Advances in classical and quantum wave dynamics on quasiperiodic lattices : a dissertation submitted for the degree of Doctor of Philosophy in Physics, Centre for Theoretical Chemistry and Physics, New Zealand Institute for Advanced Study, Massey University, Albany, New Zealand

Lattices and discrete networks are cornerstones of a number of scientific subjects. In condensed matter, optical lattices allowed the experimental realization of several theoretically predicted phenomena. Indeed, these structures constitute ideal benchmarks for light and wave propagation experiments involving interacting particles, such as clouds of ultra-cold atoms that Bose-Einstein condensate. Moreover, they allow experimental design of particular lattice topologies, as well as the implementation of several classes of spatial perturbations. For example, Anderson localization being observed for the first time in atomic Bose-Einstein condensate experiments and Aubry-André localization discovered with light propagating through networks of optical waveguide. This thesis considers different types of lattices in the presence of quasiperiodic modulations, mainly the celebrated Aubry-André potential. Particular attention will be given to spectral properties of models, localization features of eigenmodes and the transition from delocalized (metallic) eigenstates to localized (insulating) ones within the energy spectrum. We additionally discuss the relation between the model’s properties and the dynamics of particles hopping along the lattice. After introducing the linear discrete Schrödinger equation, we first discuss the spectral properties of the Aubry-André model. We then study the transition between metallic and insulating regimes of a class of quasiperiodic potentials constructed as an iterative superposition of periodic potentials with increasing spatial period. Next, we discuss the Aubry-André perturbation of flat-band topologies, their energy-dependent transition (mobility edge), which can be expressed in analytical forms in case of specific onsite energy correlations, highlighting existence of zeroes, singularities and divergences. We then discuss two cases of driven one-dimensional lattices, namely an Aubry-André chain with a weak time-space periodic driving and an Anderson chain with a quasiperiodic multi-frequency driving. We show anaytically and numerically how drivings can lift the respective localization and generate delocalization by design. Finally we discuss the problem of the possible generation of correlated metallic states of two interacting particles problem in one dimensional Aubry-André chains, under a coherent drive of the interaction

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.

Changes in the Indicator Properties of Narrow Monetary Aggregates

Although many countries have abandoned monetary targeting in recent decades, monetary aggregates are still useful indicators of future economic activity. Past research has shown that, compared with other monetary aggregates and expressed in real terms, net M1 and gross M1 have traditionally provided superior leading information for output growth. Yet financial innovations and the elimination of reserve requirements over the past two decades have made it increasingly difficult for financial institutions to differentiate between demand and notice deposits, suggesting the need to re-examine the information content of narrow monetary aggregates that depend on such a distinction. Based on an analysis over a sample period from 1975Q1 to 2005Q1, the authors determine that the leading-indicator properties of the narrow monetary aggregates for output growth have shifted over time and that, since 1993, real M1+ has become a better indicator of future output growth than real gross and net M1.

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