Propagation dynamics

Propagation of pulses of intense light through condensed media opens a plethora of new possibilities over and above those that derive from free-space propagation. At the same time, there is a price to be paid in that concomitantly, the condensed medium also presents much more complexity as far as physical descriptions of the gamut of processes that determine the propagation dynamics are concerned. Nevertheless, there are several compelling reasons... 

A.A. Zozulya, S.A. Diddams, A.G.Van Engen, T.S. Clement, Propagation dynamics of intense femtosecond pulses multiple splitting, coalescence and continuum generation , Phys.Rev.Lett. 82, 1430-1433 (1999). 

Rapid crack propagation, dynamic fracture toughness, crack arrest, polyethylene pipes, pressure vessels... 

These measures of delay all provide useful indicators of the effective delay, but they do not in themselves indicate whether the effect of the delay prevents a disturbance from being rejected before causing constraint violations. In Holt and Morari s analysis, the disturbances are assumed to appear as steps on the outputs, making the question of whether the disturbance causes constraint violation trivial. In practice, disturbances are often well approximated by steps, but the effect of the step usually propagates dynamically through part of the process before affecting the outputs. This means that the effect of the process dynamics in attenuating the disturbance should be included in order to assess disturbance rejection. 

The addition of trace levels (>1M) of bis(bipyridine)cobalt(II) to O2-saturated solutions of aldehydes in acetonitrile initiates their rapid autooxidation to carboxylic acids. 0 Figure 6-1 illustrates the CoIKbpy)2 -induced autooxidation of hexanal [CH3(CH2)4CH(O)] for 02-saturated (8.1 mM) and air-saturated (1.6 mM) acetonitrile. The apparent reaction dynamics for the catalyzed auto-oxidation of PhCH(O) and of CH3(CH2)4CH(O) during the first hour of their auto-oxidation is summarized in Table 6-1. The initial reaction rates appear to be first order in catalyst concentration, first order in substrate concentration, and first order in O2 concentration (Fig. 6-1). However, within one hour the autooxidation process is almost independent of catalyst concentration. Although the Fellfbpy) and Mnii(bpy)complexes also induce the auto-oxidation of aldehydes, they are much less effective initiators, and the propagation dynamics are much slower. 

Light propagation dynamics near an induced photonic bandgap... 

In this subsection, we will investigate the propagation dynamics of an incident probe pulse in ultracold atoms aroimd a photonic bandgap induced by a time-independent SW coupling. Then it is necessary to resort to the Maxwell wave equations coupled with the density matrix equations, i.e. the cowpled Maxwell-Liouville equations. In particular, when the probe is very weak,... 

In this subsection, we will study the propagation dynamics of a probe pulse incident upon a sample of ultracold Rb atoms dressed by a time-modulated SW coupling, and pay special attention to the stationary light generation during the process where the two coupling components are switched on and off as in Fig. 13. In Fig. 14, we focus on and together with... 

Fig.l4 (color online) Nonlinear propagation dynamics of an incident probe pulse having a 1/e full width of 4.0//5 with the scaled 0.p+, Pfi P illustrated. The... 

Fig.l6 (color online) Nonlinear propagation dynamics of the same incident probe pulse and the accompanied coherence components with the same parameters as in Fig. 14 except that Eqs. (27) ate truncated at n =0. 

Fig. 8. Vibration-induced creep fracture, (a) Radially propagating dynamic fatigue fracture inside the material and (b) dynamic creep fracture in PS samples.

Lightly crossUnked acrylic networks Bulk rheological properties, elastic modulus, resistance to interfacial crack propagation Dynamic mechanical spectroscopy 129... 

H. Ruppe, S. Rutz, E. Schreiber, and L. Woste, Femtosecond Wave Packet Propagation Dynamics in the Dissociative K3 Molecule , Chem. Phys. Lett. 257, 356 (1996). 

Plume propagation dynamics of complex oxides in oxygen.. Appl Phys., 104, 053304. 

The kinematics of moving fronts and interfaces has been studied in different physical contexts for over two hundred years. Most notable are the studies of free surfaces in ocean hydrodynamics and vortex sheets in free space (e.g., see Lamb, 1945), and more recently, flame propagation dynamics in combustion analyses. The following derivation, which applies to fluid fronts in porous media, is given in Chin (1993a). Let us consider a moving front or interface located anywhere within a three-dimensional Darcy flow (e.g., any surface marked by red dye), and let (()(x,y,z) denote the porosity. Furthermore, denote by u, v, and w the Eulerian speed components, and describe our interface by the surface locus of points... 

Molecules move from node to node by deterministic propagation dynamics which models the free streaming real molecules undergo between the effective (strong) collisions (cf below). Thus at each time step molecules move one lattice unit in the directions specified by their velocities. This propagation step will be denoted by the operator P. 

Compaction by man-made explosions can also be employed to density loose liquefiable deposits. By detonating explosive charges placed at various depths in boreholes across the site in a controlled manner, the explosions propagate dynamic shear stresses through the ground which can induce liquefaction. The postliquefaction consolidation following the... 

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