Gn blending multiple surfaces in polar coordinates

International audienceThis paper proposes a method of Gn blending multiple parametric surfaces in polar coordinates. It models the geometric continuity conditions of parametric surfaces in polar coordinates and presents a mechanism of converting a Cartesian parametric surface into its polar coordinate form. The basic idea is first to reparameterize the parametric blendees into the form of polar coordinates. Then they are blended simultaneously by a basis function in the complex domain. To extend its compatibility, we also propose a method of converting polar coordinate blending surface into N NURBS patches. One application of this technique is to fill N-sided holes. Examples are presented to show its feasibility and practicability

A GPU-Parallelized Interpolation-Based Fast Multipole Method for the Relativistic Space-Charge Field Calculation

The fast multipole method (FMM) has received growing attention in the beam physics simulation. In this study, we formulate an interpolation-based FMM for the computation of the relativistic space-charge field. Different to the quasi-electrostatic model, our FMM is formulated in the lab-frame and can be applied without the assistance of the Lorentz transformation. In particular, we derive a modified admissibility condition which can effectively control the interpolation error of the proposed FMM. The algorithms and their GPU parallelization are discussed in detail. A package containing serial and GPU-parallelized solvers is implemented in the Julia programming language. The GPU-parallelized solver can reach a speedup of more than a hundred compared to the execution on a single CPU core.Comment: 30 pages, 10 figure

Polar NURBS surface with curvature continuity

International audiencePolar NURBS surface is a kind of periodic NURBS surface, one boundary of which shrinks to a degenerate polarpoint. The specific topology of its control-point mesh offers the ability to represent a cap-like surface, which iscommon in geometric modeling. However, there is a critical and challenging problem that hinders its application:curvature continuity at the extraordinary singular pole. We first propose a sufficient and necessary condition ofcurvature continuity at the pole. Then, we present constructive methods for the two key problems respectively:how to construct a polar NURBS surface with curvature continuity and how to reform an ordinary polar NURBSsurface to curvature continuous. The algorithms only depend on the symbolic representation and operations ofNURBS, and they introduce no restrictions on the degree or the knot vectors. Examples and comparisons demonstratethe applications of the curvature-continuous polar NURBS surface in hole-filling and free-shape modeling

Filling n-sided regions with G1 triangular Coons B-spline patches

International audienceFilling n-sided regions is an essential operation in shape and surface modeling. Positional and tangential continuities are highly required in designing and manufacturing. We propose a method for filling n-sided regions with untrimmed triangular Coons B-spline patches, preserving G1 continuity exactly. The algorithm first computes a central point, a central normal, the central, and the corner derivative vectors. Then the region is split into n triangular areas by connecting the central point to each corner of the boundary. These inner curves and all cross-boundary derivatives are computed fulfilling G1 compatibility conditions. And finally, the triangular patches are generated in the Coons B-spline form, one boundary of which is regressed to the central vertex. Neither positional nor tangential error is introduced by this method. And only one degree elevation is needed

Entanglement Structure: Entanglement Partitioning in Multipartite Systems and Its Experimental Detection Using Optimizable Witnesses

Creating large-scale entanglement lies at the heart of many quantum information processing protocols and the investigation of fundamental physics. For multipartite quantum systems, it is crucial to identify not only the presence of entanglement but also its detailed structure. This is because in a generic experimental situation with sufficiently many subsystems involved, the production of so-called genuine multipartite entanglement remains a formidable challenge. Consequently, focusing exclusively on the identification of this strongest type of entanglement may result in an all or nothing situation where some inherently quantum aspects of the resource are overlooked. On the contrary, even if the system is not genuinely multipartite entangled, there may still be many-body entanglement present in the system. An identification of the entanglement structure may thus provide us with a hint about where imperfections in the setup may occur, as well as where we can identify groups of subsystems that can still exhibit strong quantum-information-processing capabilities. However, there is no known efficient methods to identify the underlying entanglement structure. Here, we propose two complementary families of witnesses for the identification of such structures. They are based on the detection of entanglement intactness and entanglement depth, each requires only the implementation of solely two local measurements. Our method is also robust against noises and other imperfections, as reflected by our experimental implementation of these tools to verify the entanglement structure of five different eight-photon entangled states. We demonstrate how their entanglement structure can be precisely and systematically inferred from the experimental data. In achieving this goal, we also illustrate how the same set of data can be classically postprocessed to learn the most about the measured system.Comment: 21 pages, 13 figure

Key Parameters Requirements for Non‐Fullerene‐Based Organic Solar Cells with Power Conversion Efficiency >20%

The reported power conversion efficiencies (PCEs) of nonfullerene acceptor (NFA) based organic photovoltaics (OPVs) now exceed 14% and 17% for single‐junction and two‐terminal tandem cells, respectively. However, increasing the PCE further requires an improved understanding of the factors limiting the device efficiency. Here, the efficiency limits of single‐junction and two‐terminal tandem NFA‐based OPV cells are examined with the aid of a numerical device simulator that takes into account the optical properties of the active material(s), charge recombination effects, and the hole and electron mobilities in the active layer of the device. The simulations reveal that single‐junction NFA OPVs can potentially reach PCE values in excess of 18% with mobility values readily achievable in existing material systems. Furthermore, it is found that balanced electron and hole mobilities of >10−3 cm2 V−1 s−1 in combination with low nongeminate recombination rate constants of 10−12 cm3 s−1 could lead to PCE values in excess of 20% and 25% for single‐junction and two‐terminal tandem OPV cells, respectively. This analysis provides the first tangible description of the practical performance targets and useful design rules for single‐junction and tandem OPVs based on NFA materials, emphasizing the need for developing new material systems that combine these desired characteristics