ABSTRACT
A type of artificial molecule, called the photonic molecule, is investigated. It consists of coupled-defect atoms in photonic crystals. We theoretically present a method to determine the frequency of each resonant mode for the photonic molecule. Within the major band gap, the photonic molecule confines the resonant modes that are closely analogous to the ground-state molecular orbitals of an analogous chemical molecule and the corresponding electromagnetic spectrum is also isomorphous to the electric energy levels. By employing the variational theory, the constraint determining the resonant coupling is formulated, which is consistent with the results of both the scattering matrix method and the group analysis. In addition, a type of photonic waveguide is proposed for the two-dimensional system that manipulates the mechanism of photon hopping between photonic benzene and offers an optical feature of twin waveguiding bandwidths.
ABSTRACT
This study presents a solvable model in renormalization group analysis for the effective eddy viscosity. It is found fruitful to take a simple hypothesis that large-scale eddies are statistically independent of those of smaller scales. A limiting operation of renormalization group analysis yields an inhomogeneous ordinary differential equation for the invariant effective eddy viscosity. The closed-form solution of the equation facilitates derivations of an expression of the Kolmogorov constant C(K) and of the Smagorinsky model for large-eddy simulation of turbulent flow. The Smagorinsky constant C(S) is proportional to C(3/4)(K). In particular, we shall illustrate that the value of C(K) ranges from 1.35 to 2.06, which is in close agreement with the generally accepted experimental values (1.2 approximately 2.2).
