An adaptive, hanging-node, discontinuous isogeometric analysis method for the first-order form of the neutron transport equation with discrete ordinate (SN) angular discretisation

In this paper a discontinuous, hanging-node, isogeometric analysis (IGA) method is developed and applied to the first-order form of the neutron transport equation with a discrete ordinate (SN) angular discretisation in two-dimensional space. The complexities involved in upwinding across curved element boundaries that contain hanging-nodes have been addressed to ensure that the scheme remains conservative. A robust algorithm for cycle-breaking has also been introduced in order to develop a unique sweep ordering of the elements for each discrete ordinates direction. The convergence rate of the scheme has been verified using the method of manufactured solutions (MMS) with a smooth solution. Heuristic error indicators have been used to drive an adaptive mesh refinement (AMR) algorithm to take advantage of the hanging-node discretisation. The effectiveness of this method is demonstrated for three test cases. The first is a homogeneous square in a vacuum with varying mean free path and a prescribed extraneous unit source. The second test case is a radiation shielding problem and the third is a 3×3 “supercell” featuring a burnable absorber. In the final test case, comparisons are made to the discontinuous Galerkin finite element method (DGFEM) using both straight-sided and curved quadratic finite elements

Using rapid scan EPR to improve the detection limit of quantitative EPR by more than one order of magnitude

X band rapid scan EPR was implemented on a commercially available Bruker ELEXSYS E580 spectrometer. Room temperature rapid scan and continuous wave EPR spectra were recorded for amorphous silicon powder samples. By comparing the resulting signal intensities the feasibility of performing quantitative rapid scan EPR is demonstrated. For different hydrogenated amorphous silicon samples, rapid scan EPR results in signal to noise improvements by factors between 10 and 50. Rapid scan EPR is thus capable of improving the detection limit of quantitative EPR by at least one order of magnitude. In addition, we provide a recipe for setting up and calibrating a conventional pulsed and continuous wave EPR spectrometer for rapid scan EP

The 1979 Southeastern Virginia Urban Plume Study (SEV-UPS): Surface and airborne studies

The operation of two surface monitoring stations (one in downtown Norfolk, Virginia, one south of the city near the Great Dismal Swamp) and the collection of 40 hours of airborne measurements is described. Surface site measurements of ozone, oxides of nitrogen, sulfur dioxide, temperature, dew point, b sub seat, and condensation nuclei were made. Instrument calibrations, quality assurance audits, and preliminary data analysis in support of the Urban Plume Study were also made. The air pollution problems that were addressed are discussed. Data handling procedures followed for the surface stations are presented. The operation of the aircraft sampling platform is described. Aircraft sampling procedures are discussed. A preliminary descriptive analysis of the aircraft data is given along with data or plots for surface sites, airborne studies, hydrocarbon species, and instrument performance audits. Several of the aircraft flights clearly show the presence of an urban ozone plume downwind of Norfolk in the direction of the mean wind flow

In situ sensors for measurements in the global trosposphere

Current techniques available for the in situ measurement of ambient trace gas species, particulate composition, and particulate size distribution are reviewed. The operational specifications of the various techniques are described. Most of the techniques described are those that have been used in airborne applications or show promise of being adaptable to airborne applications. Some of the instruments described are specialty items that are not commercially-available. In situ measurement techniques for several meteorological parameters important in the study of the distribution and transport of ambient air pollutants are discussed. Some remote measurement techniques for meteorological parameters are also discussed. State-of-the-art measurement capabilities are compared with a list of capabilities and specifications desired by NASA for ambient measurements in the global troposphere

Isogeometric analysis for the multigroup neutron diffusion equation with applications in reactor physics

Isogeometric Analysis (IGA) has been applied to heterogeneous reactor physics problems using the multigroup neutron dif- fusion equation. IGA uses a computer-aided design (CAD) description of the geometry commonly built from Non-Uniform Rational B-Splines (NURBS), which can exactly represent complicated curved shapes such as circles and cylinders, common features in reactor design. This work has focused on comparing IGA to nite element analysis (FEA) for heterogeneous reactor physics problems, including the OECD/NEA C5G7 LWR benchmark. The exact geometry and increased basis function continuity contribute to the accuracy of IGA and an improvement over comparable FEA calculations has been observed

Optimal trace inequality constants for interior penalty discontinuous Galerkin discretisations of elliptic operators using arbitrary elements with non-constant Jacobians

