Incompressible, homogeneous and isotropic turbulence is studied by solving the Navier-Stokes equations on a reduced set of Fourier modes, belonging to a fractal set of dimension D . By tuning the fractal dimension parameter, we study the dynamical effects of Fourier decimation on the vortex stretching mechanism and on the statistics of the velocity and the velocity gradient tensor. In particula...

Periodic solutions of the Hamilton-Jacobi equation determine invariant tori in phase space. The Fourier spectrum of a torus with respect to angular coordinates gives useful information about nonlinear resonances and their potential for causing instabilities. We describe a method to solve the Hamilton-Jacobi equation for an arbitrary accelerator lattice. The method works with Fourier modes of th...

A short analysis is presented of the effects on the cepheid light curve shape, i.e. on the Fourier parameters usually adopted for its description, of the blending of the stellar image with other close stars. The conclusion is that, within reasonable error, the effects are in general small and the Fourier decomposition is confirmed to be a useful tool for pulsation mode discrimination. A large e...

We propose the adaptive S-method-based technique for imaging of SAR and ISAR targets. This approach can be applied in the 1D and 2D modes. It is a postprocessing technique, since the first stage is the standard radar imaging with the 2D Fourier transform. In addition, selection of the adaptive parameter in this technique is efficient and can be performed based on simple rules in real time. The ...

For dielectric periodic gratings, we propose the combination of a spectral-domain volume integral equation and Fourier factorization rules to address the Gibbs phenomenon caused by jumps in both the fields and the permittivity. From a theoretical point of view we discuss two ways to overcome the computational complexity caused by the inverse rule by changing the fundamental unknowns of the unde...

This paper presents a spectral analysis algorithm for monitoring the characteristics of the damped oscillating “modes” which are set up after a disturbance in an electric power distribution system. This monitoring is necessary so that one can detect early whether any modes are “inverse damped” (ie. exponentially growing), and hence likely to create instability in the power system. In this appli...

We examine the outer Galactic HI disk for deviations from the b = 0 plane by constructing maps of disk surface density, mean height, and thickness. We find that the Galactic warp is well described by a vertical offset plus two Fourier modes of frequency 1 and 2, all of which grow with Galactocentric radius. Adding the m = 2 mode accounts for the large asymmetry between the northern and southern...

Classical model reduction techniques approximate the solution of a physical model by a limited number of global modes. These modes are usually determined by variants of principal component analysis. Global modes can lead to reduced models that perform well in terms of stability and accuracy. However, when the physics of the model is mainly characterized by advection, the nonlocal representation...

We investigate Bessel-like modes guided in a double cladding fiber where the outer cladding is an aircladding. For very high order LP(0X) -modes, the azimuthal symmetry is broken and the mode is no longer linearly polarized. This is observed experimentally and confirmed numerically. The effect is investigated numerically using a full vectorial modesolver and is observed to be dependent on the f...

All attempts to generalize the three-dimensional Lorenz model by selecting higher-order Fourier modes can be divided into three categories, namely: vertical, horizontal and vertical–horizontal mode truncations. The previous study showed that the first method allowed only construction of a nine-dimensional system when the selected modes were energy-conserving. The results presented in this paper...