frequency domain can be decomposed into a sum of a longitudinal and a transversal part known as a Helmholtz decomposition. The Cartesian components of both the longitudinal and transverse fields satisfy scalar Helmholtz equations that can be solved using a desingularized boundary element method framework. The curl free longitudinal and divergence free transversal conditions can also be cast as additional scalar Helmholtz equations. The numerical implementation of this approach is benchmarked against the 3D elastic wave field generated by a rigid vibrating sphere embedded in an infinite linear elastic medium for which an analytical solution has been derived. In the static zero frequency limit, the Helmholtz decomposition becomes non-unique, and both the longitudinal and transverse components contain divergent terms that are proportional to the in- verse square of the frequency. However, these divergences are equal and opposite so that their sum, that is the physical displacement field, remains finite in the zero frequency limit.
S. J. Flanders, Q. Sun, A. M. Siddiquee, D. Y. C. Chan, J. W. M. Chon
Analytical model for light scattering of plasmonic gold nanorods with size up to 200 nm
ACS Photonics [PH-2018-01196y Submitted 29 Aug 2018]. pdf, supp
Recently, various linear and nonlinear emission processes of shape-controlled plasmonic gold nanorods have been applied in biolabelling and photothermal cancer therapy. One of the most fundamental knowledge required for understanding these processes is the field around the nanorod. Here, we present a simple analytical theoretical model for calculating near- and far-fields around prolate spheroidal (PS) and hemispherically capped cylindrical (HCC) gold nanorods beyond the quasistatic limit, for rods up to 200 nm in length (ka ~ 1.13, corresponding to a wavelength ~ 500 nm) and aspect ratio 5, which encompasses the parameter range of most of the biolabelling applications. We achieve this by solving the field directly from classical electrostatic model for ellipsoids, and then by introducing correction factors for different size beyond quasistatic limit and then for the shape of HCC nanorods. We validate the model with numerical simulations and correlated single particle scattering cross-section measurements using confocal laser scanning microscopy (CLSM) and transmission electron microscopy (TEM). The simple and accurate expressions will be useful in determining efficiency in any linear or nonlinear emission processes for biolabelling application that require accurate knowledge of the field around these nanorods.