Bulletin of the American Physical Society
APS April Meeting 2016
Volume 61, Number 6
Saturday–Tuesday, April 16–19, 2016; Salt Lake City, Utah
Session C11: Computational Physics |
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Sponsoring Units: DCOMP Room: 250C |
Saturday, April 16, 2016 1:30PM - 1:42PM |
C11.00001: Analysis of High-Speed Rotating Flow in 2D Polar \textbf{\textit{(r - }}$\theta $\textbf{\textit{) }}\textbf{ Coordinate} S. Pradhan The generalized analytical model for the radial boundary layer in a high-speed rotating cylinder is formulated for studying the gas flow field due to insertion of mass, momentum and energy into the rotating cylinder in the polar $(r - \theta ) $ plane. The analytical solution includes the sixth order differential equation for the radial boundary layer at the cylindrical curved surface in terms of master potential ($\chi )$, which is derived from the equations of motion in a polar $(r - \theta )$ plane. The linearization approximation (Wood {\&} Morton, \textit{J. Fluid Mech}-1980; Pradhan {\&} Kumaran, \textit{J. Fluid Mech}-2011; Kumaran {\&} Pradhan, \textit{J. Fluid Mech}-2014) is used, where the equations of motion are truncated at linear order in the velocity and pressure disturbances to the base flow, which is a solid-body rotation. Additional assumptions in the analytical model include constant temperature in the base state (isothermal condition), and high Reynolds number, but there is no limitation on the stratification parameter. In this limit, the gas flow is restricted to a boundary layer of thickness \textit{(Re\textasciicircum \textbraceleft }$-$\textit{1/3\textbraceright R)} at the wall of the cylinder. Here, the stratification parameter $A = \surd ((m \Omega $\textit{\textasciicircum 2 R\textasciicircum 2)/(2 k\textunderscore B T)).} This parameter $A $is the ratio of the peripheral speed, $\Omega R$, to the most probable molecular speed, $\surd $\textit{(2 k\textunderscore B T/m),} the Reynolds number Re $= \quad (\rho $\textit{\textunderscore w }$\Omega $\textit{ R\textasciicircum 2/}$\mu )$, where $m$ is the molecular mass, $\Omega $ and $R$ are the rotational speed and radius of the cylinder, \textit{k\textunderscore B} is the Boltzmann constant, $T$ is the gas temperature, $\rho $\textit{\textunderscore w} is the gas density at wall, and $\mu $ is the gas viscosity. The analytical solutions are then compared with direct simulation Monte Carlo (DSMC) simulations. [Preview Abstract] |
Saturday, April 16, 2016 1:42PM - 1:54PM |
C11.00002: High-order wavelet reconstruction/differentiation filters and Gibbs phenomena Richard Lombardini, Ramiro Acevedo, Alexander Kuczala, Kerry Keys, Carl Goodrich, Bruce Johnson We have developed an efficient method to accurately represent 1D or 2D, smooth or discontinuous, solutions to partial differential equations (PDE's), such as Schrodinger or Maxwell's equations, in an orthogonal Daubechies wavelet basis. This is a crucial step in the future development of a wavelet method that solves these PDE's. There are two main developments from this research. First, a reconstruction transform for smooth functions, discovered in previous works [Keinert and Kwon (1997) and Neelov and Goedecker (2006)], is generalized in order to develop a systematic way of tuning its error. This transform converts the wavelet basis representation back to the actual point values of the function. Since this reconstruction can far exceed the wavelet approximation order, it is shown that shorter wavelets can be used while maintaining a high-order accuracy resulting in an increase of computational efficiency. Second, a new ``truncated'' reconstruction transform is developed, using pieces of wavelets, or ``tail functions'', which can be applied to discontinuous functions. Not only does it avoid the wavelet Gibbs phenomenon, but also maintains a tunable accuracy similar to the smooth function case. [Preview Abstract] |
Saturday, April 16, 2016 1:54PM - 2:06PM |
C11.00003: Space-Pseudo-Time Method: Application to the One-Dimensional Coulomb Potential and Density Funtional Theory Charles Weatherford, Daniel Gebremedhin A new and efficient way of evolving a solution to an ordinary differential equation is presented. A finite element method is used where we expand in a convenient local basis set of functions that enforce both function and first derivative continuity across the boundaries of each element. We also implement an adaptive step size choice for each element that is based on a Taylor series expansion. The method is applied to solve for the eigenpairs of the one-dimensional soft-coulomb potential and the hard-coulomb limit is studied. The method is then used to calculate a numerical solution of the Kohn--Sham differential equation within the local density approximation is presented and is applied to the helium atom. [Preview Abstract] |
Saturday, April 16, 2016 2:06PM - 2:18PM |
C11.00004: Clustered Numerical Data Analysis Using Markov Lie Monoid Based Networks Joseph Johnson We have designed and build an optimal numerical standardization algorithm that links numerical values with their associated units, error level, and defining metadata thus supporting automated data exchange and new levels of artificial intelligence (AI). The software manages all dimensional and error analysis and computational tracing. Tables of entities verses properties of these generalized numbers (called ``metanumbers'') support a transformation of each table into a network among the entities and another network among their properties where the network connection matrix is based upon a proximity metric between the two items. We previously proved that every network is isomorphic to the Lie algebra that generates continuous Markov transformations. We have also shown that the eigenvectors of these Markov matrices provide an agnostic clustering of the underlying patterns. We will present this methodology and show how our new work on conversion of scientific numerical data through this process can reveal underlying information clusters ordered by the eigenvalues. We will also show how the linking of clusters from different tables can be used to form a ``supernet'' of all numerical information supporting new initiatives in AI. [Preview Abstract] |
