737 research outputs found

    Optimization of the Collection Efficiency of a Hexagonal Light Collector using Quadratic and Cubic B\'ezier Curves

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    Reflective light collectors with hexagonal entrance and exit apertures are frequently used in front of the focal-plane camera of a very-high-energy gamma-ray telescope to increase the collection efficiency of atmospheric Cherenkov photons and reduce the night-sky background entering at large incident angles. The shape of a hexagonal light collector is usually based on Winston's design, which is optimized for only two-dimensional optical systems. However, it is not known whether a hexagonal Winston cone is optimal for the real three-dimensional optical systems of gamma-ray telescopes. For the first time we optimize the shape of a hexagonal light collector using quadratic and cubic B\'ezier curves. We demonstrate that our optimized designs simultaneously achieve a higher collection efficiency and background reduction rate than traditional designs.Comment: 9 pages, 9 figure

    Fast Isogeometric Boundary Element Method based on Independent Field Approximation

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    An isogeometric boundary element method for problems in elasticity is presented, which is based on an independent approximation for the geometry, traction and displacement field. This enables a flexible choice of refinement strategies, permits an efficient evaluation of geometry related information, a mixed collocation scheme which deals with discontinuous tractions along non-smooth boundaries and a significant reduction of the right hand side of the system of equations for common boundary conditions. All these benefits are achieved without any loss of accuracy compared to conventional isogeometric formulations. The system matrices are approximated by means of hierarchical matrices to reduce the computational complexity for large scale analysis. For the required geometrical bisection of the domain, a strategy for the evaluation of bounding boxes containing the supports of NURBS basis functions is presented. The versatility and accuracy of the proposed methodology is demonstrated by convergence studies showing optimal rates and real world examples in two and three dimensions.Comment: 32 pages, 27 figure

    Curves with rational chord-length parametrization

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    It has been recently proved that rational quadratic circles in standard Bezier form are parameterized by chord-length. If we consider that standard circles coincide with the isoparametric curves in a system of bipolar coordinates, this property comes as a straightforward consequence. General curves with chord-length parametrization are simply the analogue in bipolar coordinates of nonparametric curves. This interpretation furnishes a compact explicit expression for all planar curves with rational chord-length parametrization. In addition to straight lines and circles in standard form, they include remarkable curves, such as the equilateral hyperbola, Lemniscate of Bernoulli and Limacon of Pascal. The extension to 3D rational curves is also tackled

    Prototyping Hexagonal Light Concentrators Using High-Reflectance Specular Films for the Large-Sized Telescopes of the Cherenkov Telescope Array

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    We have developed a prototype hexagonal light concentrator for the Large-Sized Telescopes of the Cherenkov Telescope Array. To maximize the photodetection efficiency of the focal-plane camera pixels for atmospheric Cherenkov photons and to lower the energy threshold, a specular film with a very high reflectance of 92-99% has been developed to cover the inner surfaces of the light concentrators. The prototype has a relative anode sensitivity (which can be roughly regarded as collection efficiency) of about 95 to 105% at the most important angles of incidence. The design, simulation, production procedure, and performance measurements of the light-concentrator prototype are reported.Comment: 21 pages, 14 figures, accepted for publication in JINS

    Flexibility of approximation in pies applied for solving elastoplastic boundary problems

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    The paper presents the flexibility of approximation in PIES applied for solving elastoplastic boundary value problems. Three various approaches to approximation of plastic strains have been tested. The first one bases on the globally applied Lagrange polynomial. The two remaining are local: inverse distance weighting (IDW) method and approximation in different zones by locally applied Lagrange polynomials. Some examples are solved and results obtained are compared with analytical solutions. Conclusions on the effectiveness of presented approaches have been drawn

    Discontinuities in numerical radiative transfer

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    Observations and magnetohydrodynamic simulations of solar and stellar atmospheres reveal an intermittent behavior or steep gradients in physical parameters, such as magnetic field, temperature, and bulk velocities. The numerical solution of the stationary radiative transfer equation is particularly challenging in such situations, because standard numerical methods may perform very inefficiently in the absence of local smoothness. However, a rigorous investigation of the numerical treatment of the radiative transfer equation in discontinuous media is still lacking. The aim of this work is to expose the limitations of standard convergence analyses for this problem and to identify the relevant issues. Moreover, specific numerical tests are performed. These show that discontinuities in the atmospheric physical parameters effectively induce first-order discontinuities in the radiative transfer equation, reducing the accuracy of the solution and thwarting high-order convergence. In addition, a survey of the existing numerical schemes for discontinuous ordinary differential systems and interpolation techniques for discontinuous discrete data is given, evaluating their applicability to the radiative transfer problem

    Accurate and efficient spin integration for particle accelerators

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    Accurate spin tracking is a valuable tool for understanding spin dynamics in particle accelerators and can help improve the performance of an accelerator. In this paper, we present a detailed discussion of the integrators in the spin tracking code gpuSpinTrack. We have implemented orbital integrators based on drift-kick, bend-kick, and matrix-kick splits. On top of the orbital integrators, we have implemented various integrators for the spin motion. These integrators use quaternions and Romberg quadratures to accelerate both the computation and the convergence of spin rotations. We evaluate their performance and accuracy in quantitative detail for individual elements as well as for the entire RHIC lattice. We exploit the inherently data-parallel nature of spin tracking to accelerate our algorithms on graphics processing units.Comment: 43 pages, 17 figure
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