Correlation time and diffusion coefficient imaging: application to a granular flow system

A parametric method for spatially resolved measurements for velocity autocorrelation functions, R(u)(tau) = , expressed as a sum of exponentials, is presented. The method is applied to a granular flow system of 2-mm oil-filled spheres rotated in a half-filled horizontal cylinder, which is an Ornstein-Uhlenbeck process with velocity autocorrelation function R(u)(tau) = e(- ||tau ||/tau(c)), where tau(c) is the correlation time and D = tau(c) is the diffusion coefficient. The pulsed-field-gradient NMR method consists of applying three different gradient pulse sequences of varying motion sensitivity to distinguish the range of correlation times present for particle motion. Time-dependent apparent diffusion coefficients are measured for these three sequences and tau(c) and D are then calculated from the apparent diffusion coefficient images. For the cylinder rotation rate of 2.3 rad/s, the axial diffusion coefficient at the top center of the free surface was 5.5 x 10(-6) m(2)/s, the correlation time was 3 ms, and the velocity fluctuation or granular temperature was 1.8 x 10(-3) m(2)/s(2). This method is also applicable to study transport in systems involving turbulence and porous media flows.     

Hydrodynamic dispersion in $ \beta$ -lactoglobulin gels measured by PGSE NMR

The displacement scale dependent molecular dynamics of solvent water molecules flowing through b \beta -lactoglobulin gels are measured by pulse gradient spin echo (PGSE) nuclear magnetic resonance (NMR). Gels formed under different p H conditions generate structures which are characterized by magnetic resonance imaging (MRI) and PGSE NMR measured dynamics as homogeneous and heterogeneous. The data presented clearly demonstrate the applicability of the theoretical framework for modeling hydrodynamic dispersion to the analysis of protein gels.     

Facile Hydrolysis and Alcoholysis of Palladium Acetate

Palladium(II) acetate is readily converted into [Pd₃(μ²‐OH)(OAc)₅] ( 1 ) in the presence of water in a range of organic solvents and is also slowly converted in the solid state. Complex 1 can also be formed in nominally anhydrous solvents. Similarly, the analogous alkoxide complexes [Pd₃(μ²‐OR)(OAc)₅] ( 3 ) are easily formed in solutions of palladium(II) acetate containing a range of alcohols. An examination of a representative Wacker‐type oxidation shows that the Pd‐OH complex 1 and a related Pd‐oxo complex 4 can be excluded as potential catalytic intermediates in the absence of exogenous water.     

Hilbert-Carleman and regularized determinants for linear operators

A general theory of regularized and Hilbert-Carleman determinants in normed algebras of operators acting in Banach spaces is proposed. In this approach regularized determinants are defined as continuous extensions of the corresponding determinants of finite dimensional operators. We characterize the algebras for which such extensions exist, describe the main properties of the extended determinants, obtain Cramer's rule and the formulas for the resolvent which are expressed via the extended tracestr(A ^k ) of iterations and regularized determinants.This paper is a continuation of the paper [GGKr].     

Packing and covering with matroid circuits

We prove a conjecture of Welsh, that for every matroid M without coloops, ν(M) + θ(M) ≤ ?(M) + κ(M) where ν(M) is the maximum number of pairwise disjoint circuits, θ(M) is the minimum number of circuits whose union is E(M), ?(M) is the corank of M, and κ(M) is the number of connected components of M. For binary matroids the result was previously proved by Oxley.