On the p,qp,q-binomial distribution and the Ising model

A completely new approach to the Ising model in 1 to 5 dimensions is developed. We employ $p,q$-binomial coefficients, a generalisation of the binomial coefficients, to describe the magnetisation distributions of the Ising model. For the complete graph this distribution corresponds exactly to the limit case $p=q$. We take our investigation to the simple $d$-dimensional lattices for $d=1,2,3,4,5$ and fit $p,q$-binomial distributions to our data, some of which are exact but most are sampled. For $d=1$ and $d=5$ the magnetisation distributions are remarkably well-fitted by $p,q$-binomial distributions. For $d=4$ we are only slightly less successful, while for $d=2,3$ we see some deviations (with exceptions!) between the $p,q$-binomial and the Ising distribution. We begin the paper by giving results on the behaviour of the $p,q$-distribution and its moment growth exponents given a certain parameterization of $p,q$. Since the moment exponents are known for the Ising model (or at least approximately for $d=3$) we can predict how $p,q$ should behave and compare this to our measured $p,q$. The results speak in favour of the $p,q$-binomial distribution's correctness regarding their general behaviour in comparison to the Ising model. The full extent to which they correctly model the Ising distribution is not settled though.Comment: 51 pages, 23 figures, submitted to PRB on Oct 23 200

A unified treatment of Ising model magnetizations

We show how the spontaneous bulk, surface and corner magnetizations in the square lattice Ising model can all be obtained within one approach. The method is based on functional equations which follow from the properties of corner transfer matrices and vertex operators and which can be derived graphically. In all cases, exact analytical expressions for general anisotropy are obtained. Known results, including several for which only numerical computation was previously possible, are verified and new results related to general anisotropy and corner angles are obtained.Comment: Plain Tex, 30 pages, 21 figures in eps format. Revised for publication in Annalen der Physi

Radial Surface Density Profiles of Gas and Dust in the Debris Disk around 49 Ceti

We present ~0.4 resolution images of CO(3-2) and associated continuum emission from the gas-bearing debris disk around the nearby A star 49 Ceti, observed with the Atacama Large Millimeter/Submillimeter Array (ALMA). We analyze the ALMA visibilities in tandem with the broad-band spectral energy distribution to measure the radial surface density profiles of dust and gas emission from the system. The dust surface density decreases with radius between ~100 and 310 au, with a marginally significant enhancement of surface density at a radius of ~110 au. The SED requires an inner disk of small grains in addition to the outer disk of larger grains resolved by ALMA. The gas disk exhibits a surface density profile that increases with radius, contrary to most previous spatially resolved observations of circumstellar gas disks. While ~80% of the CO flux is well described by an axisymmetric power-law disk in Keplerian rotation about the central star, residuals at ~20% of the peak flux exhibit a departure from axisymmetry suggestive of spiral arms or a warp in the gas disk. The radial extent of the gas disk (~220 au) is smaller than that of the dust disk (~300 au), consistent with recent observations of other gas-bearing debris disks. While there are so far only three broad debris disks with well characterized radial dust profiles at millimeter wavelengths, 49 Ceti's disk shows a markedly different structure from two radially resolved gas-poor debris disks, implying that the physical processes generating and sculpting the gas and dust are fundamentally different.Comment: 20 pages, 8 figures, accepted for publication in ApJ March 31, 2017 (submitted Nov 2016

Functional Multi-Layer Perceptron: a Nonlinear Tool for Functional Data Analysis

In this paper, we study a natural extension of Multi-Layer Perceptrons (MLP) to functional inputs. We show that fundamental results for classical MLP can be extended to functional MLP. We obtain universal approximation results that show the expressive power of functional MLP is comparable to that of numerical MLP. We obtain consistency results which imply that the estimation of optimal parameters for functional MLP is statistically well defined. We finally show on simulated and real world data that the proposed model performs in a very satisfactory way.Comment: http://www.sciencedirect.com/science/journal/0893608

The Genetic Drift Inventory: A Tool for Measuring What Advanced Undergraduates Have Mastered about Genetic Drift

