Foliated Lie systems: Theory and applications

A $\mathcal{F}$- foliated Lie system is a first-order system of ordinary differential equations whose particular solutions are contained in the leaves of the foliation $\mathcal{F}$ and all particular solutions within any leaf can be written as a certain function, a so-called foliated superposition rule, of a family of particular solutions of the system within the same leaf and several parameters. We analyse the properties of such systems and we illustrate our results by studying Lax pairs and a class of $t$-dependent Hamiltonian systems. We finally study foliated Lie systems through Poisson structures and $r$-matrices.Comment: 24 page

Spin injection from a half-metal at finite temperatures

Spin injection from a half-metallic electrode in the presence of thermal spin disorder is analyzed using a combination of random matrix theory, spin-diffusion theory, and explicit simulations for the tight-binding s-d model. It is shown that efficient spin injection from a half-metal is possible as long as the effective resistance of the normal metal does not exceed a characteristic value, which does not depend on the resistance of the half-metallic electrode, but is rather controlled by spin-flip scattering at the interface. This condition can be formulated as \alpha<(l/L)/T, where \alpha is the relative deviation of the magnetization from saturation, l and L the mean-free path and the spin-diffusion length in the non-magnetic channel, and T the transparency of the tunnel barrier at the interface (if present). The general conclusions are confirmed by tight-binding s-d model calculations. A rough estimate suggests that efficient spin injection from true half-metallic ferromagnets into silicon or copper may be possible at room temperature across a transparent interface.Comment: 9 pages, 4 figures, revtex4-1; expanded introduction, added references, additional comments in Section V, fixed typo

Portfolio preferences of foreign institutional investors

The authors examine the relationship between foreign investment and the attributes of emerging market countries and firms in which investment is made. Their findings indicate that countries with higher levels of economic development and floating exchange rate regimes tend to have greater ability to obtain foreign capital. After controlling for the country's level of economic development, they find that firms in countries with stronger shareholder rights and legal framework attract more foreign capital. The authors also find that foreign institutions allocate more of their assets to firms with better corporate governance after controlling for other country and firm attributes. The main firm-level measures of corporate governance are derived from accounting quality variables. Their results imply that steps can be taken both at the country and the firm level to create an environment conducive to foreign portfolio investment. The analysis is based on a unique dataset consisting of equity positions of U.S. mutual funds in emerging markets.Payment Systems&Infrastructure,Economic Theory&Research,Labor Policies,International Terrorism&Counterterrorism,Financial Intermediation,International Terrorism&Counterterrorism,Economic Theory&Research,Financial Intermediation,Environmental Economics&Policies,Banks&Banking Reform

Obstacles to Inclusion: One Early Childhood Inclusive Teacher’s Perspective

In spite of the attention given to the topic of including children and youth diagnosed with emotional and behavioral disorders in general education classrooms; there has been an absence of empirically sound research to guide policy and practice. With the passage of The Individuals with Disabilities Education Act (IDEA) there has been an increase of students with cognitive, social and emotional disorders included in general education classrooms. Significant debate continues to surround the issue of students with emotional and behavior disorders and other disabilities for placement in general education settings. This chapter will explore the experience of one such environment in which several students with emotional disturbances are included in a first grade classroom. The frustrated teacher expressed a perceived lack of knowledge in handling behaviors and persistent feelings of helplessness. She struggled with how to handle the behaviors of the students with emotional disturbances and questioned if their inclusion in the general education classroom was best for all. Although the outbursts and negative behaviors did not cease; it was observed with consistent approaches to addressing behavior, the teacher was successful at cultivating empathy among students and examples of positive behaviors and care were shown in student interactions

Explaining LIGO's observations via isolated binary evolution with natal kicks

We compare binary evolution models with different assumptions about black-hole natal kicks to the first gravitational-wave observations performed by the LIGO detectors. Our comparisons attempt to reconcile merger rate, masses, spins, and spin-orbit misalignments of all current observations with state-of-the-art formation scenarios of binary black holes formed in isolation. We estimate that black holes (BHs) should receive natal kicks at birth of the order of $\sigma\simeq 200$ (50) km/s if tidal processes do (not) realign stellar spins. Our estimate is driven by two simple factors. The natal kick dispersion $\sigma$ is bounded from above because large kicks disrupt too many binaries (reducing the merger rate below the observed value). Conversely, the natal kick distribution is bounded from below because modest kicks are needed to produce a range of spin-orbit misalignments. A distribution of misalignments increases our models' compatibility with LIGO's observations, if all BHs are likely to have natal spins. Unlike related work which adopts a concrete BH natal spin prescription, we explore a range of possible BH natal spin distributions. Within the context of our models, for all of the choices of $\sigma$ used here and within the context of one simple fiducial parameterized spin distribution, observations favor low BH natal spin.Comment: 19 pages, 14 figures, as published in PR

First-principles analysis of spin-disorder resistivity of Fe and Ni

Spin-disorder resistivity of Fe and Ni and its temperature dependence are analyzed using noncollinear density functional calculations within the supercell method. Different models of thermal spin disorder are considered, including the mean-field approximation and the nearest-neighbor Heisenberg model. Spin-disorder resistivity is found to depend weakly on magnetic short-range order. If the local moments are kept frozen at their zero-temperature values, very good agreement with experiment is obtained for Fe, but for Ni the resistivity at elevated temperatures is significantly overestimated. Agreement with experiment for Fe is improved if the local moments are iterated to self-consistency. The overestimation of the resistivity for paramagnetic Ni is attributed to the reduction of the local moments down to 0.35 Bohr magnetons. Overall, the results suggest that low-energy spin fluctuations in Fe and Ni are better viewed as classical rotations of local moments rather than quantized spin fluctuations that would require an (S+1)/S correction.Comment: 10 pages (RevTeX), 6 eps figure

Calculations of spin-disorder resistivity from first principles

Spin-disorder resistivity of Fe and Ni is studied using the noncollinear density functional theory. The Landauer conductance is averaged over random disorder configurations and fitted to Ohm's law. The distribution function is approximated by the mean-field theory. The dependence of spin-disorder resistivity on magnetization in Fe is found to be in excellent agreement with the results for the isotropic s-d model. In the fully disordered state, spin-disorder resistivity for Fe is close to experiment, while for fcc Ni it exceeds the experimental value by a factor of 2.3. This result indicates strong magnetic short-range order in Ni at the Curie temperature.Comment: 3 pages, 3 figure