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1, 2, N 1, and N (For more information, see Supplementary Information B). Thus, the discrete (quantized) five modes' wave numbers of the collective vortex gyrations in the five disk array are coincident with the values of , where m = 1, 2, 3, 4, 5. Here, to extract the dispersion ( k relation) of all of the modes, we perform FFTs of the collective core profiles for the individual modes according to (where m = 1, 2, 3, 4, 5) with a fixed value of dint = 2250nm for the real sample. Figure 4 shows the FFT powers in the k spectra obtained from the experimental data, micromagnetic simulation (for = 0. 01) and numerical calculation of coupled Thiele equation (for both cases of = 0. 01 and = 0).
From the inverse FFT of all of the peaks of each mode, we can extract the spatial correlations of core motions in the individual Nike Lebron Soldier 9 White
disks for each mode i. Figure 3(b) shows the trajectories of the orbiting cores in motion in the individual disks along with the profiles of the CnYn component of the core positions in the five disk array. For all of the modes i, the individual core' gyration amplitudes are markedly distinct among the disks and modes. More interestingly, the collective motions of the individual cores in the whole array represent certain wave forms of different wavelengths. The gyration amplitudes for all of the modes are symmetric with respect to the center of the array, and are also completely pinned at imaginary disks at both ends, denoted disk 0 and disk 6 for the case of N = 5. These features represent a Hypershift Nike Review
In this case, the boundary condition is given as , where denotes the displacement of beads, N is the number of elements, and dint is the inter distance between the elements. From this boundary condition, the wave vectors of the allowed modes can be expressed simply as , where m = Nike Dunk Low
standing wave form of a certain wavelength in terms of collective vortex gyration motions, being quite analogous to a string, the ends of which are attached to the left and right walls respectively, thus having no displacement. Accordingly, we can interpret the collective and discrete wave modes as in the no damping case, based on the fixed boundary condition in such a 1D array of finite disk number N.
Using such reduced parameters of CnXn and CnYn, we can consider only the polarity ordering for comparison between experimental a.
ulation for = 0. In order to clarify the presence of fundamental Nike Hyperlive Basketball Shoes discrete modes, we conduct further numerical calculation of coupled Thiele equation on a five disk model of the same dimensions and material parameters as those in the real sample, but with zero damping. The right panel of Fig. 3a shows the characteristic frequency spectrum of each disk. From disk 1 through disk 5, different peaks of contrasting FFT powers are observed. All of the five distinct peaks marked by i (where i = 1, 2, 3, 4, 5) are shown in disks 1 and 5. By contrast, the 3 peak disappears in disks 2 and 4, while the 2 and 5 peaks disappear in disk 3. Each of the peaks of all of the modes is located at the same position in all of the disks.
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