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Forward Modeling
Published in Jeffrey P. Simmons, Lawrence F. Drummy, Charles A. Bouman, Marc De Graef, Statistical Methods for Materials Science, 2019
Figure 4.3 shows stereographic projections of the exit BSE distributions as a function of electron energy for a 20-keV incident electron energy. A stereographic projection is an equal-angle projection from the surface of a sphere to a 2D disk, and is used in materials science to represent functions on a sphere in a convenient 2D projection; in particular, circles on the sphere remain circles in the projection. For each energy level, the projection represents all electrons within 0.5-keV from the indicated energy. The incident beam is incident from the top, at 20° above the horizontal plane (corresponding to the standard sample tilt angle of 70°). The rightmost pattern shows the sum of all the individual patterns (which were computed for 0.5 keV step sizes between 5 and 20 keV). The sum projection clearly shows that the BSE process is a highly directional process, and that the best detector position is around the lower half of the projection.
Structural geology and data interpretation
Published in Duncan C. Wyllie, Christopher W. Mah, Rock Slope Engineering, 2017
Duncan C. Wyllie, Christopher W. Mah
The primary purpose of plotting great circles of discontinuity sets in a slope is to determine the shape of blocks formed by intersecting discontinuities, and the direction in which they may slide. For example, in Figure 2.1 the slope failures only occurred for conditions where single discontinuities (Figure 2.1(a)), or pairs of intersecting discontinuities (Figure 2.1(b)), dip out of the face. It is, of course, important to identify such potential failures before movement and collapse occurs. This requires an ability to visualize the three-dimensional shape of the wedge from the traces of the discontinuities on the face of the original slope. The stereographic projection is a convenient means of carrying out the required three-dimensional analysis, keeping in mind that this procedure examines only the orientation of the discontinuities and not their position or dimensions. If the stereonet shows the possible occurrence of a potentially unstable block, examination of the location of the discontinuities on the geological map would help to determine if they intersect the slope.
Structural geology and data interpretation
Published in Duncan C. Wyllie, Rock Slope Engineering, 2017
The primary purpose of plotting great circles of discontinuity sets in a slope is to determine the shape of blocks formed by intersecting discontinuities, and the direction in which they may slide. For example, in Figure 2.1, the slope failures only occurred for conditions where single discontinuities (Figure 2.1a), or pairs of intersecting discontinuities (Figure 2.1b), dip out of the face. It is, of course, important to identify such potential failures before movement and collapse occurs. This requires an ability to visualise the three-dimensional shape of the wedge from the traces of the discontinuities on the face of the original slope. The stereographic projection is a convenient means of carrying out the required three-dimensional analysis, keeping in mind that this procedure examines only the orientation of the discontinuities and not their physical position or dimensions. If the stereonet shows the possible occurrence of a potentially unstable block, examination of the location of the discontinuities on the geological map would help to determine if they intersect the slope.
Application of UAVs in the mining industry and towards an integrated UAV-AI-MR technology for mine rehabilitation surveillance
Published in Mining Technology, 2023
Phillip Stothard, Roohollah Shirani Faradonbeh
Salvini et al. (2018) applied UAVs to slope identification, stability monitoring, and geological engineering investigations. A Class 3d UAV was applied to this project (Table 3). UAV data was used to create a detailed 3D model from high-resolution images that were processed using SfM techniques. Salvini et al. (2018) applied geometrical and radiometric information to determine rock mass characterization. Two large blocks were identified that posed a significant hazard. Salvini et al. (2018) obtained the geometric characteristic of the two blocks, including the orientation of the intersecting discontinuities and the volume of the meshed block. Via stereographic projection, the orientation of 154 discontinuity planes was selected on the point cloud, and based on the characteristics of discontinuity derived from surveys. Salvini et al. (2018) performed a preliminary stability analysis to demonstrate the potential application of remotely piloted aircraft systems (RPAS) information in engineering geology to identify and reduce possible geo-hazards.
Determination of particular singular configurations of Stewart platform type of fixator by the stereographic projection method
Published in Inverse Problems in Science and Engineering, 2021
Doğan Dönmez, İbrahim Deniz Akçalı, Ercan Avşar, Ahmet Aydın, Hüseyin Mutlu
Since any plane perpendicular to diametral axes of the sphere will involve the projected circles passing through the points to in accordance with the stereographic projection method, centre coordinates , being also on plane, will have to satisfy the following equations: where is the radius of the bottom ring on plane. The unique solution of Equations (19) and (20) for four unknowns is accomplished on a set of three linear equations obtained by subtracting the first equation from the second and third equations. As a check, coordinates will also fall on the same circle with radius and centre at .
Secondary twinning in zinc
Published in Philosophical Magazine Letters, 2018
Václav Paidar, Jaroslav Čapek, Andriy Ostapovets
The angle between the intersection of the habit plane of the secondary twin (dashed-circle in Figure 3 for Tw D) with the matrix basal plane (perpendicular to z represented by the large circle of the stereographic projection) and the matrix direction along the x axis is about 42°. The basal plane of the primary twin Tw A is close to the plane perpendicular to the y axis in Figure 3, i.e. about 4° below the x–z plane. The normal of the secondary twin Tw D lies on this Tw A basal plane. The intersection of the habit plane of the conjugate secondary twin and the matrix basal plane is approximately perpendicular to the intersection of the original secondary twin with the matrix basal plane. Four secondary twins (conjugate twins are denoted by an additional C) that may appear inside the primary twin Tw A are shown in Figure 4. The remaining two secondary twins (that are not depicted) would cause detwinning, i.e. the transition of the primary twin back to the matrix orientation.