Interest And Interest-Driven Learning

This entry addresses the role of people’s interest in out-of-school learning contexts (including everyday experiences and hobbies) and participation in designed settings (e.g., museum exhibits) or programs (e.g., 4-H groups), although interest can be triggered and supported to develop both in school and out of school. It provides information about the definition of interest, the development of interest, and indicators for measuring interest and its change over time

How hosts control worms

No abstract available

Gravitational waveforms with controlled accuracy

A partially first-order form of the characteristic formulation is introduced to control the accuracy in the computation of gravitational waveforms produced by highly distorted single black hole spacetimes. Our approach is to reduce the system of equations to first-order differential form on the angular derivatives, while retaining the proven radial and time integration schemes of the standard characteristic formulation. This results in significantly improved accuracy over the standard mixed-order approach in the extremely nonlinear post-merger regime of binary black hole collisions.Comment: Revised version, published in Phys. Rev. D, RevTeX, 16 pages, 4 figure

Systematic Inclusion of High-Order Multi-Spin Correlations for the Spin-121\over2 XXZXXZ Models

We apply the microscopic coupled-cluster method (CCM) to the spin-$1\over2$ $XXZ$ models on both the one-dimensional chain and the two-dimensional square lattice. Based on a systematic approximation scheme of the CCM developed by us previously, we carry out high-order {\it ab initio} calculations using computer-algebraic techniques. The ground-state properties of the models are obtained with high accuracy as functions of the anisotropy parameter. Furthermore, our CCM analysis enables us to study their quantum critical behavior in a systematic and unbiased manner.Comment: (to appear in PRL). 4 pages, ReVTeX, two figures available upon request. UMIST Preprint MA-000-000

Bondian frames to couple matter with radiation

A study is presented for the non linear evolution of a self gravitating distribution of matter coupled to a massless scalar field. The characteristic formulation for numerical relativity is used to follow the evolution by a sequence of light cones open to the future. Bondian frames are used to endow physical meaning to the matter variables and to the massless scalar field. Asymptotic approaches to the origin and to infinity are achieved; at the boundary surface interior and exterior solutions are matched guaranteeing the Darmois--Lichnerowicz conditions. To show how the scheme works some numerical models are discussed. We exemplify evolving scalar waves on the following fixed backgrounds: A) an atmosphere between the boundary surface of an incompressible mixtured fluid and infinity; B) a polytropic distribution matched to a Schwarzschild exterior; C) a Schwarzschild- Schwarzschild spacetime. The conservation of energy, the Newman--Penrose constant preservation and other expected features are observed.Comment: 20 pages, 6 figures; to appear in General Relativity and Gravitatio

Complete adiabatic waveform templates for a test-mass in the Schwarzschild spacetime: VIRGO and Advanced LIGO studies

Post-Newtonian expansions of the binding energy and gravitational wave flux truncated at the {\it same relative} post-Newtonian order form the basis of the {\it standard adiabatic} approximation to the phasing of gravitational waves from inspiralling compact binaries. Viewed in terms of the dynamics of the binary, the standard approximation is equivalent to neglecting certain conservative post-Newtonian terms in the acceleration. In an earlier work, we had proposed a new {\it complete adiabatic} approximant constructed from the energy and flux functions. At the leading order it employs the 2PN energy function rather than the 0PN one in the standard approximation, so that, effectively the approximation corresponds to the dynamics where there are no missing post-Newtonian terms in the acceleration. In this paper, we compare the overlaps of the standard and complete adiabatic templates with the exact waveform in the adiabatic approximation of a test-mass motion in the Schwarzschild spacetime, for the VIRGO and the Advanced LIGO noise spectra. It is found that the complete adiabatic approximants lead to a remarkable improvement in the {\it effectualness} at lower PN ($<$ 3PN) orders, while standard approximants of order $\geq$ 3PN provide a good lower-bound to the complete approximants for the construction of effectual templates. {\it Faithfulness} of complete approximants is better than that of standard approximants except for a few post-Newtonian orders. Standard and complete approximants beyond the adiabatic approximation are also studied using the Lagrangian templates of Buonanno, Chen and Vallisneri.Comment: Proceedings of the GWDAW-9, Accepted for publication in Class. Quant. Gra

Influence of quantum fluctuations on zero-temperature phase transitions between collinear and noncollinear states in frustrated spin systems

We study a square-lattice spin-half Heisenberg model where frustration is introduced by competing nearest-neighbor bonds of different signs. We discuss the influence of quantum fluctuations on the nature of the zero-temperature phase transitions from phases with collinear magnetic order at small frustration to phases with noncollinear spiral order at large frustration. We use the coupled cluster method (CCM) for high orders of approximation (up to LSUB6) and the exact diagonalization of finite systems (up to 32 sites) to calculate ground-state properties. The role of quantum fluctuations is examined by comparing the ferromagnetic-spiral and the antiferromagnetic-spiral transition within the same model. We find clear evidence that quantum fluctuations prefer collinear order and that they may favour a first order transition instead of a second order transition in case of no quantum fluctuations.Comment: 6 pages, 6 Postscipt figures; Accepted for publication in Phys. Rev.