Influence Of Current Leads On Critical Current For Spin Precession In Magnetic Multilayers

In magnetic multilayers, a dc current induces a spin precession above a certain critical current. Drive torques responsible for this can be calculated from the spin accumulation $\bar{\Delta\mu}$. Existing calculations of $\bar{\Delta\mu}$ assume a uniform cross section of conductors. But most multilayer samples are pillars with current leads flaring out immediately to a much wider cross-section area than that of the pillar itself. We write spin-diffusion equations of a form valid for variable cross section, and solve the case of flat electrodes with radial current distribution perpendicular to the axis of the pillar. Because of the increased volume available for conduction-electron spin relaxation in such leads, $\bar{\Delta\mu}$ is reduced in the pillar by at least a factor of 2 below its value for uniform cross section, for given current density in the pillar. Also, $\bar{\Delta\mu}$ and the critical current density for spin precession become nearly independent of the thickness of the pinned magnetic layer, and more dependent on the thickness of the spacer, in better agreement with measurements by Albert et al. (2002).Comment: To appear in J. Magn. Magn. Mate

Why Solve the Hamiltonian Constraint in Numerical Relativity?

The indefinite sign of the Hamiltonian constraint means that solutions to Einstein's equations must achieve a delicate balance--often among numerically large terms that nearly cancel. If numerical errors cause a violation of the Hamiltonian constraint, the failure of the delicate balance could lead to qualitatively wrong behavior rather than just decreased accuracy. This issue is different from instabilities caused by constraint-violating modes. Examples of stable numerical simulations of collapsing cosmological spacetimes exhibiting local mixmaster dynamics with and without Hamiltonian constraint enforcement are presented.Comment: Submitted to a volume in honor of Michael P. Ryan, Jr. Based on talk given at GR1

Persistent bundles over a two dimensional compact set

The $C^1$-structurally stable diffeomorphims of a compact manifold are those that satisfy Axiom A and the strong transversality condition (AS). We generalize the concept of AS from diffeomorphisms to invariant compact subsets. Among other properties, we show the structural stability of the AS invariant compact sets $K$ of surface diffeomorphisms $f$. Moreover if $\hat f$ is the dynamics of a compact manifold, which fibers over $f$ and such that the bundle is normally hyperbolic over the non-wandering set of $f_{|K}$, then the bundle over $K$ is persistent. This provides non trivial examples of persistent laminations that are not normally hyperbolic.Comment: 32 p. The proof is much more (10 p.) detailed than previousl

Multivariable Lubin-Tate (\phi,\Gamma)-modules and filtered \phi-modules

We define some rings of power series in several variables, that are attached to a Lubin-Tate formal module. We then give some examples of (\phi,\Gamma)-modules over those rings. They are the global sections of some reflexive sheaves on the p-adic open unit polydisk, that are constructed from a filtered \phi-module using a modification process. We prove that we obtain every crystalline (\phi,\Gamma)-module over those rings in this way.Comment: This version corrects a mistake from v1: the module M^+(D) is reflexive, but I do not know whether or not it is projective in general. The main theorems and various definitions have been amended as a result. Some other less significant mistakes have been corrected as well. 22 page

Review Of Hiring And Firing Public Officials: Rethinking The Purpose Of Elections By J. Buchler

Few books can be called workmanlike as well as exciting, analytic as well as poignant. Hiring and Firing Public Officials achieves those rare pairings by methodically pursuing an academic coup. Justin Buchler aims to replace electoral theory's dominant “market paradigm”—whose pioneers include Joseph Schumpeter (Capitalism, Socialism and Democracy, 1942) and Anthony Downs (An Economic Model of Democracy, 1957)—with a more accurate “employment model,” and to defend that new model against all manner of attack. Buchler prosecutes his goals doggedly, repetitively, and quite effectively. The result is an intelligent, important new book that may not dazzle but will challenge settled convictions and change more than a few minds. The author's occasionally defensive tone is understandable given the nature of his ambition. His book advocates paradigmatic revolution and, to borrow from Mao Zedong, revolution is not a dinner party.</jats:p