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Mastizaade (2016) Bollywood Full Movie Watch Online Sunny Leone, Tusshar.. Tag: Download Mastizaade Full Movie in HD 720p/1080p Direct & Torrent Download .$$\frac{dx}{dt} = \frac{g}{J_{0}}\sum\limits_{\ell\ell’}M_{i}M_{j}\cos\theta_{\ell\ell’}J_{i}J_{j}\cos\theta_{i}^{k}\cos\theta_{j}^{k}$$

Equation (2) is linear in $M_{i}$, and therefore the resulting magnetization can be written as the solution to the following matrix eigenvalue problem:

$$\frac{d}{dt}(M_{i}) = \sum\limits_{j}A_{ij}M_{j}$$

Note that, similar to Eq. (5), a biased field acting on one of the moments can drive the dynamics in the lab frame.

$$\frac{d}{dt}(M_{i}) = \sum\limits_{j}A_{ij}M_{j} + \frac{\gamma}{\mu_{0}}(B_{i} – M_{i}B_{i})$$

The required matrix is

$$A_{ij} = \frac{1}{J_{0}}\left[\frac{g}{J_{0}}\sum\limits_{\ell\ell’}J_{i}J_{j}\cos\theta_{\ell\ell’}J_{i}J_{j}\cos\theta_{i}^{k}\cos\theta_{j}^{k} + \frac{1}{\mu_{0}}B_{i}B_{j}\right]$$

Numerical Simulations of the Nano-Magnonic Circuits
===================================================

As shown in the main text, the dynamics of a nano-magnetic vortex can be controlled by engineering time-dependent magnetic fields and bias fields. Here, we numerically simulate such controlled scenarios with a minimal numerical model of the circuit, where the dynamics of individual magnetic vortices in
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