In this paper, a new method to numerically calculate the trace inequality constants, which arise in the calculation of penalty parameters for interior penalty discretisations of elliptic operators, is presented. These constants are provably optimal for the inequality of interest. As their calculation is based on the solution of a generalised eigenvalue problem involving the volumetric and face stiffness matrices, the method is applicable to any element type for which these matrices can be calculated, including standard finite elements and the non-uniform rational B-splines of isogeometric analysis. In particular, the presented method does not require the Jacobian of the element to be constant, and so can be applied to a much wider variety of element shapes than are currently available in the literature. Numerical results are presented for a variety of finite element and isogeometric cases. When the Jacobian is constant, it is demonstrated that the new method produces lower penalty parameters than existing methods in the literature in all cases, which translates directly into savings in the solution time of the resulting linear system. When the Jacobian is not constant, it is shown that the naive application of existing approaches can result in penalty parameters that do not guarantee coercivity of the bilinear form, and by extension, the stability of the solution. The method of manufactured solutions is applied to a model reaction-diffusion equation with a range of parameters, and it is found that using penalty parameters based on the new trace inequality constants result in better conditioned linear systems, which can be solved approximately 11% faster than those produced by the methods from the literature

Numerical simulations of mixed states quantum computation

We describe quantum-octave package of functions useful for simulations of quantum algorithms and protocols. Presented package allows to perform simulations with mixed states. We present numerical implementation of important quantum mechanical operations - partial trace and partial transpose. Those operations are used as building blocks of algorithms for analysis of entanglement and quantum error correction codes. Simulation of Shor's algorithm is presented as an example of package capabilities.Comment: 6 pages, 4 figures, presented at Foundations of Quantum Information, 16th-19th April 2004, Camerino, Ital

Energy dependent mesh adaptivity of discontinuous isogeometric discrete ordinate methods with dual weighted residual error estimators

In this paper a hanging-node, discontinuous Galerkin, isogeometric discretisation of the multigroup, discrete ordinates () equations is presented in which each energy group has its own mesh. The equations are discretised using Non-Uniform Rational B-Splines (NURBS), which allows the coarsest mesh to exactly represent the geometry for a wide range of engineering problems of interest; this would not be the case using straight-sided finite elements. Information is transferred between meshes via the construction of a supermesh. This is a non-trivial task for two arbitrary meshes, but is significantly simplified here by deriving every mesh from a common coarsest initial mesh. In order to take full advantage of this flexible discretisation, goal-based error estimators are derived for the multigroup, discrete ordinates equations with both fixed (extraneous) and fission sources, and these estimators are used to drive an adaptive mesh refinement (AMR) procedure. The method is applied to a variety of test cases for both fixed and fission source problems. The error estimators are found to be extremely accurate for linear NURBS discretisations, with degraded performance for quadratic discretisations owing to a reduction in relative accuracy of the “exact” adjoint solution required to calculate the estimators. Nevertheless, the method seems to produce optimal meshes in the AMR process for both linear and quadratic discretisations, and is ≈×100 more accurate than uniform refinement for the same amount of computational effort for a 67 group deep penetration shielding problem

A geometry preserving, conservative, mesh-to-mesh isogeometric interpolation algorithm for spatial adaptivity of the multigroup, second-order even-parity form of the neutron transport equation

In this paper a method is presented for the application of energy-dependent spatial meshes applied to the multigroup, second-order, even-parity form of the neutron transport equation using Isogeometric Analysis (IGA). The computation of the inter-group regenerative source terms is based on conservative interpolation by Galerkin projection. The use of Non-Uniform Rational B-splines (NURBS) from the original computer-aided design (CAD) model allows for efficient implementation and calculation of the spatial projection operations while avoiding the complications of matching different geometric approximations faced by traditional finite element methods (FEM). The rate-of-convergence was verified using the method of manufactured solutions (MMS) and found to preserve the theoretical rates when interpolating between spatial meshes of different refinements. The scheme’s numerical efficiency was then studied using a series of two-energy group pincell test cases where a significant saving in the number of degrees-of-freedom can be found if the energy group with a complex variation in the solution is refined more than an energy group with a simpler solution function. Finally, the method was applied to a heterogeneous, seven-group reactor pincell where the spatial meshes for each energy group were adaptively selected for refinement. It was observed that by refining selected energy groups a reduction in the total number of degrees-of-freedom for the same total L2 error can be obtained