Signatures of primordial gravitational waves in matter power spectrum

We simulate the evolution of a dust universe from $z=1089$ to $z=0$ by numerically integrating the Einstein's equation for a spatially flat Friedmann-Lemaire-Robertson-Walker (FLRW) background spacetime with scalar perturbations which are derived from the matter power spectrum produced with the Code for Anisotropies in the Microwave Background (CAMB). To investigate the effects of primordial gravitational waves (GWs) on the inhomogeneity of the universe, we add an additional decaying, divergenceless and traceless primordial tensor perturbation with its initial amplitude being $3\times 10^{-4}$ to the above metric. We find that this primordial tensor perturbation suppresses the matter power spectrum by about $0.01\%$ at $z=0$ for modes with wave number similar to its. This suppression may be a possible probe of a GWs background in the future.Comment: 8 pages, 5 figure

Nonlinear bias dependence of spin-transfer torque from atomic first principles

We report first-principles analysis on the bias dependence of spin-transfer torque (STT) in Fe/MgO/Fe magnetic tunnel junctions. The in-plane STT changes from linear to nonlinear dependence as the bias voltage is increased from zero. The angle dependence of STT is symmetric at low bias but asymmetric at high bias. The nonlinear behavior is marked by a threshold point in the STT versus bias curve. The high-bias nonlinear STT is found to be controlled by a resonant transmission channel in the anti-parallel configuration of the magnetic moments. Disorder scattering due to oxygen vacancies in MgO significantly changes the STT threshold bias.Comment: 6page,4figure

Solving systems of phaseless equations via Kaczmarz methods: A proof of concept study

We study the Kaczmarz methods for solving systems of quadratic equations, i.e., the generalized phase retrieval problem. The methods extend the Kaczmarz methods for solving systems of linear equations by integrating a phase selection heuristic in each iteration and overall have the same per iteration computational complexity. Extensive empirical performance comparisons establish the computational advantages of the Kaczmarz methods over other state-of-the-art phase retrieval algorithms both in terms of the number of measurements needed for successful recovery and in terms of computation time. Preliminary convergence analysis is presented for the randomized Kaczmarz methods