Propagation particle interaction

As already stated in Chap. 3, there is a significant influence of particle interaction on the macroscopic properties of colloidal suspensions (e.g. viscosity, sedimentation, light scattering, sound propagation). Moreover, the attractive part of the particle interaction ultimately causes aggregation (or coagulation) in colloidal systems. 

In one study, Steiglitz, Irfan Kamal, and Arthur Watson (1988) designed a particular class of CAs—the one-dimensional, binary-state, parity-rule filter automata — to perform arithmetic. This class of automata has the property that propagating periodic structures often act as solitons —that is, they can pass through each other in space-time without destroying eax h other, but only shifting each others phase. It turns out that such a feature can be useful for implementing arithmetic operations in CAs via particle interactions. 

This frequency is a measure of the vibration rate of the electrons relative to the ions which are considered stationary. Eor tme plasma behavior, plasma frequency, COp, must exceed the particle-coUision rate, This plays a central role in the interactions of electromagnetic waves with plasmas. The frequencies of electron plasma waves depend on the plasma frequency and the thermal electron velocity. They propagate in plasmas because the presence of the plasma oscillation at any one point is communicated to nearby regions by the thermal motion. The frequencies of ion plasma waves, also called ion acoustic or plasma sound waves, depend on the electron and ion temperatures as well as on the ion mass. Both electron and ion waves, ie, electrostatic waves, are longitudinal in nature that is, they consist of compressions and rarefactions (areas of lower density, eg, the area between two compression waves) along the direction of motion. 

We will be concerned with the interaction of waves with boundaries and with other waves throughout this text. To determine how these interactions take place, it is important to consider that discontinuities in either pressure or particle velocity cannot be sustained in any material. If a discontinuity in either of these variables is created at some point by impact or wave interaction, the resulting motion will be such that the pressure and particle velocity become continuous across the boundary or point of interaction. Unless the material separates at that point, the motion will consist of one or more waves propagating away from the point of the discontinuity. For pressure discontinuities, it is easy to see that waves must propagate by again considering an... 

We assume that in (4.38) and (4.39), all velocities are measured with respect to the same coordinate system (at rest in the laboratory) and the particle velocity is normal to the shock front. When a plane shock wave propagates from one material into another the pressure (stress) and particle velocity across the interface are continuous. Therefore, the pressure-particle velocity plane representation proves a convenient framework from which to describe the plane Impact of a gun- or explosive-accelerated flyer plate with a sample target. Also of importance (and discussed below) is the interaction of plane shock waves with a free surface or higher- or lower-impedance media. 

The physical state of the sample before and after impact is sketched in Fig. 4.6(a). Positive velocity, indicating mass motion to the right (in the laboratory), is plotted toward the positive, u, axis. Hence, in the initial state 0, the target B is at Up = 0 and P = 0, whereas the initial state in the flyer plate O is Up = Ufp and P = 0. Upon interaction of flyer plate A with target B, a shock wave propagates forward in the sample and rearward in the flyer plate. Because the pressure and particle velocity are continuous at the flyer-... 

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