Elementary Secondary Education Act, Title II Print Expenditures for 1965 – 1966 in Washington State Public Schools

The purpose of this thesis was to compile and report the data showing existing print materials for the public schools in the State of Washington, as shown in the library inventories for the school year 1965-66, and to show the expenditures for Title II, Public Law 89-10 during the same school year, for print materials

The Diversity of Exoplanets: From Interior Dynamics to Surface Expressions

The coupled interior–atmosphere system of terrestrial exoplanets remains poorly understood. Exoplanets show a wide variety of sizes, densities, surface temperatures, and interior structures, with important knock-on effects for this coupled system. Many exoplanets are predicted to have a “stagnant lid” at the surface, with a rigid stationary crust, sluggish mantle convection, and only minor volcanism. However, if exoplanets have Earth-like plate tectonics, which involves several discrete, slowly moving plates and vigorous tectono-magmatic activity, then this may be critical for planetary habitability and have implications for the development (and evolution) of life in the galaxy. Here, we summarize our current knowledge of coupled planetary dynamics in the context of exoplanet diversity

Decision-Directed Detector For Overlapping PCM/NRZ Signals

A decision-directed (DD) technique for the detection of overlapping PCM/NRZ signals in the presence of white Gaussian noise is investigated. The performance of the DD detector is represented by probability of error PE versus input signal-to-noise ratio (SNR). To examine how much improvement in performance can be achieved with this technique, PE\u27s with and without DD feedback are evaluated in parallel. Further, analytical results are compared with those found by Monte Carlo simulations. The results are shown in good agreement. © 1973, IEEE. All rights reserved

Logarithmic delocalization of end spins in the S=3/2 antiferromagnetic Heisenberg chain

Using the DMRG method we calculate the surface spin correlation function, $C_L(l)=$, in the spin $S=3/2$ antiferromagnetic Heisenberg chain. For comparison we also investigate the $S=1/2$ chain with S=1 impurity end spins and the S=1 chain. In the half-integer spin models the end-to-end correlations are found to decay to zero logarithmically, $C_L(1)\sim (\log L)^{-2d}$, with $d=0.13(2)$. We find no surface order, in clear contrast with the behavior of the S=1 chain, where exponentially localized end spins induce finite surface correlations. The lack of surface order implies that end spins do not exist in the strict sense. However, the system possesses a logarithmically weakly delocalizing boundary excitation, which, for any chain lengths attainable numerically or even experimentally, creates the illusion of an end spin. This mode is responsible for the first gap, which vanishes asymptotically as $\Delta_1 \approx (\pi v_S d)/(L\ln L)$, where $v_S$ is the sound velocity and $d$ is the logarithmic decay exponent. For the half-integer spin models our results on the surface correlations and on the first gap support universality. Those for the second gap are less conclusive, due to strong higher-order corrections.Comment: 10 pages, 8 figure

Quantum criticality of dipolar spin chains

We show that a chain of Heisenberg spins interacting with long-range dipolar forces in a magnetic field h perpendicular to the chain exhibits a quantum critical point belonging to the two-dimensional Ising universality class. Within linear spin-wave theory the magnon dispersion for small momenta k is [Delta^2 + v_k^2 k^2]^{1/2}, where Delta^2 \propto |h - h_c| and v_k^2 \propto |ln k|. For fields close to h_c linear spin-wave theory breaks down and we investigate the system using density-matrix and functional renormalization group methods. The Ginzburg regime where non-Gaussian fluctuations are important is found to be rather narrow on the ordered side of the transition, and very broad on the disordered side.Comment: 6 pages, 5 figure

Cluster-based feedback control of turbulent post-stall separated flows

We propose a novel model-free self-learning cluster-based control strategy for general nonlinear feedback flow control technique, benchmarked for high-fidelity simulations of post-stall separated flows over an airfoil. The present approach partitions the flow trajectories (force measurements) into clusters, which correspond to characteristic coarse-grained phases in a low-dimensional feature space. A feedback control law is then sought for each cluster state through iterative evaluation and downhill simplex search to minimize power consumption in flight. Unsupervised clustering of the flow trajectories for in-situ learning and optimization of coarse-grained control laws are implemented in an automated manner as key enablers. Re-routing the flow trajectories, the optimized control laws shift the cluster populations to the aerodynamically favorable states. Utilizing limited number of sensor measurements for both clustering and optimization, these feedback laws were determined in only $O(10)$ iterations. The objective of the present work is not necessarily to suppress flow separation but to minimize the desired cost function to achieve enhanced aerodynamic performance. The present control approach is applied to the control of two and three-dimensional separated flows over a NACA 0012 airfoil with large-eddy simulations at an angle of attack of $9^\circ$, Reynolds number $Re = 23,000$ and free-stream Mach number $M_\infty = 0.3$. The optimized control laws effectively minimize the flight power consumption enabling the flows to reach a low-drag state. The present work aims to address the challenges associated with adaptive feedback control design for turbulent separated flows at moderate Reynolds number.Comment: 32 pages, 18 figure

Condensation of magnons and spinons in a frustrated ladder

Motivated by the ever-increasing experimental effort devoted to the properties of frustrated quantum magnets in a magnetic field, we present a careful and detailed theoretical analysis of a one-dimensional version of this problem, a frustrated ladder with a magnetization plateau at m=1/2. We show that even for purely isotropic Heisenberg interactions, the magnetization curve exhibits a rather complex behavior that can be fully accounted for in terms of simple elementary excitations. The introduction of anisotropic interactions (e.g., Dzyaloshinskii-Moriya interactions) modifies significantly the picture and reveals an essential difference between integer and fractional plateaux. In particular, anisotropic interactions generically open a gap in the region between the plateaux, but we show that this gap closes upon entering fractional plateaux. All of these conclusions, based on analytical arguments, are supported by extensive Density Matrix Renormalization Group calculations.Comment: 15 pages, 15 figures. minor changes in tex