Rayleigh particles

The particles may not be spherical or, if spherical, they may agglomerate into nonspherical clumps. Contrary to much common opinion, absorption by Rayleigh particles can be quite shape dependent, as we have shown in Chapter 12. 

The Rayleigh particle is the same particle as the Brownian particle, but studied on a finer time scale. Time differences At are regarded that are small compared to the time in which the velocity relaxes, but, of course, still large compared to the duration of single collisions with the gas molecules. Thus the stochastic function to be considered is the velocity rather than the position. It is sufficient to confine the treatment to one dimension this is sometimes emphasized by the name Rayleigh piston . 0... 

The process X(t) is now fully specified since it is Gaussian and the first two moments are known. But it is not the same as the Wiener process determined by (3.1), because the autocorrelation function is more complicated than (IV.2.7a). In fact, X(t) is not even Markovian, owing to the fact that it is still described on the fine time scale belonging to the Rayleigh particle. On the coarse time scale only time differences much larger than the damping time l/y of the velocity are admitted,... 

Exercise. Take an ensemble of Rayleigh particles whose position at t = 0 is the origin and whose initial velocities have a Maxwell distribution. Show... 

Exercise. Formulate the process described by the V and X of a Rayleigh particle as a composite Markov process in the sense of VII.7. 

Example. The Rayleigh particle. The velocity V is governed by an M-equation with W(V V ) given by (VIII.4.14). The jumps in V are caused by collisions of the gas molecules and are therefore of order (m/M)v, where v is a typical velocity characterizing the velocity distribution F. They can be made small by choosing M large accordingly we take Q = M/m. The variable in which the jumps remain of the same size is the momentum P = MV. This is our variable X, while mV serves as intensive variable x. The transition probability in the variable X is... 

Exercise. Find the coefficients a in (2.16) explicitly for the Rayleigh particle using (2.5). 

Svoboda K, Block SM (1994) Optical trapping of metallic Rayleigh particles. Opt Lett... 

Lips, A. Levine, S. Light Scattering by Two Spherical Rayleigh Particles... 

Figure 3. Normalized polarization Mueller matrix elements calculated for a small Rayleigh particle placed a distance X/4.7 from a substrate (/ sub = 0-5 + 3.5i) illuminated at 6o = 79 (dotted). Superimposed are the experimental matrix elements measured by lafelice and Bickel [31] of a perfect (solid) and decayed (dashed) mirror surface, X = 0.4416 m. lafelice and Bick el noted the presence of defects ranging in size from 0.2 to 1.0 m. The size rang e did not vary per sample, but the number density for the perfect sur face was approximately five times less than for the decayed surface.

Let us define a relation between the correlation functions of the internal structure of a liquid and the phenomenon of light scattering (Skryshevsky, 1980). The total amplitude of the waves scattered by a given configuration of structural elements, each approximated by a Rayleigh particle, in the case of vertically polarized light is expressed by (Kquations 2.1 -51,-18,-d9)... 

Ng LN, Luf BJ, Zervas MN, Wilkinson JS (2000) Forces on a Rayleigh particle in the cover region of a planar waveguide. 1 Lightwave Technol 18(3) 388-400... 

The physical interpretation given by Troei-STRA is that the floes arc relatively dense, resembling more the highly scattering Rayleigh particles, when the repulsive action of the double layer is not completely discarded ... 

---