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These include bounding volume hierarchies like sphere trees [39,40], OBB-trees (Oriented Bounding Boxes) [41], AABB (axis-oriented bounding box) trees [42] and hierarchies of k-DOPs (Discrete Orientation Polytopes) [43], as well as spatial partitioning like octrees (octant trees) [44], kd-trees [45] and position code algorithms [46 48].
Thermal activation is described as a hopping process over a multidimensional energy landscape using the discrete orientation model limit of the Landau Lifshitz Gilbert dynamics.
Here we show that such patterns can be simulated by one discrete orientation relationship and two continuous rotations that correspond to a trace of the transformation mechanisms.
In this procedure, the result for each step provides the isotropic design, continuous fiber orientation design, and functionally graded discrete orientation design, respectively.
In modeling the linear elastic behavior of a polycrystalline material on the microscopic level, a special problem is to determine a so-called discrete orientation distributions (DODs) which satisfy the isotropy condition.
For solving the optimization problem which involves multiple design variables such as the density variable, fiber orientation variable, and target discrete orientation set, a three-step sequential optimization procedure is proposed.
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The paper is concerned with the novel method of pseudo-grain discretization based on the optimal selection of pseudo-grains discrete orientations and corresponding weights.
The ODF is recovered using a and A and numerically computed at a number of discrete orientations.
The discrete orientations of the orbits explain some of the magnetic field effects—namely, the so-called normal Zeeman effect, which is the splitting of a spectral line into three separate subsidiary lines.
However, conventional coding based approaches usually extract only one dominant orientation feature by adopting filters with discrete orientations, which is sensitive to the noise and rotation.
Problems of this type arise for example if the codf has to be reconstructed from discrete orientations or if one looks for a physical interpretation of the codf.
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