Epitaxial silicon grown on CeO2/Si(111) structure by molecular beam epitaxy

Using electron beam evaporation, a Si/CeO2/Si(111) structure has been grown in a molecular beam epitaxy machine. In situ low energy electron diffraction, cross sectional transmission electron microscopy, selected area diffraction, and atomic force microscopy have been used to structurally characterize the overlying silicon layer and show it to be single crystalline and epitaxially oriented. Rutherford backscattering and energy dispersive x-ray analysis have been used to confirm the presence of a continuous 23 Å CeO2 layer at the interface. Rutherford backscattering and x-ray photoemission spectroscopy show an additional presence of cerium both at the exposed silicon surface and incorporated in low levels (~ 1%) within the silicon film, suggesting a growth mechanism with cerium riding atop the silicon growth front leaving behind small amounts of cerium incorporated in the growing silicon crystal

Cosmic ray diffusion: Report of the Workshop in Cosmic Ray Diffusion Theory

A workshop in cosmic ray diffusion theory was held at Goddard Space Flight Center on May 16-17, 1974. Topics discussed and summarized are: (1) cosmic ray measurements as related to diffusion theory; (2) quasi-linear theory, nonlinear theory, and computer simulation of cosmic ray pitch-angle diffusion; and (3) magnetic field fluctuation measurements as related to diffusion theory

Two techniques for digital filter design

Digital controllers, one using a special-purpose computer and the other using a combination of digital and analog techniques, are designed around /1/ computers that simulate the transfer function and interface with the system, and /2/ analog and digital circuits, converters, amplifiers, constant multipliers, and delay lines that form a digital filter

The partially averaged field approach to cosmic ray diffusion

The kinetic equation for particles interacting with turbulent fluctuations is derived by a new nonlinear technique which successfully corrects the difficulties associated with quasilinear theory. In this new method the effects of the fluctuations are evaluated along particle orbits which themselves include the effects of a statistically averaged subset of the possible configurations of the turbulence. The new method is illustrated by calculating the pitch angle diffusion coefficient D sub Mu Mu for particles interacting with slab model magnetic turbulence, i.e., magnetic fluctuations linearly polarized transverse to a mean magnetic field. Results are compared with those of quasilinear theory and also with those of Monte Carlo calculations. The major effect of the nonlinear treatment in this illustration is the determination of D sub Mu Mu in the vicinity of 90 deg pitch angles where quasilinear theory breaks down. The spatial diffusion coefficient parallel to a mean magnetic field is evaluated using D sub Mu Mu as calculated by this technique. It is argued that the partially averaged field method is not limited to small amplitude fluctuating fields and is hence not a perturbation theory

Constrained LQR Using Online Decomposition Techniques

This paper presents an algorithm to solve the infinite horizon constrained linear quadratic regulator (CLQR) problem using operator splitting methods. First, the CLQR problem is reformulated as a (finite-time) model predictive control (MPC) problem without terminal constraints. Second, the MPC problem is decomposed into smaller subproblems of fixed dimension independent of the horizon length. Third, using the fast alternating minimization algorithm to solve the subproblems, the horizon length is estimated online, by adding or removing subproblems based on a periodic check on the state of the last subproblem to determine whether it belongs to a given control invariant set. We show that the estimated horizon length is bounded and that the control sequence computed using the proposed algorithm is an optimal solution of the CLQR problem. Compared to state-of-the-art algorithms proposed to solve the CLQR problem, our design solves at each iteration only unconstrained least-squares problems and simple gradient calculations. Furthermore, our technique allows the horizon length to decrease online (a useful feature if the initial guess on the horizon is too conservative). Numerical results on a planar system show the potential of our algorithm.Comment: This technical report is an extended version of the paper titled "Constrained LQR Using Online Decomposition Techniques" submitted to the 2016 Conference on Decision and Contro