Connecting Mathematics and the Applied Science of Energy Conservation

To effectively teach science in the elementary classroom, pre-service K-8 teachers need a basic understanding of the underlying concepts of physics, which demand a strong foundation in mathematics. Unfortunately, the depth of mathematics understanding of prospective elementary teachers has been a growing and serious concern for several decades. To overcome this challenge, a two-pronged attack was used in this study. First. students in mathematics courses were coupled with physical science courses by linking registration to ensure co-requisites were taken. This alone improved passing rates. Secondly, an energy conservation project was introduced in both classes that intimately tied the theoretical mathematics base knowledge to problems in physical science, energy efficiency, and household economics. These connections made the mathematics highly relevant to the students and improved both their theoretical understanding and their grades. Together, the two approaches of tying mathematics to physical science and applying mathematical skills to solving energy efficiency problems have shown to be extremely effective at improving student performance. This five-year study not only exhibited record improvements in student performance, but also can be easily replicated at other institutions experiencing similar challenges in training pre-service elementary school teachers

PECHCV, PECHFV, PEFHCV and PEFHFV: A set of atmospheric, primitive equation forecast models for the Northern Hemisphere, volume 3

As part of the SEASAT program of NASA, a set of four hemispheric, atmospheric prediction models were developed. The models, which use a polar stereographic grid in the horizontal and a sigma coordinate in the vertical, are: (1) PECHCV - five sigma layers and a 63 x 63 horizontal grid, (2) PECHFV - ten sigma layers and a 63 x 63 horizontal grid, (3) PEFHCV - five sigma layers and a 187 x 187 horizontal grid, and (4) PEFHFV - ten sigma layers and a 187 x 187 horizontal grid. The models and associated computer programs are described

Simulation of associative learning with the replaced elements model

Associative learning theories can be categorised according to whether they treat the representation of stimulus compounds in an elemental or configural manner. Since it is clear that a simple elemental approach to stimulus representation is inadequate there have been several attempts to produce more elaborate elemental models. One recent approach, the Replaced Elements Model (Wagner, 2003), reproduces many results that have until recently been uniquely predicted by Pearce’s Configural Theory (Pearce, 1994). Although it is possible to simulate the Replaced Elements Model using “standard” simulation programs the generation of the correct stimulus representation is complex. The current paper describes a method for simulation of the Replaced Elements Model and presents the results of two example simulations that show differential predictions of Replaced Elements and Pearce’s Configural Theor

Optimal traps in graphene

We transform the two-dimensional Dirac-Weyl equation, which governs the charge carriers in graphene, into a non-linear first-order differential equation for scattering phase shift, using the so-called variable phase method. This allows us to utilize the Levinson Theorem to find zero-energy bound states created electrostatically in realistic structures. These confined states are formed at critical potential strengths, which leads to us posit the use of `optimal traps' to combat the chiral tunneling found in graphene, which could be explored experimentally with an artificial network of point charges held above the graphene layer. We also discuss scattering on these states and find the zero angular momentum states create a dominant peak in scattering cross-section as energy tends towards the Dirac point energy, suggesting a dominant contribution to resistivity.Comment: 11 pages, 5 figure

Hydra: An Adaptive--Mesh Implementation of PPPM--SPH

We present an implementation of Smoothed Particle Hydrodynamics (SPH) in an adaptive-mesh PPPM algorithm. The code evolves a mixture of purely gravitational particles and gas particles. The code retains the desirable properties of previous PPPM--SPH implementations; speed under light clustering, naturally periodic boundary conditions and accurate pairwise forces. Under heavy clustering the cycle time of the new code is only 2--3 times slower than for a uniform particle distribution, overcoming the principal disadvantage of previous implementations\dash a dramatic loss of efficiency as clustering develops. A 1000 step simulation with 65,536 particles (half dark, half gas) runs in one day on a Sun Sparc10 workstation. The choice of time integration scheme is investigated in detail. A simple single-step Predictor--Corrector type integrator is most efficient. A method for generating an initial distribution of particles by allowing a a uniform temperature gas of SPH particles to relax within a periodic box is presented. The average SPH density that results varies by $\sim\pm1.3$\%. We present a modified form of the Layzer--Irvine equation which includes the thermal contribution of the gas together with radiative cooling. Tests of sound waves, shocks, spherical infall and collapse are presented. Appropriate timestep constraints sufficient to ensure both energy and entropy conservation are discussed. A cluster simulation, repeating Thomas andComment: 29 pp, uuencoded Postscrip

Integrals of Motion for Critical Dense Polymers and Symplectic Fermions

We consider critical dense polymers ${\cal L}(1,2)$. We obtain for this model the eigenvalues of the local integrals of motion of the underlying Conformal Field Theory by means of Thermodynamic Bethe Ansatz. We give a detailed description of the relation between this model and Symplectic Fermions including the indecomposable structure of the transfer matrix. Integrals of motion are defined directly on the lattice in terms of the Temperley Lieb Algebra and their eigenvalues are obtained and expressed as an infinite sum of the eigenvalues of the continuum integrals of motion. An elegant decomposition of the transfer matrix in terms of a finite number of lattice integrals of motion is obtained thus providing a reason for their introduction.Comment: 53 pages, version accepted for publishing on JSTA