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Due to the fact that the space is becoming increasingly congested, there is a high requirement for the orbit prediction accuracy of space targets to support collision warning tasks. This is especially true for space debris with high area-to-mass ratio and low orbit altitude. This paper focuses on the along-track position error caused by the atmospheric density error and area-to-mass ratio error for targets with near-circular orbit in the orbit prediction. We derive a semi-analytical expression to describe the along-track position error, and the expression’s validity is evaluated by a goodness-of-fit index compared with the simulated “true” along-track position error. The simulation is based on Encke’s special perturbation method, in which the drag error is treated as a perturbation. The drag error is modeled by the difference between the JB2008 and MISIS density model and the sinusoidal oscillation error model concerning the inexact area-to-mass ratio. Furthermore, targets with various orbit altitudes ranging from 300km to 800km are selected to investigate whether the along-track position error can meet the collision warning requirements.

At present, it has become a trend to realize indoor actual measurement by reconstructing indoor 3D information with dense point cloud. Considering the large time consumption of traditional manual measurement and data overload of 3D reconstruction for a construction, the paper presents a global measurement method based on sparse point cloud for indoor actual measurement of flatness and verticality. First, given the point cloud is present with low density, our data size is much smaller than that in 3D reconstruction, which greatly reduces time consumption for data processing. Second, we calculate surface flatness degree by using a tolerance formula in machinery industry as reference after we conduct fitting of surfaces by least square method. As for the measurement of verticality, making use of the more orderly and effective point cloud clustering plus surface fitting based on sparse point cloud, we are able to calculate the verticality degree easily by a mathematical method. Compared with existing methods, this approach might feature a more tailored or specialized measurement method for actual measurement of flatness and verticality in acceptance of construction work in indoor scenes. To validate this approach, we present our experimental results and examine the systematic error by the mathematical assessment modelling. It is proved that the systematic error of the measurement method based on sparse point cloud is nearly ignorable.

We prove that the excluded volume of convex shapes and with equal volumes attains its minimum only if coincides with the inversion of relative to its centroid. It follows that if is a cylindrically symmetric shape, and is a replica of rotated in space, then the excluded volume of and attains its minimum when and are in the antiparallel configuration. This suggests that ensembles of such hard particles may experience the same geometric frustration as spins in the Ising model for antiferromagnetism on certain lattices.

Cells alter their shape and morphology and interact with their surrounding environment. Mechanical forces developed by cells to their surrounding environments are fundamental to many physiological processes, such as cell growth, division, migration and apoptosis. In this paper, a novel optical Moire based biomechanol force sensor was developed for cell traction force mapping. We utilized coherent laser beams to illuminate periodic polymeric substrates where isolated cells were cultured. We demonstrated one-dimensional and two-dimensional traction force mapping via optical Moire for both cardiac myocytes and vascular smooth muscle cells. The magnification effect of the Moire fringe pattern permits a real time monitoring of the mechanical interaction between isolated cells and their underlying periodic polymeric structures.