Saturday, April 16, 2016 2:18PM - 2:30PM |
C11.00005: A wavelet approach to binary blackholes with asynchronous multitasking Hyun Lim, Eric Hirschmann, David Neilsen, Matthew Anderson, Jackson DeBuhr, Bo Zhang Highly accurate simulations of binary black holes and neutron stars are needed to address a variety of interesting problems in relativistic astrophysics. We present a new method for the solving the Einstein equations (BSSN formulation) using iterated interpolating wavelets. Wavelet coefficients provide a direct measure of the local approximation error for the solution and place collocation points that naturally adapt to features of the solution. Further, they exhibit exponential convergence on unevenly spaced collection points. The parallel implementation of the wavelet simulation framework presented here deviates from conventional practice in combining multi-threading with a form of message-driven computation sometimes referred to as asynchronous multitasking. [Preview Abstract] |
Saturday, April 16, 2016 2:30PM - 2:42PM |
C11.00006: Adaptive wavelets and relativistic magnetohydrodynamics Eric Hirschmann, David Neilsen, Matthe Anderson, Jackson DeBuhr, Bo Zhang We present a method for integrating the relativistic magnetohydrodynamics equations using iterated interpolating wavelets. Such provide an adaptive implementation for simulations in multidimensions. A measure of the local approximation error for the solution is provided by the wavelet coefficients. They place collocation points in locations naturally adapted to the flow while providing expected conservation. We present demanding 1D and 2D tests includingthe Kelvin-Helmholtz instability and the Rayleigh-Taylor instability. Finally, we consider an outgoing blast wave that models a GRB outflow. [Preview Abstract] |
Saturday, April 16, 2016 2:42PM - 2:54PM |
C11.00007: Simulation of Twisted Electron Mott Scattering John Madsen Recently, several groups have demonstrated the ability to produce coherent vortex beams of electrons. These ``twisted'' beams, generated by imprinting an azimuthal phase dependence via holographic diffraction gratings, are able to carry orbital angular momentum up to O(100h). The possibility of using this twistedness as a degree of freedom in accelerator based scattering experiments presents a potential avenue for direct measurement of the quark OAM contribution to nucleon spin. A more thorough understanding of the differences between planar and twisted electron Mott scattering in the relativistic domain is sought using a wavefunction based simulation. [Preview Abstract] |
Saturday, April 16, 2016 2:54PM - 3:06PM |
C11.00008: Simulating an Exploding Fission-Bomb Core Cameron Reed A time-dependent desktop-computer simulation of the core of an exploding fission bomb (nuclear weapon) has been developed. The simulation models a core comprising a mixture of two isotopes: a fissile one (such as U-235) and an inert one (such as U-238) that captures neutrons and removes them from circulation. The user sets the enrichment percentage and scattering and fission cross-sections of the fissile isotope, the capture cross-section of the inert isotope, the number of neutrons liberated per fission, the number of ``initiator'' neutrons, the radius of the core, and the neutron-reflection efficiency of a surrounding tamper. The simulation, which is predicated on ordinary kinematics, follows the three-dimensional motions and fates of neutrons as they travel through the core. Limitations of time and computer memory render it impossible to model a real-life core, but results of numerous runs clearly demonstrate the existence of a critical mass for a given set of parameters and the dramatic effects of enrichment and tamper efficiency on the growth (or decay) of the neutron population. The logic of the simulation will be described and results of typical runs will be presented and discussed. [Preview Abstract] |
Saturday, April 16, 2016 3:06PM - 3:18PM |
C11.00009: A new method for solving non-perturbative QFTs on the lattice Hadi Papei, Vitaly Vanchurin, Yi-Zen Chu We write a code to solve 1-dimensional Euclidean field theories nonperturbatively. This code uses a novel method to generate a random field for any given Lagrangian with a spatially invariant potential and by generating many realizations, it can compute n-point correlators nonperturbatively. We prove that these discretized fields have Markovian property so to generate the field at a point you just need the value of the field of the former point. We use this property by starting from one of the boundaries and generating the field point by point. Because the field is Markovian it will approach to the ground state of the Hamiltonian, so the boundary conditions obeyed by the fields do not affect the calculated n-point correlators, as long as you throw away the field values close to the boundaries. Once this is done, the result amounts to computing the expectation value of products of fields, with respect to the ground state. We test the code for some theories with an exact solution like the massive scalar field. We also calculate the 2-point correlation of the $\phi^4$ theory and the result was consistent with perturbative solutions. Our final goal is to use this statistical tools to find a theory that describe the large scale structure of the universe in nonlinear scales. [Preview Abstract] |
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