Charge transport in a spin-polarized 2D electron system in silicon

The temperature dependences of the conductivity σ(T) of a strongly interacting 2D electron system in silicon have been analyzed both in zero magnetic field and in a spin-polarizing magnetic field of 14.2 T that is parallel to the sample plane. The measurements were carried out in a wide temperature range of 1.4–9 K in the ballistic regime of electron-electron interaction, i.e., for Tτ > 1. In zero magnetic field, the data obtained for σ(T) are quantitatively described by the theory of interaction corrections. In the fully spin-polarized state, the measured σ(T) dependences are not linear and even nonmonotonic in the same temperature range, where the dependences σ(T) are monotonic in the absence of the field. Nevertheless, the low-temperature parts of the experimental σ(T) dependences are linear and qualitatively consistent with the calculated quantum corrections.     

Convergence Theory for Preconditioned Eigenvalue Solvers in a Nutshell

Preconditioned iterative methods for numerical solution of large matrix eigenvalue problems are increasingly gaining importance in various application areas, ranging from material sciences to data mining. Some of them, e.g., those using multilevel preconditioning for elliptic differential operators or graph Laplacian eigenvalue problems, exhibit almost optimal complexity in practice; i.e., their computational costs to calculate a fixed number of eigenvalues and eigenvectors grow linearly with the matrix problem size. Theoretical justification of their optimality requires convergence rate bounds that do not deteriorate with the increase of the problem size. Such bounds were pioneered by E. D’yakonov over three decades ago, but to date only a handful have been derived, mostly for symmetric eigenvalue problems. Just a few of known bounds are sharp. One of them is proved in doi: 10.1016/S0024-3795(01)00461-X for the simplest preconditioned eigensolver with a fixed step size. The original proof has been greatly simplified and shortened in doi: 10.1137/080727567 by using a gradient flow integration approach. In the present work, we give an even more succinct proof, using novel ideas based on Karush–Kuhn–Tucker theory and nonlinear programming.     

High-temperature X-ray diffraction studies of compounds in the M 2 I O-Ga2O3-TiO2 system

Compounds that are formed in the M ₂ ^I O-Ga₂O₃-TiO₂ system and crystallize in three structural types were prepared by solid-phase reactions. The M ₂ ^I Ga₂Ti₆O₁₆ (M^I = Na, K, Rb, Cs) compounds were prepared for the first time. The thermal expansion coefficients of LiGaTiO₄, Na₂Ga₂Ti₆O₁₆, K₂Ga₂Ti₆O₁₆, Rb₂Ga₂Ti₆O₁₆, and Cs₂Ga₂Ti₆O₁₆ were determined by high-temperature X-ray diffraction. Some tendencies of thermal distortions in M ₂ ^I A ₂ ^III Ti₆O₁₆ and LiA^IIITiO₄ (M^I = Na, K, Rb, Cs; A^III = Al, Cr, Fe, Ga) were disclosed.     

Selective adsorption of proteins on single-wall carbon nanotubes by using a protective surfactant

The dispersion of highly hydrophobic carbon materials such as carbon nanotubes in biological media is a challenging issue. Indeed, the nonspecific adsorption of proteins occurs readily when the nanotubes are introduced in biological media; therefore, a methodology to control adsorption is in high demand. To address this issue, we developed a bifunctional linker derived from pyrene that selectively enables or prevents the adsorption of proteins on single-wall carbon nanotubes (SWNTs). We demonstrated that it is possible to decrease or completely suppress the adsorption of proteins on the nanotube sidewall by using proper functionalization (either covalent or noncovalent). By subsequently activating the functional groups on the nanotube derivatives, protein adsorption can be recovered and, therefore, controlled. Our approach is simple, straightforward, and potentially suitable for other biomolecules that contain thio or amino groups available for coupling.     

Optical spectroscopy and electronic structure of compounds HoNi5 − x Al x (x = 0, 1, 2)

The optical properties of the compounds HoNi_{5 ? x} Al _x (x = 0, 1, 2) have been investigated using the ellipsometric method in the wavelength range from 0.22 to 16 μm. The electronic structure of these intermetallic compounds has been calculated in the local electron-spin density approximation with the correction for strong electronic interactions in the 4f shell of the holmium ions. The experimental dispersion dependences of optical conductivity in the region of interband light absorption have been interpreted based on the results of the calculation of the electron density of states. The plasma and relaxation frequencies of electrons have been determined.     

Extension theorems for Stokes and Lamé equations for nearly incompressible media and their applications to numerical solution of problems with highly discontinuous coefficients

We prove extension theorems in the norms described by Stokes and Lamé operators for the three‐dimensional case with periodic boundary conditions. For the Lamé equations, we show that the extension theorem holds for nearly incompressible media, but may fail in the opposite limit, i.e. for case of absolutely compressible media. We study carefully the latter case and associate it with the Cosserat problem. Extension theorems serve as an important tool in many applications, e.g. in domain decomposition and fictitious domain methods, and in analysis of finite element methods. We consider an application of established extension theorems to an efficient iterative solution technique for the isotropic linear elasticity equations for nearly incompressible media and for the Stokes equations with highly discontinuous coefficients. The iterative method involves a special choice for an initial guess and a preconditioner based on solving a constant coefficient problem. Such preconditioner allows the use of well‐known fast algorithms for preconditioning. Under some natural assumptions on smoothness and topological properties of subdomains with small coefficients, we prove convergence of the simplest Richardson method uniform in the jump of coefficients. For the Lamé equations, the convergence is also uniform in the incompressible limit. Our preliminary numerical results for two‐dimensional diffusion problems show fast convergence uniform in the jump and in the mesh size parameter. Copyright © 2002 John Wiley & Sons, Ltd.