The Collective Beam-Beam interaction is studied in the framework of maps with a “kick-lattice” model in the 4-D phase space of the transverse motion. A novel approach to the classical method of averaging is used to derive an approximate map which is equivalent to a flow within the averaging approximation. The flow equation is a continuous-time Vlasov equation which we call the averaged Vlasov e...

Precise and effective identification of modal parameters is important for a civil structure throughout the structural lifetime. A time-frequency method parameter developed based on recently adaptive signal decomposition, i.e., empirical Fourier decomposition (EFD). The EFD used to separate multi-component free vibration response into summation several mono-component responses. frequencies dampi...

The pseudo-spectral method is proposed for following the evolution of density and velocity uctuations at the weakly non-linear stage in the expanding universe with a good accuracy. In this method, the evolution of density and velocity uctuations is integrated in the Fourier Space with using FFT. This method is very useful to investigate accurately the non-linear dynamics in the weakly non-linea...

The Fourier coefficient path-integral representation of the quantum density matrix is used to carry out direct, accurate calculations of coupled vibrational partition functions. The present implementation of the Fourier path-integral method incorporates two noteworthy features. First, we use a Gaussian in Fourier space as a probability density function, which is sampled using the Box-Muller alg...

This paper is the second part of a threefold article, aimed at solving numerically the Poisson problem in three-dimensional prismatic or axisymmetric domains. In the first part of this series, the Fourier Singular Complement Method was introduced and analysed, in prismatic domains. In this second part, the FSCM is studied in axisymmetric domains with conical vertices, whereas, in the third part...

This paper is the second part of a threefold article, aimed at solving numerically the Poisson problem in three-dimensional prismatic or axisymmetric domains. In the first part of this series, the Fourier Singular Complement Method was introduced and analysed, in prismatic domains. In this second part, the FSCM is studied in axisymmetric domains with conical vertices, whereas, in the third part...

ABSTRACT We numerically investigate the non-Gaussianities in late-time cosmological density field Fourier space. explore various statistics, including two- and three-point probability distribution function (PDF) of phase modulus, their correlation function. Significant non-Gaussianity is observed for certain configurations. Comparing measurement from simulation with theoretical expansion predic...

Spiral arm modulation in NGC 4062 (an optical flocculent) is detected for the first time; the Fourier spectra of NGC 4062 and NGC 5248 (a classic grand design in optical images) are almost identical. Within the framework of the Density Wave Theory (Lin and Shu 1964) and the the modal theory of galactic spiral structure (Bertin et al. 1989) the characteristic signature of a two-armed grand desig...

In addition to their inestimable importance in mathematics and its applications, Fourier series also serve as the entry point into the wonderful world of Fourier analysis and its wide-ranging extensions and generalizations. An entire industry is devoted to developing the theory and enlarging the scope of applications of Fourier–inspired methods. New directions in Fourier analysis continue to be...

We demonstrate new types of dielectric-band photonic crystal lasers in a two-dimensional modified single-cell cavity with enlarged air holes. Finite-difference time-domain simulations performed in real and Fourier spaces show that the dielectric-band cavity modes originating from the first band edge point in the dielectric band have mode patterns that are distinguishable from conventional air-b...