N-dimensional geometries and Einstein equations from systems of PDE's

The aim of the present work is twofold: first, we show how all the $n$-dimensional Riemannian and Lorentzian metrics can be constructed from a certain class of systems of second-order PDE's which are in duality to the Hamilton-Jacobi equation and second we impose the Einstein equations to these PDE's

Frequency Modulation of Spin-Transfer Oscillators

Spin-polarized dc electric current flowing into a magnetic layer can induce precession of the magnetization at a frequency that depends on current. We show that addition of an ac current to this dc bias current results in a frequency modulated (FM) spectral output, generating sidebands spaced at the modulation frequency. The sideband amplitudes and shift of the center frequency with drive amplitude are in good agreement with a nonlinear FM model that takes into account the nonlinear frequency-current relation generally induced by spin transfer. Single-domain simulations show that ac current modulates the cone angle of the magnetization precession, in turn modulating the frequency via the demagnetizing field. These results are promising for communications and signal processing applications of spin-transfer oscillators.Comment: 13 pages, 3 Figure