Wave structures

The combustion wave of GAP copolymer is divided into three zones zone I is a non-reactive heat-conduction zone, zone II is a condensed-phase reaction zone. 

Using Eqs. (5.1) and (5.2), the heat flux in zone II, n, and the heat flux in zone III (Am) are determined from temperature profile data in the combustion wave. As shown in Fig. 5.18, both n and Am increase linearly with increasing pressure in a log-log plot II -pO-75 and Am The heat of reaction in zone 11, Qn, is deter- 

Using Eqs. (5.1) and (5.2), the heat flitx in zone II, n, and the heat flux in zone III (Ajii) are determined from temperature profile data in the combustion wave. As shown in Fig. 5.18, both n and Am increase linearly with increasing pressure in a log-log plot n p0 75 nd Am po-8o he heat of reaction in zone II, Qji, is determined as 624 kj kg b[44] It is noteworthy that the heat of reaction of HMX in zone II is 300 kJ kg even though the adiabatic flame temperature of HMX is 1900 K higher than that of GAP copolymer. Furthermore, Am of GAP is of the same order of magnitude as Am of HMX, despite the fact that n of GAP is approximately ten times larger than the n of HMX shown in Fig. 5.6. 

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What are the characteristic mechanical responses of solids to shock loading This question is most clearly addressed through the relation between stress-volume relations and wave structures. 

At loading stresses between the HEL and the strong shock threshold, a two-wave structure is observed with an elastic precursor followed by a viscoplastic wave. The region between the two waves is in transition between the elastic and the viscoplastic states. The risetime of the trailing wave is strongly dependent on the loading stress amplitude [5]. 

Although much as been done, much work remains. Improved material models for anisotropic materials, brittle materials, and chemically reacting materials challenge the numerical methods to provide greater accuracy and challenge the computer manufacturers to provide more memory and speed. Phenomena with different time and length scales need to be coupled so shock waves, structural motions, electromagnetic, and thermal effects can be analyzed in a consistent manner. Smarter codes must be developed to adapt the mesh and solution techniques to optimize the accuracy without human intervention. 

The dotted segments represent the region of two-wave structure for those materials exhibiting transitions the lines have been drawn on the basis of the shock velocity of the first wave. The dashed curves represent reflected shocks and rarefaction release loci from the 2024 A1 Hugoniot at the pressures listed. The three heavy curves are the Hugoniots of 2024 Al, Cu, and U-3 wt.% Mo alloy which were determined independently. These were used as standards to determine the Hugoniots of the other materials. 

Curran [61C01] has pointed out that under certain unusual conditions the second-order phase transition might cause a cusp in the stress-volume relation resulting in a multiple wave structure, as is the case for a first-order transition. His shock-wave compression measurements on Invar (36-wt% Ni-Fe) showed large compressibilities in the low stress region but no distinct transition. 

The indicated transition pressure of 15 GPa is in agreement with the published data with shock-wave structure measurements on a 3% silicon-iron alloy, the nominal composition of Silectron. A mixed phase region from 15 to 22.5 GPa appears quite reasonable based on shock pressure-volume data. Thus, the direct measure of magnetization appears to offer a sensitive measure of characteristics of shock-induced, first-order phase transitions involving a change in magnetization. 

Strehlow, R. A. 1970. Multi-dimensional detonation wave structure. Astronautica Acta 15 345-357. 

R. Takai, K. Yoneda, and T. Hikita, Study of detonation wave structure. Proceedings 15th Symposium (International) on Combustion, The Combustion Institute, Pittsburg, pp. 69-78, 1974. 

Measurement of liquid film thickness. A variety of techniques have been used to measure the time variation of local film thickness and the data on wave structure that can be deduced therefrom (Dukler and Taitel, 1991a) ... 

Due to lack of understanding of the wave structure and motions, modeling of the interfacial shear remains empirical. 

Frames exposed 0.07 sec apart. Wave structure on liquid film... 

Xing L., Zuoqing W., Cheng J.K., Viens M., Cheeke J.D.N., Ultrasonic thin-walled tube wave structure for sensing devices, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control 1996 43 331-336. 

