Kinematics properties

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... 

Equation (8.46) applies to the motion until fracture is complete. After this the form of (8.45) applies. Kipp and Grady (1985) have shown that the time to fracture (time from inception to completion of failure at the fracture zone) depends on the material and kinematic properties of the problem according to... 

The important observation from this data, however, is that it tends to support the basic premise suggested in the previous section namely, geometric statistics appear to provide for the gross trend of the distribution data, without alluding to specific material or kinematic properties. More specific... 

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... 

Figure 8.8 shows a marked increase in the scatter of [a/Fe] as one goes down through [Fe/H] = -0.4, at which point there is also a marked change in kinematic properties, notably the dispersion of velocities W perpendicular to the Galactic... 

The oscillating magnetic field is most effective in causing transitions when its direction is perpendicular to the static field and causes no transitions when parallel to the static field. The reason for this behavior is made clear by an examination of the kinematical properties of a magnetic moment in a static magnetic field. 

As the wash ratio increases the mechanism being used to remove the solute changes from displacement and other effects such as dispersion, mixiag and diffiision become significant. A great deal of theoretical work has been done to describe these effects in capillary tubes and many workers have applied the same arguments to the problem as it occurs in porous media. Brenner [1962], for example, discusses the behaviour of an initially sharp interfece between two miscible liquids, having identical dynamical and kinematical properties, in terms of the concentration Cj of solute at a distance x fi om the point of introduction of the wash hquid at time /. The process is described by the equation ... 

Bearing in mind the former remarks about the choice of an equation for fitting procedure of a set of experimental data, it should be noted that correlation functions for viscosity values generally can be safely employed both for kinematic and dynamic quantities, this fact being stated and ascertained in many reports. Therefore, the equations scrutinized in this review satisfy these requirements even if more emphasis will be given on considering kinematic properties in particular. 

An interface, as in Figure 16-5, is defined by the kinematic property that fluid does not cross it. Hence, the velocity of the fluid normal to the interface must be equal to the velocity of the interface normal to itself. The velocity perpendicular to the surface, from vector algebra, is equal to -f (x,y,z,t)/V(fx ... 

The kinematic separator takes advantage of the kinematic properties of recoiling compound nuclei, whose direction and velocity are simply defined by the Newtonian laws of motion. The velocities of the recoil species are such that they... 

Therefore, represents a performance index describing synthetically both kinematic properties and inertial characteristics of a manipulator which can be considered as fundamental in a robot design, at least from a mechanical point of view. 

Finally, it should be pointed out that dissociative ionization yields fragment ions with small to moderate kinetic energies. To describe the dissociative ionization process completely, these kinematic properties must be known. 

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