Propagation horizontal

Figure 9.11 The relative effects of reaction-diffusion, buoyancy and Marangoni convection were demonstrated by Simoyi and colleagues in the chlorite-thiourea-barium chloride reaction system (Hauser and Simoyi, 1994b). The front rises along the tilted side of the container faster than it propagates horizontally. When the front reaches the interface, its horizontal propagation accelerates because of surface-tension-induced convection. (Courtesy of R. Simoyi.)...

FIG. 5-14. Stroboscope photograph of a wave of shear strain double refraction in a 1% solution of sodium deoxyribonucleate at 2S°C, frequency 125 Hz. The driving plate is oscillated vertically shear waves propagated horizontally to the right produce patterns of strain double refraction. Each boundary between black and white provides the same information the inclination of the base lines is specified by the angle between the axes of the Babinet compensator and the analyzing Polaroid (from reference 117). ... 

All known valence states of carbon are laid down on the graph of all 139 valence states of atoms. The quadruplets of valence states 1 >,V3,V4 (Sect. 4.3), denoted here as N, S, D, T, respectively, are encircled. The numbers of lone electrons (N) on the top two lines are propagated vertically down for all vectors, the triplets (SDT) on the left are propagated horizontally. Carbon valence states intercon-vertable by elementary conversions are Joined by heavy lines. For example, the vertex (2200), which lies in the line beginning with description (200) under the circle for N=2, represents the carbon in... 

In the future, it is expected to be possible to make more routine use of additional wave types, specifically shear or S waves (polarised to horizontal and vertical components) which have a transverse mode of propagation, and are sensitive to a different set of rock properties than P waves. The potential then exists for increasing the number of independent attributes measured in reflection surveys and increasing the resolution of the subsurface image. 

Figure Al.6.21. Bra and ket wavepacket dynamics which detennine the coherence overlap, (( ) ( ) ). Vertical arrows mark the transitions between electronic states and horizontal arrows indicate free propagation on the potential surface. Full curves are used for the ket wavepacket, while dashed curves indicate the bra wavepacket. (a) Stimulated emission, (b) Excited state (transient) absorption (from [41]).

Fig. 3. Stepsize r used in the simulation of the collinear photo dissociation of ArHCl the adaptive Verlet-baaed exponential integrator using the Lanczos iteration (dash-dotted line) for the quantum propagation, and a stepsize controlling scheme based on PICKABACK (solid line). For a better understanding we have added horizontal lines marking the collisions (same tolerance TOL). We observe that the quantal H-Cl collision does not lead to any significant stepsize restrictions.

Fig. 1. Pressure required for propagation of decomposition flame through commercially pure acetylene free of solvent and water vapor in long horizontal pipes. Gas initially at room temperature ignition by thermal nonshock sources. Curve shows approximate least pressure for propagation (0), detonation,...

The presence of horizontal or vertical obstacles (Figure 4.4) in the propane cloud hardly influenced flame propagation. On the other hand, flame propagation was influenced significantly when obstacles were covered by steel plates. Within the partially confined obstacle array, flame speeds up to 66 m/s were observed (Table 4.2) they were clearly higher than flame speeds in unconfined areas. However, at points where flames left areas of partial confinement, flame speeds dropped to their original, low, unconflned levels. 

Architectural models explicitly specify the di.stribution of roots in space. An alternative approach, which is also useful for rhizosphere studies, is the continuum approach where only the amount of roots per unit soil volume is specified. Rules are defined that specify how roots propagate in the vertical and horizontal dimensions, and root propagation is u.sually viewed as a diffusive phenomenon (i.e., root proliferation favors unexploited soil). This defines the exploitation intensity per unit volume of soil and, under the assumption of even di.stribution, provides the necessary information for the integration step above. Acock and Pachepsky (68) provide an excellent review of the different assumptions made in the various continuum models formulated and show how such models can explain root distribution data relating to chrysanthemum. 

Figure 2.10. Direction of electric vector in (a) unpolarized and (b) polarized light the direction of propagation of the light wave is along the horizontal from left to right.

Femandez-Pello, A.C., Ray, S.R. and Glassman, I., A study of heat transfer mechanisms in horizontal flame propagation, J. Heat Transfer, 1980, 102(2), 357-63. 

In the trough test, the sample (only solids) is introduced in a horizontal wire mesh cage with an inner volume of 11 liters. The substance is initiated at one end of this trough by a gas burner or electrical heating source and the propagation of the deflagration front is established and noted. 

It is important to note that the velocity of the wave in the direction of propagation is not the same as the speed of movement of the medium through which the wave is traveling, as is shown by the motion of a cork on water. Whilst the wave travels across the surface of the water, the cork merely moves up and down in the same place the movement of the medium is in the vertical plane, but the wave itself travels in the horizontal plane. Another important property of wave motion is that when two or more waves traverse the same space, the resulting wave motion can be completely described by the sum of the two wave equations - the principle of superposition. Thus, if we have two waves of the same frequency v, but with amplitudes A and A2 and phase angles

resulting wave can be written as ... 

Fig. 6. MR wave image of acoustic refraction. Shear waves generated in the upper part of an agar gel phantom (horizontal motion) propagate vertically in the stiff part of the phantom (/i 50 kPa cT 7.5 cm/s) and are refracted by the oblique lower part of soft gel (fi 15 kPa cT 4 cm/s). Note the marked reduction of wavelength in the softer medium. From Ref. 23, reprinted by permission of Wiley-Liss, Inc., a subsidiary of John Wiley Sons, Inc.

We shall draw a horizontal line to represent the propagation of each of the n particles. These lines are connected two by two by vertical lines which correspond to the binary interactions. To each horizontal line is associated a wave vector k, (s = 1,2,.. ., n) of the particle s. The wave vectors are modified by the interactions with the following selection rule ... 

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