We prove that the any Markov solution to the 3D stochastic Navier-Stokes equations driven by a mildly degenerate noise (i. e. all but finitely many Fourier modes are forced) is uniquely ergodic. This follows by proving strong Feller regularity and irreducibility.

Three-wave nonlinear coupling among spatial Fourier modes of density and magnetic fluctuations is directly measured in a magnetically confined toroidal plasma. Density fluctuations are observed to gain (lose) energy from (to) either equilibrium or fluctuating fields depending on the mode number. Experiments indicate that nonlinear interactions alter the phase relation between density and magnet...

Contents Introduction xv Chapter 1. Fourier series: some motivation 1 1.1. Some examples and key definitions 1 1.2. Main questions 5 1.3. Fourier series and Fourier coefficients 7 1.4. A little history, and motivation from the physical world 11 Chapter 2. Interlude 17 2.1. Nested classes of functions on bounded intervals 17 2.2. Modes of convergence 28 2.3. Interchanging limit operations 34 2.4...

By employing an embedding result due to Mañé, and its recent strengthening due to Foias & Olson it is shown that a global attractor with finite fractal (box counting) dimension d lies within an arbitrarily small neighbourhood of a smooth graph over the space spanned by the first [[2d+1]] Fourier-Galerkin modes. The proof is, however, non-constructive.

We experimentally demonstrate degenerate, forward four-wave mixing effects in a self-defocusing photorefractive medium, in both one and two transverse dimensions. We observe the nonlinear evolution of new modes as a function of propagation distance, in both the near-field and far-field (Fourier space) regions.

We show a non-negligible cross-talk between nonlinear modes in Nonlinear Frequency-Division Multiplexed system when data is modulated over the nonlinear Fourier spectrum and transmitted over a lumped amplified fiber link. We evaluate the performance loss if the cross-talks are neglected.

An almost-Markovian model equation is proposed for Fourier modes of velocity field of isotropic turbulence whose statistical properties are identical to those governed by equations of Local Energy Transfer theory of turbulence [McComb et. al., J. Fluid Mech. 245, 279 (1992)] compatible with the Kolmogorov spectrum.

This paper presents a software defined radio using Ofdm for high data rate transmission. to demonstrate the concepts of SDR we use a low power fixed-point digital signal processor. for reducing the complexity we use only two operational modes BPSK and QPSK .the adoptability nature using these two modes of OFDM system is discussed. Here we use a straight line method for getting fewer clock signa...

Abstract The mechanical behavior of a periodic heterogeneous microstructure may be predicted by using fast Fourier transform (FFT) based simulation approach. To reduce the computational effort this method, we introduced model order reduction (MOR) technique utilizing reduced set modes for computations in space. increase accuracy MOR developed geometrically adapted sampling pattern choosing cons...

The Fourier series expansion method is a useful tool to approach the problems of discontinuities in optical waveguides, and it applies to analyze the Floquet-modes of photonic crystal waveguides. This paper shows that the Floquet-mode calculation with large truncation order is limited and explains the reason. Furthermore, two techniques of the formulation are presented to relieve this limitatio...