MODELLING THE ELECTRON WITH COSSERAT ELASTICITY

Interactions between a finite number of bodies and the surrounding fluid, in a channel for instance, are investigated theoretically. In the planar model here the bodies or modelled grains are thin solid bodies free to move in a nearly parallel formation within a quasi-inviscid fluid. The investigation involves numerical and analytical studies and comparisons. The three main features that appear are a linear instability about a state of uniform motion, a clashing of the bodies (or of a body with a side wall) within a finite scaled time when nonlinear interaction takes effect, and a continuum-limit description of the body–fluid interaction holding for the case of many bodies

One-sided Cauchy-Stieltjes Kernel Families

This paper continues the study of a kernel family which uses the Cauchy-Stieltjes kernel in place of the celebrated exponential kernel of the exponential families theory. We extend the theory to cover generating measures with support that is unbounded on one side. We illustrate the need for such an extension by showing that cubic pseudo-variance functions correspond to free-infinitely divisible laws without the first moment. We also determine the domain of means, advancing the understanding of Cauchy-Stieltjes kernel families also for compactly supported generating measures

On the structure of contraction operators with applications to invariant subspaces

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/26407/1/0000494.pd

Intersections of Schubert varieties and eigenvalue inequalities in an arbitrary finite factor

It is known that the eigenvalues of selfadjoint elements a,b,c with a+b+c=0 in the factor R^omega (ultrapower of the hyperfinite II1 factor) are characterized by a system of inequalities analogous to the classical Horn inequalities of linear algebra. We prove that these inequalities are in fact true for elements of an arbitrary finite factor. A matricial (`complete') form of this result is equivalent to an embedding question formulated by Connes.Comment: 41 pages, many figure

Dilation theory and systems of simultaneous equations in the predual of an operator algebra. II

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46272/1/209_2005_Article_BF01163170.pd

Geodynamo and mantle convection simulations on the Earth Simulator using the Yin-Yang grid

We have developed finite difference codes based on the Yin-Yang grid for the geodynamo simulation and the mantle convection simulation. The Yin-Yang grid is a kind of spherical overset grid that is composed of two identical component grids. The intrinsic simplicity of the mesh configuration of the Yin-Yang grid enables us to develop highly optimized simulation codes on massively parallel supercomputers. The Yin-Yang geodynamo code has achieved 15.2 Tflops with 4096 processors on the Earth Simulator. This represents 46% of the theoretical peak performance. The Yin-Yang mantle code has enabled us to carry out mantle convection simulations in realistic regimes with a Rayleigh number of $10^7$ including strongly temperature-dependent viscosity with spatial contrast up to $10^6$.Comment: Plenary talk at SciDAC 200

Laws of large numbers for eigenvectors and eigenvalues associated to random subspaces in a tensor product

Given two positive integers $n$ and $k$ and a parameter $t\in (0,1)$, we choose at random a vector subspace $V_{n}\subset \mathbb{C}^{k}\otimes\mathbb{C}^{n}$ of dimension $N\sim tnk$. We show that the set of $k$-tuples of singular values of all unit vectors in $V_n$ fills asymptotically (as $n$ tends to infinity) a deterministic convex set $K_{k,t}$ that we describe using a new norm in $\R^k$. Our proof relies on free probability, random matrix theory, complex analysis and matrix analysis techniques. The main result result comes together with a law of large numbers for the singular value decomposition of the eigenvectors corresponding to large eigenvalues of a random truncation of a matrix with high eigenvalue degeneracy.Comment: v3 changes: minor typographic improvements; accepted versio

Rigorous mean field model for CPA: Anderson model with free random variables

A model of a randomly disordered system with site-diagonal random energy fluctuations is introduced. It is an extension of Wegner's $n$-orbital model to arbitrary eigenvalue distribution in the electronic level space. The new feature is that the random energy values are not assumed to be independent at different sites but free. Freeness of random variables is an analogue of the concept of independence for non-commuting random operators. A possible realization is the ensemble of at different lattice-sites randomly rotated matrices. The one- and two-particle Green functions of the proposed hamiltonian are calculated exactly. The eigenstates are extended and the conductivity is nonvanishing everywhere inside the band. The long-range behaviour and the zero-frequency limit of the two-particle Green function are universal with respect to the eigenvalue distribution in the electronic level space. The solutions solve the CPA-equation for the one- and two-particle Green function of the corresponding Anderson model. Thus our (multi-site) model is a rigorous mean field model for the (single-site) CPA. We show how the Llyod model is included in our model and treat various kinds of noises.Comment: 24 pages, 2 diagrams, Rev-Tex. Diagrams are available from the authors upon reques

African ancestry allelic variation at the MYH9 gene contributes to increased susceptibility to non-diabetic end-stage kidney disease in Hispanic Americans

Recent studies identified MYH9 as a major susceptibility gene for common forms of non-diabetic end-stage kidney disease (ESKD). A set of African ancestry DNA sequence variants comprising the E-1 haplotype, was significantly associated with ESKD. In order to determine whether African ancestry variants are also associated with disease susceptibility in admixed populations with differing genomic backgrounds, we genotyped a total of 1425 African and Hispanic American subjects comprising dialysis patients with diabetic and non-diabetic ESKD and controls, using 42 single nucleotide polymorphisms (SNPs) within the MYH9 gene and 40 genome-wide and 38 chromosome 22 ancestry informative markers. Following ancestry correction, logistic regression demonstrated that three of the E-1 SNPs are also associated with non-diabetic ESKD in the new sample sets of both African and Hispanic Americans, with a stronger association in Hispanic Americans. We also identified MYH9 SNPs that are even more powerfully associated with the disease phenotype than the E-1 SNPs. These newly associated SNPs, could be divided into those comprising a haplotype termed S-1 whose association was significant under a recessive or additive inheritance mode (rs5750248, OR 4.21, P < 0.01, Hispanic Americans, recessive), and those comprising a haplotype termed F-1 whose association was significant under a dominant or additive inheritance mode (rs11912763, OR 4.59, P < 0.01, Hispanic Americans, dominant). These findings strengthen the contention that a sequence variant of MYH9, common in populations with varying degrees of African ancestry admixture, and in strong linkage disequilibrium with the associated SNPs and haplotypes reported herein, strongly predisposes to non-diabetic ESKD