Renormalization-group theory for rotating 4He near the superfluid transition

The influence of a uniform rotation with frequency Omega on the critical behavior of liquid 4He near T_lambda is investigated. We apply our recently developed approach which is a renormalization-group theory based on model F starting with the calculation of the Green's function in Hartree approximation. We calculate the specific heat, the correlation length, and the thermal resistivity tensor as functions of the temperature T for fixed values of the rotation frequency Omega. For nonzero Omega we find that all physical quantities are smooth near T_lambda so that the superfluid transition is a smooth crossover. We define a frequency-dependent transition temperature T_lambda(Omega) by the maximum of the specific heat and present a power law prediction. For T<T_lambda(Omega) we find mutual friction between the superfluid and the normal-fluid component caused implicitly by the motion of vortex lines and calculate the Vinen coefficients B and B'.Comment: 16 pages, 4 figure

The Influence of Beating of Pulp on Fiber Length and Fiber Length Distribution

1. Introduction Recent studies and researchers assume that certain relationships exist between different properties of pulp - such as between bulk, tearing resistance, bursting strength, tensile strength, freeness, and fiber length index. It has been found furthermore that such relations are different for different types of pulp and that some may even vary from pulp to pulp of the same type

The symplectic ideal and a double centraliser theorem

Let G be a reductive connected linear algebraic group over an algebraically closed field of positive characteristic and let g be its Lie algebra. First we correct and generalise a well-known result about the Picard group of G. Then we prove that, if the derived group is simply connected and \g satisfies a mild condition, the algebra K[G]^g of regular functions on G that are invariant under the action of g derived from the conjugation action, is a unique factorisation domain

Band width estimates via the Dirac operator

Let $M$ be a closed connected spin manifold such that its spinor Dirac operator has non-vanishing (Rosenberg) index. We prove that for any Riemannian metric on $V = M \times [-1,1]$ with scalar curvature bounded below by $\sigma > 0$, the distance between the boundary components of $V$ is at most $C_n/\sqrt{\sigma}$, where $C_n = \sqrt{(n-1)/{n}} \cdot C$ with $C < 8(1+\sqrt{2})$ being a universal constant. This verifies a conjecture of Gromov for such manifolds. In particular, our result applies to all high-dimensional closed simply connected manifolds $M$ which do not admit a metric of positive scalar curvature. We also establish a quadratic decay estimate for the scalar curvature of complete metrics on manifolds, such as $M \times \mathbb{R}^2$, which contain $M$ as a codimension two submanifold in a suitable way. Furthermore, we introduce the "$\mathcal{KO}$-width" of a closed manifold and deduce that infinite $\mathcal{KO}$-width is an obstruction to positive scalar curvature.Comment: 24 pages, 2 figures; v2: minor additions and improvements; v3: minor corrections and slightly improved estimates. To appear in J. Differential Geo

Coarse median structures and homomorphisms from Kazhdan groups

We study Bowditch's notion of a coarse median on a metric space and formally introduce the concept of a coarse median structure as an equivalence class of coarse medians up to closeness. We show that a group which possesses a uniformly left-invariant coarse median structure admits only finitely many conjugacy classes of homomorphisms from a given group with Kazhdan's property (T). This is a common generalization of a theorem due to Paulin about the outer automorphism group of a hyperbolic group with property (T) as well as of a result of Behrstock-Drutu-Sapir on the mapping class groups of orientable surfaces. We discuss a metric approximation property of finite subsets in coarse median spaces extending the classical result on approximation of Gromov hyperbolic spaces by trees.Comment: 23 pages, v2: Minor revision following the referee's suggestions. The final publication is available at link.springer.com via https://doi.org/10.1007/s10711-015-0090-