In addition to studies of diacetylene single crystals, current research, activities are focused on studies of the second X and third x order nonlinear optical responses of disubstituted diacetylene polymer films as active optical guided wave structures. Diacetylene polymers possess X values comparable to germanium(j 7). In the first stage, three major questions are being addressed ... 

A family of vacuum-tube MMW sources is based on the propagation of an electron beam through a so-called slow-wave or periodic structure. Radiation propagates on the slow-wave structure at the speed of the electron beam, allowing the beam and radiation field to interact. Devices in this category are the traveling-wave tube (TWT), the backward-wave oscillator (BWO) and the extended interaction oscillator (EIO) klystron. TWTs are characterized by wide bandwidths and intermediate power output. These devices operate well at frequencies up to 100 GHz. BWOs, so called because the radiation within the vacuum tube travels in a direction opposite to that of the electron beam, have very wide bandwidths and low output powers. These sources operate at frequencies up to 1.3 THz and are extensively used in THZ spectroscopic applications [10] [11] [12]. The EIO is a high-power, narrow band tube that has an output power of 1 kW at 95 GHz and about 100 W at 230 GHz. It is available in both oscillator and amplifier, CW and pulsed versions. This source has been extensively used in MMW radar applications with some success [13]. 

When the tube is closed at one end and ignited there, the propagating wave undergoes a transition from subsonic to supersonic speeds. The supersonic wave is called a detonation. In a detonation heat conduction and radical diffusion do not control the velocity rather, the shock wave structure of the developed supersonic wave raises the temperature and pressure substantially to cause explosive reaction and the energy release that sustains the wave propagation. 

Then it became apparent that certain physical principles could be used to simplify the complete equations so they could be solved relatively easily. Such a simplification was first carried out by von Karman and Penner [9], Their approach was considered one of the more significant advances in laminar flame propagation, but it could not have been developed and verified if it were not for the extensive work of Hirschfelder and his collaborators. The major simplification that von Karman and Penner introduced is the fact that the eigenvalue solution of the equations is the same for all ignition temperatures, whether it be near T or not. More recently, asymptotic analyses have been developed that provide formulas with greater accuracy and further clarification of the wave structure. These developments are described in detail in three books [10-12],... 

Reasonable models for the detonation wave structure have been presented by Zeldovich [9], von Neumann [10], and Doring [11], Essentially, they constructed the detonation wave to be a planar shock followed by a reaction zone initiated after an induction delay. This structure, which is generally referred to as the ZND model, will be discussed further in a later section. 

As in consideration of deflagration phenomena, other parameters are of import in detonation research. These parameters—detonation limits, initiation energy, critical tube diameter, quenching diameter, and thickness of the supporting reaction zone—require a knowledge of the wave structure and hence of chemical reaction rates. Lee [6] refers to these parameters as dynamic to distinguish them from the equilibrium static detonation states, which permit the calculation of the detonation velocity by C-J theory. 

Calculation of the dynamic parameters using a ZND wave structure model do not agree with experimental measurements, mainly because the ZND structure is unstable and is never observed experimentally except under transient conditions. This disagreement is not surprising, as numerous experimental observations show that all self-sustained detonations have a three-dimensional cell structure that comes about because reacting blast wavelets collide with each other to form a series of waves which transverse to the direction of propagation. Currently, there are no suitable theories that define this three-dimensional cell structure. 

Let us consider a multilayer structure plotted schematically in Fig. 1. It will be taken as a fundamental building block of any more complex guided-wave structure considered here. Let the optical wave propagate along the longitudinal coordinate z, and x is the transversal coordinate. 

Bistability controlled by input intensity (wavelength fixed) can also be observed. Figure 3 shows input-output intensity characteristics (yt = 2 tr being the normalised intensity of transmitted wave) when A > Ao and demonstrates that the use of slow-wave structures significantly affects appearance of bistability and its threshold. 

I described a simple method suitable for rigorous modelling of nonlinear one-dimensional structures in the frequency domain. The method was applied to model COST Pll task on slow-wave optieal structures. It was demonstrated that the use of slow-wave structures significantly decreases bistablity threshold. 

In general, the plume flow field is divided into the near-field, transition, and far-held regions [5]. The near-held region which is shown in Fig. 29.1 consists of a nearly inviscid jet core dominated by strong wave structures and a thin... 

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