A unified approach to compute foliations, inertial manifolds, and tracking initial conditions

Several algorithms are presented for the accurate computation of the leaves in the foliation of an ODE near a hyperbolic fixed point. They are variations of a contraction mapping method in [25] to compute inertial manifolds, which represents a particular leaf in the unstable foliation. Such a mapping is combined with one for the leaf in the stable foliation to compute the tracking initial condition for a given solution. The algorithms are demonstrated on the Kuramoto-Sivashinsky equation

Induced Lorentz- and CPT-violating Chern-Simons term in QED: Fock-Schwinger proper time method

Using the Fock-Schwinger proper time method, we calculate the induced Chern-Simons term arising from the Lorentz- and CPT-violating sector of quantum electrodynamics with a $b_\mu \bar{\psi}\gamma^\mu \gamma_5 \psi$ term. Our result to all orders in $b$ coincides with a recent linear-in-$b$ calculation by Chaichian et al. [hep-th/0010129 v2]. The coincidence was pointed out by Chung [Phys. Lett. {\bf B461} (1999) 138] and P\'{e}rez-Victoria [Phys. Rev. Lett. {\bf 83} (1999) 2518] in the standard Feynman diagram calculation with the nonperturbative-in-$b$ propagator.Comment: 11 pages, no figur

Non-equilibrium spatial distribution of Rashba spin torque in ferromagnetic metal layer

We study the spatial distribution of spin torque induced by a strong Rashba spin-orbit coupling (RSOC) in a ferromagnetic (FM) metal layer, using the Keldysh non-equilibrium Green's function method. In the presence of the s-d interaction between the non-equilibrium conduction electrons and the local magnetic moments, the RSOC effect induces a torque on the moments, which we term as the Rashba spin torque. A correlation between the Rashba spin torque and the spatial spin current is presented in this work, clearly mapping the spatial distribution of Rashba Spin torque in a nano-sized ferromagnetic device. When local magnetism is turned on, the out-of-plane (Sz) Spin Hall effect (SHE) is disrupted, but rather unexpectedly an in-plane (Sy) SHE is detected. We also study the effect of Rashba strength (\alpha_R) and splitting exchange (\Delta) on the non-equilibrium Rashba spin torque averaged over the device. Rashba spin torque allows an efficient transfer of spin momentum such that a typical switching field of 20 mT can be attained with a low current density of less than 10^6 A/cm^2

Calculation of a Class of Three-Loop Vacuum Diagrams with Two Different Mass Values

We calculate analytically a class of three-loop vacuum diagrams with two different mass values, one of which is one-third as large as the other, using the method of Chetyrkin, Misiak, and M\"{u}nz in the dimensional regularization scheme. All pole terms in \epsilon=4-D (D being the space-time dimensions in a dimensional regularization scheme) plus finite terms containing the logarithm of mass are kept in our calculation of each diagram. It is shown that three-loop effective potential calculated using three-loop integrals obtained in this paper agrees, in the large-N limit, with the overlap part of leading-order (in the large-N limit) calculation of Coleman, Jackiw, and Politzer [Phys. Rev. D {\bf 10}, 2491 (1974)].Comment: RevTex, 15 pages, 4 postscript figures, minor corrections in K(c), Appendix B removed, typos corrected, acknowledgements change

Phase equilibrium modeling for high temperature metallization on GaAs solar cells

Recent trends in performance specifications and functional requirements have brought about the need for high temperature metallization technology to be developed for survivable DOD space systems and to enhance solar cell reliability. The temperature constitution phase diagrams of selected binary and ternary systems were reviewed to determine the temperature and type of phase transformation present in the alloy systems. Of paramount interest are the liquid-solid and solid-solid transformations. Data are being utilized to aid in the selection of electrical contact materials to gallium arsenide solar cells. Published data on the phase diagrams for binary systems is readily available. However, information for ternary systems is limited. A computer model is being developed which will enable the phase equilibrium predictions for ternary systems where experimental data is lacking

Covariant Helicity-Coupling Amplitudes: A New Formulation

We have worked out covariant amplitudes for any two-body decay of a resonance with an arbitrary non-zero mass, which involves arbitrary integer spins in the initial and the final states. One key new ingredient for this work is the application of the total intrinsic spin operator $\vec S$ which is given directly in terms of the generators of the Poincar\'e group. Using the results of this study, we show how to explore the Lorentz factors which appear naturally, if the momentum-space wave functions are used to form the covariant decay amplitudes. We have devised a method of constructing our covariant decay amplitudes, such that they lead to the Zemach amplitudes when the Lorentz factors are set one

Parker-Jeans Instability of Gaseous Disks Including the Effect of Cosmic Rays

We use linear analysis to examine the effect of cosmic rays (CRs) on the Parker-Jeans instability of magnetized self-gravitating gaseous disks. We adopt a slab equilibrium model in which the gravity (including self-gravity) is perpendicular to the mid-plane, the magnetic field lies along the slab. CR is described as a fluid and only along magnetic field lines diffusion is considered. The linearised equations are solved numerically. The system is susceptible to Parker-Jeans instability. In general the system is less unstable when the CR diffusion coefficient is smaller (i.e., the coupling between the CRs and plasma is stronger). The system is also less unstable if CR pressure is larger. This is a reminiscence of the fact that Jeans instability and Parker instability are less unstable when the gas pressure is larger (or temperature is higher). Moreover, for large CR diffusion coefficient (or small CR pressure), perturbations parallel to the magnetic field are more unstable than those perpendicular to it. The other governing factor on the growth rate of the perturbations in different directions is the thickness of the disk or the strength of the external pressure on the disk. In fact, this is the determining factor in some parameter regimes.Comment: 19pages, 14figures submitted to Ap