A low dimensional dynamical system for the wall layer

Low dimensional dynamical systems which model a fully developed turbulent wall layer were derived.The model is based on the optimally fast convergent proper orthogonal decomposition, or Karhunen-Loeve expansion. This decomposition provides a set of eigenfunctions which are derived from the autocorrelation tensor at zero time lag. Via Galerkin projection, low dimensional sets of ordinary differential equations in time, for the coefficients of the expansion, were derived from the Navier-Stokes equations. The energy loss to the unresolved modes was modeled by an eddy viscosity representation, analogous to Heisenberg's spectral model. A set of eigenfunctions and eigenvalues were obtained from direct numerical simulation of a plane channel at a Reynolds number of 6600, based on the mean centerline velocity and the channel width flow and compared with previous work done by Herzog. Using the new eigenvalues and eigenfunctions, a new ten dimensional set of ordinary differential equations were derived using five non-zero cross-stream Fourier modes with a periodic length of 377 wall units. The dynamical system was integrated for a range of the eddy viscosity prameter alpha. This work is encouraging

Recent Developments in the Monetary Aggregates and Their Implications

Narrow Money-Transactions Money The growth rate of the narrow monetary aggregates picked up in 1999, reflecting the expansion in economic activity and the stabilization of interest rates. The sharp acceleration of the narrow aggregates in recent months suggests buoyant growth in GDP in coming quarters. Signs of a possible rise in inflation are also emerging. Over the longer run, for inflation to remain in the Bank's 1 to 3 per cent target range, the growth of narrow money would have to slow down from its current pace. In 1999, the growth rate of M1 also began to converge with that of the other narrow aggregates, M1+ and M1++. This suggests that the influence of the special factors that have been affecting the growth rate of M1 has diminished. Broad Money-"Store of Value" Household savings represent deferred consumption, and therefore the broad monetary aggregate provides information about future spending and, hence, inflation. In 1999, the very broad measure of money, M2++, grew at much the same rate as it did in 1998. This outcome is in line with inflation remaining in the inflation-control target range over the next couple of years.

Foreign Accents, Language Acquisition, And Cerebral Dominance 1

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/98150/1/j.1467-1770.1969.tb00466.x.pd