Propagation Subject

Edwards, V. H., Ko, R.C. and Balogh, S.A. (1972) Dynamics and Control of Continuous Microbial Propagators Subject to Substrate Inhibition, Biotechnol. Bioeng. 14, 939-974. 

The result of this approximation is that each mode is subject to an effective average potential created by all the expectation values of the other modes. Usually the modes are propagated self-consistently. The effective potentials governing die evolution of the mean-field modes will change in time as the system evolves. The advantage of this method is that a multi-dimensional problem is reduced to several one-dimensional problems. 

Fig. 2. Illustrations of forces to which adhesive bonds are subjected, (a) A standard lap shear specimen where the black area shows the adhesive. The adherends are usually 25 mm wide and the lap area is 312.5 mm. The arrows show the direction of the normal apphcation of load, (b) A peel test where the loading configuration, shown by the arrows, is for a 180° peel test, (c) A double cantilever beam test specimen used in the evaluation of the resistance to crack propagation of an adhesive. The normal application of load is shown by the arrows. This load is appHed by a tensile testing machine or other...

The criteria for insensitive explosives subjected to ha2ard tests permit no reaction more violent than burning in slow and fast cook-off tests and fragment and bullet tests, no propagation in sympathetic detonation tests, no detonation when stmck by a shaped charge jet, no sustained burning when hit by a small fragment, and such special tests as may be required by the use of the explosive. 

This optimum condition is designed to ensure that the botes of all components yield at the same time. If the cylinder is subjected to fatigue conditions, it has been suggested (39) that a better design criterion would arrange for the maximum normal stress, which controls fatigue crack propagation, to be the same in each component. 

Plants. AsexuaHy reproducing plants, ie, those not propagated by means of seed, also represent a legally recognized class of patentable subject matter under U.S. patent laws. Additionally, the inventor must have discovered and asexuaHy reproduced the plant that is to be the subject of the patent apphcation. Plant patents are assigned a different series of numbers than the majority of patents discussed in the foregoing, such as U.S. Plant Patent No. 3,360 titled "Peach Tree" (7). 

The effect of temperature, pressure, and oil composition on oil recovery efficiency have all been the subjects of intensive study (241). Surfactant propagation is a critical factor in determining the EOR process economics (242). Surfactant retention owing to partitioning into residual cmde oil can be significant compared to adsorption and reduce surfactant propagation rate appreciably (243). 

The mechanism of anionic polymerization of cyclosiloxanes has been the subject of several studies (96,97). The first kinetic analysis in this area was carried out in the early 1950s (98). In the general scheme of this process, the propagation/depropagation step involves the nucleophilic attack of the silanolate anion on the sUicon, which results in the cleavage of the siloxane bond and formation of the new silanolate active center (eq. 17). 

Taylor instabilities involve effects of buoyancy or acceleration in fluids with variable density a light fluid beneath a heavy fluid is unstable by the Taylor mechanism. The upward propagation of premixed flames in tubes is subject to Taylor instability (11). 

The condition for propagation of a mode 1 edge crack, that is, a crack that is subjected to pure opening (tensile) stresses appHed perpendicular to the crack plane, is given by (35) ... 

Overview Reconciliation adjusts the measurements to close constraints subject to their uncertainty. The numerical methods for reconciliation are based on the restriction that the measurements are only subject to random errors. Since all measurements have some unknown bias, this restriction is violated. The resultant adjusted measurements propagate these biases. Since troubleshooting, model development, ana parameter estimation will ultimately be based on these adjusted measurements, the biases will be incorporated into the conclusions, models, and parameter estimates. This potentially leads to errors in operation, control, and design. 

Shock-compression processes are encountered when material bodies are subjected to rapid impulsive loading, whose time of load application is short compared to the time for the body to respond inertially. The inertial responses are stress pulses propagating through the body to communicate the presence of loads to interior points. In our everyday experience, such loadings are the result of impact or explosion. To the untrained observer, such events evoke an image of utter chaos and confusion. Nevertheless, what is experienced by the human senses are the rigid-body effects the time and pressure resolution are not sufficient to sense the wave phenomena. 

For a shock wave in a solid, the analogous picture is shown schematically in Fig. 2.6(a). Consider a compression wave on which there are two small compressional disturbances, one ahead of the other. The first wavelet moves with respect to its surroundings at the local sound speed of Aj, which depends on the pressure at that point. Since the medium through which it is propagating is moving with respect to stationary coordinates at a particle velocity Uj, the actual speed of the disturbance in the laboratory reference frame is Aj - -Ui- Similarly, the second disturbance advances at fl2 + 2- Thus the second wavelet overtakes the first, since both sound speed and particle velocity increase with pressure. Just as a shallow water wave steepens, so does the shock. Unlike the surf, a shock wave is not subject to gravitational instabilities, so there is no way for it to overturn. 

When an isotropic material is subjected to planar shock compression, it experiences a relatively large compressive strain in the direction of the shock propagation, but zero strain in the two lateral directions. Any real planar shock has a limited lateral extent, of course. Nevertheless, the finite lateral dimensions can affect the uniaxial strain nature of a planar shock only after the edge effects have had time to propagate from a lateral boundary to the point in question. Edge effects travel at the speed of sound in the compressed material. Measurements taken before the arrival of edge effects are the same as if the lateral dimensions were infinite, and such early measurements are crucial to shock-compression science. It is the independence of lateral dimensions which so greatly simplifies the translation of planar shock-wave experimental data into fundamental material property information. 

The objective in these gauges is to measure the time-resolved material (particle) velocity in a specimen subjected to shock loading. In many cases, especially at lower impact pressures, the impact shock is unstable and breaks up into two or more shocks, or partially or wholly degrades into a longer risetime stress wave as opposed to a single shock wave. Time-resolved particle velocity gauges are one means by which the actual profile of the propagating wave front can be accurately measured. 

The velocity propagation is subject to relatively large errors, on the order O(At-). Recall that an accurate estimate of the velocity is required for the kinetic energy evaluations. An added inconvenience is that v can be computed only if r +i is already known. 

Figures 2b and 3 demonstrate that X rays are produced over a range of depth into the sample. The X rays must propagate along a finite path through the specimen to reach the detector, and are subject to photoelectric absorption and scattering, which follows an exponential relation ...

This chapter overviews the techniques for incorporating external events into a PSA. The discussion was primarily aimed at nuclear power plants but is equally applicable to chemical process plants. The types of external events discussed were earthquakes, fires and floods. Notably absent were severe winds and tornados. Tornados are analyzed as missiles impacting the structures and causing common-cause failures of systems (EPRINP-768). Missile propagation and the resulting damage is a specialized subject usually solved with computer codes. 

Solid substances are forced into unusual and distinctive conditions when subjected to powerful releases of energy such that their inertial properties result in the propagation of high pressure mechanical waves within the solid body. The very high stress, microsecond-duration, conditions irreversibly force materials into states not fully encountered in any other excitation. It is the study of solids under this unique compression-and-release process that provides the scientific and technological interest in shock-compression science. 

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