A three-dimensional wave packet generated by a local disturbance in a two-dimensional hypersonic boundary layer flow is studied with the aid of the previously solved initial-value problem. The solution to this problem can be expanded in a biorthogonal eigenfunction system as a sum of modes consisting of continuous and discrete spectra of temporal stability theory. A specific disturbance consist...

For a complementary view to the approach employed in the main text, here we present an alternative formulation of the plasmon equations of motion. Rather than focusing on the semiclassical equations of motion for the particle and velocity density fields, here we work with the charge density ρ(r, t) = −en(r, t), the current density j(r, t), and the conductivity tensor σ. As we will be interested...

The symmetry, Fourier space and space group properties of two-dimensional photonic crystal waveguides are discussed. The modes of the standard single missing line defect waveguide can be classified as even or odd along the transverse direction. This is contrasted with the modes of line defect waveguides with a glide plane along the propagation direction. In this case the spatial Fourier series ...

In this paper, we investigate the performance of pseudo-spectral methods in computing nearly singular solutions of fluid dynamics equations. We consider two different ways of removing the aliasing errors in a pseudo-spectral method. The first one is the traditional 2/3 dealiasing rule. The second one is a high (36th) order Fourier smoothing which keeps a significant portion of the Fourier modes...

The basic idea of this new method resides in the fact that the major part of the relative information to the solution to calculate is contained in the small modes of a development of Fourier series; the raised modes of which the coefficients associated being small, being negligible to every instant, however, the effect of these modes on a long interval of time is not negligible. The nonlinear G...

A method is described for predicting statistical properties of turbulence. Collections of Fourier amplitudes are represented by nonuniformly spaced modes with enhanced coupling coefficients. The statistics of the full dynamics can be recovered from the time-averaged predictions of the reduced model. A Liouville theorem leads to inviscid equipartition solutions. Excellent agreement is obtained w...