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Dispersion relations of numerical calculation (blue color spectra) for N = 201 for which core gyration in the middle (101th disk) of the whole array is displaced to 200nm, and of the numerical calculation Nike Zoom Air Flight

Hypervenom Nike

Hypervenom Nike

Hypervenom Nike

Hypervenom Nike

The numerical calculation of the analytical form of for four different types of vortex state ordering noted above are displayed by the white lines in Fig. 5a, which are in excellent agreement with the dispersion spectrum from the FFTs of the Xn components of the individual disks, which are obtained from the numerical calculation of N coupled Thiele equations for the N = 201 system with damping ( = 0. 01). While performing the FFTs, we imposed a periodic boundary condition to describe such a semi infinite system in terms of traveling waves. Accordingly, the resultant k values are given as , where m is any integer value under the constraint of . All of the dispersion curves are symmetric with respect to k = 0, because the gyration is supposed to propagate from the center towards both ends. (a) Nike Hypervenom Phantom

Hypervenom Nike

Hypervenom Nike

(b) Dynamic dipolar interaction energy densities as a function of time for both k = 0 and k = kBZ, which are obtained from the analytical form of an infinite 1D array. The gray colored wide arrows in each disk indicate the effective net magnetizations Mn> induced by core shifts at the given core positions. The size does not indicate the magnitude of the dynamic effective magnetizations. Specific Mn> configurations are indicated by three disks and corresponding gray arrows. We stress here that the overall shape of dispersion is determined by the sign of pnpn+1CnCn+1; such that concave up for pnpn+1CnCn+1 = 1, and concave down for pnpn+1CnCn+1 = 1. Also, the band width is wider for the case of the antiparallel p ordering than for the parall.

by dipolar interaction between only NN disks32,33. Here, for simplicity, we assume 1D arrays of an infinite number of equal dimension disks. For zero damping ( = 0), the dispersion relation can be written as with and , where is the stiffness coefficient of the potential energy for isolated disks. and represent the interaction strength along the x (here x is the bonding axis) and y axes, respectively (for the detailed derivation procedure, see Supplementary Information C). pnpn+1 = +1(1) and CnCn+1 = 1(1) indicate parallel (antiparallel) p and C ordering, respectively, between the NN disks. In this case, the wave vector k has a continuous value due to the infinite number of existing modes in such an infinite 1D array. This explicit analytical form indicates that the dispersion relation is a function of an isolated disk's eigenfrequency 0 and the coupling strength between Hypervenom Nike the NN disks, that is, and , as well as those special p and C ordering.

(white thick lines) of the analytically derived equation for a 1D infinite array.

Hypervenom Nike

Hypervenom Nike

Hypervenom Nike

´╗┐nd antiparallel C ordering. Considering those additional degrees of freedom for both the p and C ordering, we analytically derive an explicit dispersion relation based on linearized Thiele equations of coupled vortex core motions, taking into account the potential energy modified Hyperdunk Nike Basketball Shoes

Hypervenom Nike

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