Adaptive grid methods for Q-tensor theory of liquid crystals : a one-dimensional feasibility study

This paper illustrates the use of moving mesh methods for solving partial differential equation (PDE) problems in Q-tensor theory of liquid crystals. We present the results of an initial study using a simple one-dimensional test problem which illustrates the feasibility of applying adaptive grid techniques in such situations. We describe how the grids are computed using an equidistribution principle, and investigate the comparative accuracy of adaptive and uniform grid strategies, both theoretically and via numerical examples

Adiabatic hyperspherical study of triatomic helium systems

The 4He3 system is studied using the adiabatic hyperspherical representation. We adopt the current state-of-the-art helium interaction potential including retardation and the nonadditive three-body term, to calculate all low-energy properties of the triatomic 4He system. The bound state energies of the 4He trimer are computed as well as the 4He+4He2 elastic scattering cross sections, the three-body recombination and collision induced dissociation rates at finite temperatures. We also treat the system that consists of two 4He and one 3He atoms, and compute the spectrum of the isotopic trimer 4He2 3He, the 3He+4He2 elastic scattering cross sections, the rates for three-body recombination and the collision induced dissociation rate at finite temperatures. The effects of retardation and the nonadditive three-body term are investigated. Retardation is found to be significant in some cases, while the three-body term plays only a minor role for these systems.Comment: 24 pages 6 figures Submitted to Physical Review

Four-nucleon scattering: Ab initio calculations in momentum space

The four-body equations of Alt, Grassberger and Sandhas are solved for \nH scattering at energies below three-body breakup threshold using various realistic interactions including one derived from chiral perturbation theory. After partial wave decomposition the equations are three-variable integral equations that are solved numerically without any approximations beyond the usual discretization of continuum variables on a finite momentum mesh. Large number of two-, three- and four-nucleon partial waves are considered until the convergence of the observables is obtained. The total \nH cross section data in the resonance region is not described by the calculations which confirms previous findings by other groups. Nevertheless the numbers we get are slightly higher and closer to the data than previously found and depend on the choice of the two-nucleon potential. Correlations between the $A_y$ deficiency in \nd elastic scattering and the total \nH cross section are studied.Comment: Corrected Eq. (10

Imaging Three Dimensional Two-particle Correlations for Heavy-Ion Reaction Studies

We report an extension of the source imaging method for analyzing three-dimensional sources from three-dimensional correlations. Our technique consists of expanding the correlation data and the underlying source function in spherical harmonics and inverting the resulting system of one-dimensional integral equations. With this strategy, we can image the source function quickly, even with the finely binned data sets common in three-dimensional analyses.Comment: 13 pages, 11 figures, submitted to Physical Review

Smoothing spline primordial power spectrum reconstruction

We reconstruct the shape of the primordial power spectrum (PPS) using a smoothing spline. Our adapted smoothing spline technique provides a complementary method to existing efforts to search for smooth features in the PPS, such as a running spectral index. With this technique we find no significant indication with WMAP first-year data that the PPS deviates from Harrison-Zeldovich and no evidence for loss of power on large scales. We also examine the effect on the cosmological parameters of the additional PPS freedom. Smooth variations in the PPS are not significantly degenerate with other cosmological parameters, but the spline reconstruction greatly increases the errors on the optical depth and baryon fraction.Comment: 12 pages, 10 figures. Accepted to PR

Three Bosons in One Dimension with Short Range Interactions I: Zero Range Potentials

We consider the three-boson problem with $\delta$-function interactions in one spatial dimension. Three different approaches are used to calculate the phase shifts, which we interpret in the context of the effective range expansion, for the scattering of one free particle a off of a bound pair. We first follow a procedure outlined by McGuire in order to obtain an analytic expression for the desired S-matrix element. This result is then compared to a variational calculation in the adiabatic hyperspherical representation, and to a numerical solution to the momentum space Faddeev equations. We find excellent agreement with the exact phase shifts, and comment on some of the important features in the scattering and bound-state sectors. In particular, we find that the 1+2 scattering length is divergent, marking the presence of a zero-energy resonance which appears as a feature when the pair-wise interactions are short-range. Finally, we consider the introduction of a three-body interaction, and comment on the cutoff dependence of the coupling.Comment: 9 figures, 2 table

On Normals and Control Nets

This paper characterizes when the normals of a spline curve or spline surface lie in the more easily computed cone of the normals of the segments of the spline control net

One-way multigrid method in electronic structure calculations

We propose a simple and efficient one-way multigrid method for self-consistent electronic structure calculations based on iterative diagonalization. Total energy calculations are performed on several different levels of grids starting from the coarsest grid, with wave functions transferred to each finer level. The only changes compared to a single grid calculation are interpolation and orthonormalization steps outside the original total energy calculation and required only for transferring between grids. This feature results in a minimal amount of code change, and enables us to employ a sophisticated interpolation method and noninteger ratio of grid spacings. Calculations employing a preconditioned conjugate gradient method are presented for two examples, a quantum dot and a charged molecular system. Use of three grid levels with grid spacings 2h, 1.5h, and h decreases the computer time by about a factor of 5 compared to single level calculations.Comment: 10 pages, 2 figures, to appear in Phys. Rev. B, Rapid Communication

BézierSketch: A Generative Model for Scalable Vector Sketches

The study of neural generative models of human sketches is a fascinating contemporary modeling problem due to the links between sketch image generation and the human drawing process. The landmark SketchRNN provided breakthrough by sequentially generating sketches as a sequence of waypoints. However this leads to low-resolution image generation, and failure to model long sketches. In this paper we present B\'ezierSketch, a novel generative model for fully vector sketches that are automatically scalable and high-resolution. To this end, we first introduce a novel inverse graphics approach to stroke embedding that trains an encoder to embed each stroke to its best fit B\'ezier curve. This enables us to treat sketches as short sequences of paramaterized strokes and thus train a recurrent sketch generator with greater capacity for longer sketches, while producing scalable high-resolution results. We report qualitative and quantitative results on the Quick, Draw! benchmark.Comment: Accepted as poster at ECCV 202

Safety surveillance and the estimation of risk in select populations: Flexible methods to control for confounding while targeting marginal comparisons via standardization

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/152565/1/sim8410_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/152565/2/sim8410.pd