Size distribution bifurcations

Smooth cells, also found in layers I and III. Those in layer I exhibit a variety of cell shapes and sizes and they are distinguished by a lack of spines on the cell body or dendrites and by the presence of beaded varicosities on the distal dendrites. Smooth cells are the most numerous nonpyramidal cells in layer III, and they are preferentially distributed in the middle and deep parts of layer III. The dendrites emerge from numerous sites on the soma, usually branch once or twice near the soma, and then extend radially in all directions, with few subsequent bifurcations. The dendritic tree typically respects the boundaries of layer III. 

The method of the normal solution expansion provides a means to obtain the critical patch size if F (0) > 0, the saddle-node bifurcation point if p iff) < 0, and the stability of the steady states. An analytical expression for the steady state can also be obtained, but it is an approximate solution since we truncate the expansion. The normal solution expansion is a well-known method to obtain solutions of the nonlinear Boltzmann equation [180, 359]. It assumes that the distribution function f(jc, v, t), describing the density of atoms or structureless molecules at position x with velocity V at time t depends on time only through the velocity moments /o(jc, t), u(x, t), Pij x, t), i.e., f(jc, V, t) f(jc, V, p(x, t), u(x, t), Pjjix, t)), where p, u, Pij are found by integrating f, fw, and fVjVj, respectively, over the full velocity space. We express the solution of (9.1) in terms of an appropriate complete set of orthogonal spatial basis functions ... 

To analyze the particle capture efficiency of the upper lung, particles of different diameters were initially released with a uniform distribution at the trachea inlet and their trajectories were analyzed. Figure 36 shows the locations at which the particles of different size were captured. It is seen that the relatively large 30-pm particles are mainly deposited on the carina by impaction mechanisms. On the other hand, the 10-nm particles have a more uniform distribution pattern. These small particles are deposited mainly by the diffusion process on the entire passage surface. Very few 1-pm particles are captured by the first lung bifurcation, since for this size range. 

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