Cell displacement dynamics

Active contour - Shape changes of the object can be precisely measured - Suited for objects with a combination of displacement and large shape changes - User must initially define the position of the active contour - Requires registration when successive positions are apart (typically, more than a diameter of the initial active contour) - Parameter settings require a skilled experience Dynamics of shape changes Cell migration dynamics... 

The atomic temperature factor, or B factor, measures the dynamic disorder caused by the temperature-dependent vibration of the atom, as well as the static disorder resulting from subtle structural differences in different unit cells throughout the crystal. For a B factor of 15 A2, displacement of an atom from its equilibrium position is approximately 0.44 A, and it is as much as 0.87 A for a B factor of 60 A2. It is very important to inspect the B factors during any structural analysis a B factor of less than 30 A2 for a particular atom usually indicates confidence in its atomic position, but a B factor of higher than 60 A2 likely indicates that the atom is disordered. 

The elements of D represent the sum over all unit cells of the interaction between a pair of atoms. D has 3n x 3n elements for a specific q and j, though the numerical value of the elements will rapidly decrease as pairs of atoms at greater distances are considered. Its eigenvectors, labeled e ( fcq), where k is the branch index, represent the directions and relative size of the displacements of the atoms for each of the normal modes of the crystal. Eigenvector ejj Icq) is a column matrix with three rows for each of the n atoms in the unit cell. Because the dynamical matrix is Hermitian, the eigenvectors obey the orthonormality condition... 

Thus, during dynamics, the particles could leave the central box. At equilibrium, it is not necessary for the particles to be brought back into the central box. However, when this must be done, the PBC procedure, which is similar to minimum imaging, can be performed. In this procedure, the particle coordinates q,- are converted to scaled coordinates s,-. These are then brought into the ntral cubic box by means of the dnint operation, and then unsealed using h to give back q, in the central cell. Because unshifted particle coordinates along the trajectory are often required (to calculate, e.g., mean-squared displacements), it is not necessary to perform PBC under equilibrium conditions. 

The displacements of atoms may take several forms (Figure 13.2). These have been described by Jack Dunitz, Verner Schomaker, and Kenneth N. Trueblood as follows The perfectly ordered crystal would have every atom firmly fixed to its own perfectly defined site in each unit cell for the entire period of observation. There are, however, various types of disorder from unit cell to unit cell. If the atom jumps to a different site, that is one kind of disorder [a mixture of static and dynamic disorder ] if it moves to and fro, that is another kind of disorder [ dynamic disorder] if it is forever in one site in a certain unit cell and in a different site in another cell, that is still another kind [static disorder]. Each of these types of vibrations, displacements, and disorder has somewhat similar effects on the intensities of Bragg reflections the effect they have in common is that they reduce these intensities by an amount that increases with increasing scattering angle, 26, as shown in Figure 13.1. 

Unlike ASE, because the leaching agent used in the dynamic mode is most often water, no desiccant need be added to the extraction cell together with the sample. As in ASE, however, additional materials such as surfactants [47] or sorption discs [39] can be placed in the cell to facilitate displacement of the analytes from the sample to the micellar medium or preconcentrate them in the sorbent, respectively. 

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