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Analysis and Design of RF Coils
Published in Jianming Jin, in Magnetic Resonance Imaging, 2018
With the formulation given above, we have to find the image for each conductor. Since the shield is of finite size, it is difficult, if not impossible, to determine the exact location of the image. However, if we introduce the approximation which assumes the shield to be of infinite size, the location of the image can be determined easily. For example, if the shield is locally flat, the location of the image would be on the other side of the shield whose position is symmetric to the original current with respect to the shield. If the shield is locally a cylindrical surface and the original current is parallel to the axis of the shield, the location of the image would be on the other side of the shield whose distance from the shield is d = Ri − Rs = Rs2/R − Rs where Rs is the radius of the shield and R is the distance between the original current and the axis of the shield (Lu and Joseph 1991). Although the approximation described above seems to be rather simple, it is accurate enough since, in most designs, the shield is placed very close to the coil and extends beyond the ends of the coil.
Strip Adjustment and Registration
Published in Jie Shan, Charles K. Toth, Topographic Laser Ranging and Scanning, 2017
With the increasing availability of LiDAR intensity data, also frequently called reflectance values, LiDAR strip adjustment methods started to exploit this additional information primarily to support the matching between different strips. As discussed in the previous paragraphs, methods that are exclusively based on the use of the LiDAR point cloud (a mass of points defined by three coordinates) require adequate terrain characteristics, such as planar or smoothly changing surface areas with different orientations, to successfully recover systematic error terms. Large areas with no surface undulations or with limited slope cannot provide for sufficient strip discrepancy determination, in particular in the horizontal direction, and consequently any 3D adjustment will fail in such cases. Intensity data, now a standard output on modern LiDAR systems, complements the blind LiDAR point cloud with a conventional image-type of data, which is similar to an image produced by a single spectral band of a hyperspectral camera. Since LiDAR intensity generally provides more variation in terms of image texture or contrast, compared to elevation data, therefore, it can support matching in areas where the height differences are limited or nonexistent. A good example, as shown in Figure 8.14, is the transportation road network (which generally represents locally flat areas), where ubiquitous pavement markings are clearly visible in the intensity image and thus can be routinely matched. Obviously, the image domain matching only provides for the determination of horizontal offsets. As LiDAR intensity and range data are perfectly coregistered, the intensity domain matching results can be directly converted to 3D strip discrepancies.
Strip Adjustment
Published in Jie Shan, Charles K. Toth, Topographic Laser Ranging and Scanning, 2018
Charles K. Toth, Zoltan Koppanyi
With the increasing availability of LiDAR intensity data, also frequently called reflectance values, LiDAR strip adjustment methods started to exploit this additional information primarily to support the matching between different strips. As discussed in the previous paragraphs, methods that are exclusively based on the use of the LiDAR point cloud (a mass of points defined by three coordinates) require adequate terrain characteristics, such as planar or smoothly changing surface areas with different orientations, to successfully recover systematic error terms. Large areas with no surface undulations or with limited slope cannot provide for sufficient strip discrepancy determination, in particular in the horizontal direction, and consequently any 3D adjustment will fail in such cases. Intensity data, now a standard output on modern LiDAR systems, complements the blind LiDAR point cloud with a conventional image-type of data, which is similar to an image produced by a single spectral band of a hyperspectral camera. As LiDAR intensity generally provides more variation in terms of image texture or contrast, compared with elevation data, therefore, it can support matching in areas where the height differences are limited or nonexistent. A good example, as shown in Figure 8.12, is the transportation road network (which generally represents locally flat areas), in which ubiquitous pavement markings are clearly visible in the intensity image and thus can be routinely matched. Obviously, the image domain matching only provides for the determination of horizontal offsets. As LiDAR intensity and range data are perfectly coregistered, the intensity domain matching results can be directly converted to 3D strip discrepancies.
Contact line motion on heated patterned surfaces
Published in Numerical Heat Transfer, Part A: Applications, 2022
Vladimir S. Ajaev, Jill Klentzman, Oleg A. Kabov
The inflow boundary conditions at x = 0 are specified using the same method as in [22] while the side and downstream conditions are those of locally flat interface shapes. A coarse N × N finite-difference mesh is introduced with local refinement near the contact line, with mesh size increased by a factor of 4. The evolution equation was solved numerically using the alternating directions implicit (ADI) method with time stepping by the standard DVODPK software package [33]. Convergence under mesh refinement was verified by running the simulations at different N from N = 41 to N = 161. To obtain an accurate approximation of the interface shape, the value of N = 101 turns out to be sufficient, so it is used in the simulations in the next section.