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

Sources of class conscousness: the experience of women workers in South Africa, 1973-1980

African Studies Center Working Paper No. 5

Strong renewal theorems and local large deviations for multivariate random walks and renewals

We study a random walk $\mathbf{S}_n$ on $\mathbb{Z}^d$ ($d\geq 1$), in the domain of attraction of an operator-stable distribution with index $\boldsymbol{\alpha}=(\alpha_1,\ldots,\alpha_d) \in (0,2]^d$: in particular, we allow the scalings to be different along the different coordinates. We prove a strong renewal theorem, $i.e.$ a sharp asymptotic of the Green function $G(\mathbf{0},\mathbf{x})$ as $\|\mathbf{x}\|\to +\infty$, along the "favorite direction or scaling": (i) if $\sum_{i=1}^d \alpha_i^{-1} < 2$ (reminiscent of Garsia-Lamperti's condition when $d=1$ [Comm. Math. Helv. $\mathbf{37}$, 1962]); (ii) if a certain $local$ condition holds (reminiscent of Doney's condition [Probab. Theory Relat. Fields $\mathbf{107}$, 1997] when $d=1$). We also provide uniform bounds on the Green function $G(\mathbf{0},\mathbf{x})$, sharpening estimates when $\mathbf{x}$ is away from this favorite direction or scaling. These results improve significantly the existing literature, which was mostly concerned with the case $\alpha_i\equiv \alpha$, in the favorite scaling, and has even left aside the case $\alpha\in[1,2)$ with non-zero mean. Most of our estimates rely on new general (multivariate) local large deviations results, that were missing in the literature and that are of interest on their own.Comment: 46 pages, comments are welcom

Comments on the Influence of Disorder for Pinning Model in Correlated Gaussian Environment

We study the random pinning model, in the case of a Gaussian environment presenting power-law decaying correlations, of exponent decay a>0. We comment on the annealed (i.e. averaged over disorder) model, which is far from being trivial, and we discuss the influence of disorder on the critical properties of the system. We show that the annealed critical exponent \nu^{ann} is the same as the homogeneous one \nu^{pur}, provided that correlations are decaying fast enough (a>2). If correlations are summable (a>1), we also show that the disordered phase transition is at least of order 2, showing disorder relevance if \nu^{pur}<2. If correlations are not summable (a<1), we show that the phase transition disappears.Comment: 23 pages, 1 figure Modifications in v2 (outside minor typos): Assumption 1 on correlations has been simplified for more clarity; Theorem 4 has been improved to a more general underlying renewal distribution; Remark 2.1 added, on the assumption on the correlations in the summable cas

Book Review: Population, Consumption, and the Environment: Religious and Secular Responses

A review of Population, Consumption, and the Environment: Religious and Secular Responses, edited by Harold Coward

Multivariable (φ,Γ)(\varphi,\Gamma)-modules and locally analytic vectors

Let $K$ be a finite extension of $\mathbf{Q}_p$ and let $G_K = \mathrm{Gal}(\bar{\mathbf{Q}}_p/K)$. There is a very useful classification of $p$-adic representations of $G_K$ in terms of cyclotomic $(\varphi,\Gamma)$-modules (cyclotomic means that $\Gamma={\rm Gal}(K_\infty/K)$ where $K_\infty$ is the cyclotomic extension of $K$). One particularly convenient feature of the cyclotomic theory is the fact that any $(\varphi,\Gamma)$-module is overconvergent. Questions pertaining to the $p$-adic local Langlands correspondence lead us to ask for a generalization of the theory of $(\varphi,\Gamma)$-modules, with the cyclotomic extension replaced by an infinitely ramified $p$-adic Lie extension $K_\infty / K$. It is not clear what shape such a generalization should have in general. Even in the case where we have such a generalization, namely the case of a Lubin-Tate extension, most $(\varphi,\Gamma)$-modules fail to be overconvergent. In this article, we develop an approach that gives a solution to both problems at the same time, by considering the locally analytic vectors for the action of $\Gamma$ inside some big modules defined using Fontaine's rings of periods. We show that, in the cyclotomic case, we recover the ususal overconvergent $(\varphi,\Gamma)$-modules. In the Lubin-Tate case, we can prove, as an application of our theory, a folklore conjecture in the field stating that $(\varphi,\Gamma)$-modules attached to $F$-analytic representations are overconvergent.Comment: v8: final version, to appear in the Duke Math Journal. (In v2, the monodromy conjecture from v1 has been proved. In v3 and then v4, the restriction on ramification has been completely removed. In v5 the introduction has been rewritten. In v6 and v7 there are some improvements