Global Steady Subsonic Flows through Infinitely Long Nozzles for the Full Euler Equations

We are concerned with global steady subsonic flows through general infinitely long nozzles for the full Euler equations. The problem is formulated as a boundary value problem in the unbounded domain for a nonlinear elliptic equation of second order in terms of the stream function. It is established that, when the oscillation of the entropy and Bernoulli functions at the upstream is sufficiently small in $C^{1,1}$ and the mass flux is in a suitable regime, there exists a unique global subsonic solution in a suitable class of general nozzles. The assumptions are required to prevent from the occurrence of supersonic bubbles inside the nozzles. The asymptotic behavior of subsonic flows at the downstream and upstream, as well as the critical mass flux, have been clarified.Comment: 32 pages, 1 figure. arXiv admin note: text overlap with arXiv:0907.3276 by other author

Iso-level tool path planning for free-form surfaces

The aim of tool path planning is to maximize the efficiency against some given precision criteria. In practice, scallop height should be kept constant to avoid unnecessary cutting, while the tool path should be smooth enough to maintain a high feed rate. However, iso-scallop and smoothness often conflict with each other. Existing methods smooth iso-scallop paths one-by-one, which make the final tool path far from being globally optimal. This paper proposes a new framework for tool path optimization. It views a family of iso-level curves of a scalar function defined over the surface as tool path so that desired tool path can be generated by finding the function that minimizes certain energy functional and different objectives can be considered simultaneously. We use the framework to plan globally optimal tool path with respect to iso-scallop and smoothness. The energy functionals for planning iso-scallop, smoothness, and optimal tool path are respectively derived, and the path topology is studied too. Experimental results are given to show effectiveness of the proposed methods

Data characterization using artificial-star tests: performance evaluation

Traditional artificial-star tests are widely applied to photometry in crowded stellar fields. However, to obtain reliable binary fractions (and their uncertainties) of remote, dense, and rich star clusters, one needs to recover huge numbers of artificial stars. Hence, this will consume much computation time for data reduction of the images to which the artificial stars must be added. In this paper, we present a new method applicable to data sets characterized by stable, well-defined point-spread functions, in which we add artificial stars to the retrieved-data catalog instead of the raw images. Taking the young Large Magellanic Cloud cluster NGC 1818 as an example, we compare results from both methods and show that they are equivalent, while our new method saves significant computational time.Comment: 23 pages, 10 figures, accepted by PAS