Kinematic wave, shock

Figure 5.15. The profile of a kinematic shock wave [17] (a) growth (b). (c) dissolution. In (b) and (c), dissolution steps advance from left to right, and shock waves appear at P and Q.

In the limit where diffusion may be neglected, the sedimentation behavior is similar in many (but not all) respects to the gravity sedimentation discussed in the last section. There will be a sharp kinematic shock wave that propagates through the fluid, separating the clarified liquid (pure solvent) from the mixture... 

This simple example Illustrates the important kinematic properties of shock waves, particularly the concepts of particle velocity and shock velocity. The particle velocity is the average velocity acquired by the beads. In this example, it is the piston velocity, v. The shock velocity is the velocity at which the disturbance travels down the string of beads. In general, at time n//2v, the disturbance has propagated to the nth bead. The distance the disturbance has traveled is therefore n d -b /), and the shock velocity is... 

The chapters presented by different experts in the field have been structured to develop an intuition for the basic principles by discussing the kinematics of shock compression, first from an extremely fundamental level. These principles include the basic concepts of x-t diagrams, shock-wave interactions, and the continuity equations, which allow the synthesis of material-property data from the measurement of the kinematic properties of shock compression. A good understanding of these principles is prerequisite... 

If these characteristics correspond to those of a shock wave they should be straight lines with slopes equal to the kinematic velocities as shown in Fig. 4—1. From the estimated LG characteristics we observe that a linear shock wave develops after... 

Speed of plane kinematic wave Speed of kinematic shock moving up from container bottom True electrophoretic velocity in electrophoresis cell Speed with which a point with ionic fraction Xg in solution moves Electroosmotic velocity in electrophoresis cell Speed of ion exchange zone front Liquid velocity in electrophoresis cell Maximum fluid velocity at center of circular or straight channel with fully developed velocity profile, Eq. (4.2.14) Velocity at free surface of... 

For the two-dimensional case depicted in Figure 6.9 another velocity, c = dx/d/, may be defined which represents the motion of kinematic waves (regions on the crystal surface with a constant slope p and velocity v). These waves do not contain the same monomolecular steps all the time, as the step velocity u = vjp can be greater or less than c. When two kinematic waves of different slope meet, a discontinuity in slope occurs, giving rise to shock waves across the surface. 

We have also demonstrated the capabilities of eFF for computing single-shock Hugoniots for lithium metal from dynamic shock wave experiments, via the shock wave and piston kinematics and initial and final densities of a 640,000-particle system (see Fig. 10). We also reported on the degree of ionization suffered by the material, a function of the explicit nuclear delocalization of electrons [90]. A simpler depiction of such dynamic shock experiments is shown in Fig. 11, wherein... 

Table 3.3 summarizes the history of the development of wave-profile measurement devices as they have developed since the early period. The devices are categorized in terms of the kinetic or kinematic parameter actually measured. From the table it should be noted that the earliest devices provided measurements of displacement versus time in either a discrete or continuous mode. The data from such measurements require differentiation to relate them to shock-conservation relations, and, unless constant pressures or particle velocities are involved, considerable accuracy can be lost in data processing. 

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