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The population balance approach characterizes particles of the dispersed phase by internal coordinates such as the particle length in crystallization processes.
Different MBS algorithms, however, employ different sets of orientation coordinates, such as Euler angles and Euler parameters, which lead to different forms of the dynamic equations of motion.
Unlike IIF, cIIF cannot be directly extended to other curvilinear coordinates, such as polar and spherical coordinates, due to the compact representation for the diffusion terms in cIIF.
The cage allows to easily introduce other restrictive criteria (e.g., avoid self-intersections), apart from the already intrinsic properties of the mean value coordinates such as smoothness [17].
Luscus can visualise structures and chemical properties, which include more than one set of Cartesian coordinates, such as trajectories, reaction coordinates and other dynamical properties.
The state-of-the-art local surface editing techniques depend on intrinsic coordinates, such as multi-resolution decompositions [1] and various shape deformation frameworks.
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To solve that problem, a lot of work has focused on developing a good calibration method in order to transform between color coordinate, depth coordinate and real world coordinate such as Microsoft Kinect SDK, Burrus [8], Tang [21].
In view of its special role, a coordinate such as Q is often termed a 'promoting' mode or vibration.
This kind of analysis also emerges from representations of the involved electronic states as functions of the proton coordinate, such as in Figure 27, reported from ref (215).
The equilibrium free energy curve along a reaction coordinate, such as that in Fig. 4a and in numerous examples in the literature, assumes that the environment is always equilibrated at each point along the reaction coordinate.
Here, q is some internal coordinate such as angle or separation of CG beads, k B is the Boltzmann factor, T is the absolute temperature, V q) and P q) are the potential-of-mean-force (PMF) and the probability/frequency distribution at q, respectively.
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