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The goaf left behind after mining has the potential to induce serious geological disasters due to the damaged internal structure of the rock. Estimating the boundary of the underground goaf can effectively control the occurrence of such disasters. However, traditional geophysical methods are inefficient and expensive and are particularly difficult to apply for a wide detection range. This paper proposes a new method for estimating the boundary of underground goaf using the differential interference synthetic aperture radar technique (DInSAR). More specifically, DInSAR is used to obtain the isoline of the subsidence basin above the goaf, and the direction of the two main sections of the goaf is then determined according to the basic law of mining subsidence. Following this, the basic principles of the probability integral and the graphical methods are combined to determine the mining boundary of the strike section and the incline section of the goaf. Finally, six geometric parameters reflecting the boundary of the goaf are obtained. Experiments on simulated and measured data indicate that the proposed method is feasible, with the average relative errors of the simulated and measured data reaching and maintained at 2.2% and 3.7%, respectively.

Rotational Risley prisms are one of the fastest two-dimensional (2D) optomechanical scanning systems. Their drawback is the strong non-linearity of the scan patterns they produce, in contrast to the most common (but slower) raster scanning modalities of 2D dual axis galvanometer scanners (GSs) or Micro-Electro-Mechanical Systems (MEMS) with oscillatory mirrors. The aim of this work is to develop a graphical method, which, to our knowledge, we have introduced to determine and characterize, using a commercially-available mechanical design program (for example CATIA V5R20 (Dassault Systems, Paris, France)) to simulate the exact scan patterns of rotational Risley prisms. Both the maximum and minimum angular and linear deviations of this type of scanner are deduced theoretically to characterize the outer diameter/Field-of-View (FOV) and the inner diameter (of the blind zone) of its ring-shaped patterns, respectively. This multi-parameter analysis is performed in correlation with the shape of the scan patterns, considering the four possible configurations of laser scanners with a pair of rotational Risley prisms, as well as all their parameters: prisms angles, refractive indexes, rotational speeds, distance between the two prisms, and the distance from the system to the scanned plane. Marshall’s synthetic parameters are also considered, i.e., the ratios of the rotational velocities and of the angles of the prisms. Rules-of-thumb for designing this optomechanical scanner are extracted from this analysis, regarding both shapes and dimensions of the scan patterns to be produced. An example of experimental validation completes the mathematical analysis and the performed simulations.

Abstract Background When researchers describe data from their studies, there is no rule defining the best way to represent results. Therefore, collecting and explaining results from personal research or understanding data from publications is not always straightforward. These issues are even worse in fields such as biomedical engineering, where researchers from different backgrounds, usually engineers and surgeons, need to interact and exchange information. For these reasons, the purpose of this study is to introduce and illustrate an innovative method to represent, concisely and intuitively, biomechanical knee behavior, called KneePrints. Methods To test the KneePrints method, a huge amount of data from previously published sensitivity analyses were used and represented both with conventional techniques and with this new graphical method. Then, a survey has been distributed among different international specialists in the orthopedic field, such as surgeons and researchers. In the survey, interviewees were asked to select the favorite method that addressed to be the most effective to show the same results. Results Collecting the outcomes from the survey, the KneePrints method resulted to be more effective than standard graphs, such as tables and histograms. KneePrints method has been selected to be clearer in representing outputs and more immediate in results understanding independently from the occupation of the interviewees by the survey. The general preference for the KneePrints is 63 %, up to 74 % being surgeons’ choice. Conclusions The innovative KneePrints method has been endorsed to be effective in representing and making more understandable knee joint outputs. This method can be extended also to other topics.

A great circle route (GCR) is the shortest route on a spherical earth model. Do we have a visual diagram to handle the shortest route? In this paper, a graphical method (GM) is proposed to solve the GCR problems based on the celestial meridian diagram (CMD) in celestial navigation. Unlike developed algebraic methods, the GM is a geometric method. Appling computer software to graph, the GM does not use any equations but is as accurate as using algebraic methods. In addition, the GM, which emphasizes the rotational surface, can depict a GCR and judge its benefit.