Understanding genetic drift is crucial for a comprehensive understanding of biology, yet it is difficult to learn because it combines the conceptual challenges of both evolution and randomness. To help assess strategies for teaching genetic drift, we have developed and evaluated the Genetic Drift Inventory (GeDI), a concept inventory that measures upper-division students’ understanding of this concept. We used an iterative approach that included extensive interviews and field tests involving 1723 students across five different undergraduate campuses. The GeDI consists of 22 agree–disagree statements that assess four key concepts and six misconceptions. Student scores ranged from 4/22 to 22/22. Statements ranged in mean difficulty from 0.29 to 0.80 and in discrimination from 0.09 to 0.46. The internal consistency, as measured with Cronbach\u27s alpha, ranged from 0.58 to 0.88 across five iterations. Test–retest analysis resulted in a coefficient of stability of 0.82. The true–false format means that the GeDI can test how well students grasp key concepts central to understanding genetic drift, while simultaneously testing for the presence of misconceptions that indicate an incomplete understanding of genetic drift. The insights gained from this testing will, over time, allow us to improve instruction about this key component of evolution

Direct observation of growth and collapse of a Bose-Einstein condensate with attractive interactions

The dynamical behavior of Bose-Einstein condensation (BEC) in a gas with attractive interactions is striking. Quantum theory predicts that BEC of a spatially homogeneous gas with attractive interactions is precluded by a conventional phase transition into either a liquid or solid. When confined to a trap, however, such a condensate can form provided that its occupation number does not exceed a limiting value. The stability limit is determined by a balance between self-attraction and a repulsion arising from position-momentum uncertainty under conditions of spatial confinement. Near the stability limit, self-attraction can overwhelm the repulsion, causing the condensate to collapse. Growth of the condensate, therefore, is punctuated by intermittent collapses, which are triggered either by macroscopic quantum tunneling or thermal fluctuation. Previous observation of growth and collapse has been hampered by the stochastic nature of these mechanisms. Here we reduce the stochasticity by controlling the initial number of condensate atoms using a two-photon transition to a diatomic molecular state. This enables us to obtain the first direct observation of the growth of a condensate with attractive interactions and its subsequent collapse.Comment: 10 PDF pages, 5 figures (2 color), 19 references, to appear in Nature Dec. 7 200

Bose-Einstein condensation with internal degrees of freedom in alkali atom gases

The Bogoliubov theory is extended to a Bose-Einstein condensation with internal degrees of freedom, realized recently in $^{23}$Na gases where several hyperfine states are simultaneously cooled optically. Starting with a Hamiltonian constructed from general gauge and spin rotation symmetry principles fundamental equations for condensate are derived. The ground state where time reversal symmetry is broken in some case and low-lying collective modes, e.g. spin and density wave modes, are discussed. Novel vortex as a topological defect can be created experimentally.Comment: 4 pages, 1 eps figur

Plasma Physics

Contains reports on seven research projects.United States Atomic Energy Commission under Contract AT(30-1)-1842Joint Services Electronics Programs (U.S. Army, U.S. Navy, and U.S. Air Force) under Contract DA 28-043-AMC-02536(E

An Integrated Approach for Fixture Layout Design and Clamping Force Optimization

Fixture Layout Design (FLD) determines the specific position of locators and clamps to orient and holds the workpiece with respect to a machine tool. The FLD approaches that use Finite Element Analysis (FEA) have been widely used in previous works and have become computationally expensive and specific to a particular problem. Further, the FLD and clamping force optimization were often performed separately by ignoring their interdependence. In the present work, the locators' contact forces are uniformly distributed by suitably varying the fixture layout and clamping force to maximize the part dimensional and form quality. The parametric rigid body model is used to depict the behaviour of the workpiece-fixture system, and it is incorporated with the genetic algorithm to optimize the design variables. A prismatic workpiece with pocket milling operation is considered to validate the proposed methodology. Stability criterion and tool-fixture interference are considered constraints. Subsequently, FEA is used to verify the integrity of the proposed approach. The results infer that the uniform distribution of maximum elastic deformation is achieved due to the uniform distribution of contact forces. The suggested approach is proven effective for designing a milling fixture to manufacture components with high dimensional and form precision