The mapped Galerkin method in solving the full-vector and quasi-vector wave equations in terms of transverse magnetic fields (H-formulation) for optical waveguides with step-index profiles is described. By transforming the whole x鈥搚 space onto a unit square and using two-dimensional Fourier ...
Fitted power-law index (s, see Formula (1)) and the least chi-square value (χ2) are shown in the lower right corner of the panel. d, e The same as (c) but for the wavelet analysis of the Tb variation in the entire CS region at 8.4 GHz, and of the time derivative of SXR ...
Equation (12) is satisfied by, e.g., saw-tooth or square wave functions. For such non-smooth forcing functions, we have the following result: Theorem 3.3 Assume that that the conditions (C1)–(C4), or equivalently condition (C4*) instead of condition (C4), are satisfied and the quasi-...
\square The potential function Q_{\mathfrak {m}}(y) = Q_{{\mathfrak {m}}}(\texttt{E},\texttt{r};y) is analytic in all its entries and, in the limit {\mathfrak {m}}\rightarrow +\infty , it approaches the singular potential \begin{aligned} Q_\infty (y) = Q_\infty (\...
The Feje´r average and the mean value of a quantity in a quasiclassical wave packet.The mean value of a quantity in an equally weighted wave packet was recently found in the classical limit to be the Feje´r average of partial sums of Fourier series expansion of the classical ...
12 shows that the ripples in dynamic pressure (proportional to the product of number density and the square of the velocity) are driven more by density than by velocity: for pressure and density the amplitudes and variations are remarkably similar, whereas for pressure and velocity they are not...
quasipatterns in the Faraday wave experiment with (a) 3 and (b,c) 2 frequency forcing. Top line: experimental photographs; bottom line: spatial Fourier transform. The circles in the Fourier spectra indicate wavenumbers that are excited by one of ...
After passing through a velocity measurement system, the bullet impacts the incident bar, generating a stress wave that travels along the bar. When the stress wave reaches the sample, it partially reflects and transmits. The transmitted wave passes through the sample and similarly reflects and ...
First, a laser beam (CW, wavelength 785 nm) was enlarged using a beam expander and reflected by the SLM (LCOS-SLM, X10468-02, Hamamatsu Photonics) to control the wavefront of the beam. The phase hologram used for the wavefront control was calculated by the iterative Fourier transform ...
The rigorous calculation to quantum motion in one infinite potential square well shows that the expectation value of a quantum mechanical quantity on equally weighted wave packet in the classical limit tends to the Fejér mean value of the Fourier series of corresponding classical quantity,rather than...