Witnessing

Nevertheless, we are witnessing most recently an important development in petroleum product specifications regarding two main factors ... 

We should therefore conclude that refining will witness a very important evolution, without revolution, but which will affect both the processes and procedures utilized, the objective being to produce clean products in a clean , energy-efficient manner. 

Hydrocarbons are of a lower density than formation water. Thus, if no mechanism is in place to stop their upward migration they will eventually seep to the surface. On seabed surveys in some offshore areas we can detect crater like features ( pock marks ) which also bear witness to the escape of oil and gas to the surface. It is assumed that throughout the geologic past vast quantities of hydrocarbons have been lost in this manner from sedimentary basins. 

The specific test was made into a specialized bunker of one partner of the CIAPES program. All the vessel was covered by AE sensors to locate witli accuracy AE sources. The corrosion defect was situated on the bottom of the vessel. The service pressure of the vessel was 8 bars, so the vessel was first submitted to a proof test at 12 bars. During this test, the pressure was increased with load holds in order to verify the assessment criteria. After the first hold at 4 bars, a cluster was located at the position of the defect. The number of events located in this cluster increased during all the test (figure 1). 

In design X-ray TV introseopes can be manufaetured both in a bunker version and witli an autonomous radiation shielding to provide radiation safety under plant eonditions... 

At each step, the computer reeords the amplitude of R.F. signal sent by the generator, witli tile eventual eorreetion made by the operator. At the end of the measurement, the software calculates the maximum deviation of linearity versus the ideal curve. 

During the construction of a ship the Surveyor monitors NDE results for completeness of testing and overall quality of welding. This role includes the evaluation of checkpoints taken specifically for classification purposes but also includes the monitoring of additional checkpoints taken for quality control purposes by the builder. In the case of tankers built to LR Class since 1994 and for bulk carriers built to Class since January 1996 the Surveyor will witness the actions listed as part of the ShipRight Construction Monitoring procedure that is now mandatory. 

The corresponding fiinctions i-, Xj etc. then define what are known as the normal coordinates of vibration, and the Hamiltonian can be written in tenns of these in precisely the fonn given by equation (AT 1.69). witli the caveat that each tenn refers not to the coordinates of a single particle, but rather to independent coordinates that involve the collective motion of many particles. An additional distinction is that treatment of the vibrational problem does not involve the complications of antisymmetry associated with identical fennions and the Pauli exclusion prmciple. Products of the nonnal coordinate fiinctions neveitlieless describe all vibrational states of the molecule (both ground and excited) in very much the same way that the product states of single-electron fiinctions describe the electronic states, although it must be emphasized that one model is based on independent motion and the other on collective motion, which are qualitatively very different. Neither model faithfully represents reality, but each serves as an extremely usefiil conceptual model and a basis for more accurate calculations. 

Figure A2.1.2. Reversible expansion of a gas witli the removal one-by-one of grains of sand atop a piston.

Combining tliis witli the Omstein-Zemike equation, we have two equations and tluee unknowns h(r),c(r) and B(r) for a given pair potential u r). The problem then is to calculate or approximate the bridge fiinctions for which there is no simple general relation, although some progress for particular classes of systems has been made recently. 

The solution detennines c(r) inside the hard core from which g(r) outside this core is obtained via the Omstein-Zemike relation. For hard spheres, the approximation is identical to tire PY approximation. Analytic solutions have been obtained for hard spheres, charged hard spheres, dipolar hard spheres and for particles interacting witli the Yukawa potential. The MS approximation for point charges (charged hard spheres in the limit of zero size) yields the Debye-Fluckel limiting law distribution fiinction. 

As in tire case of themial conductivity, we see that the viscosity is independent of the density at low densities, and grows witli the square root of the gas temperature. This latter prediction is modified by a more systematic calculation based upon the Boltzmaim equation, but the independence of viscosity on density remains valid in the Boltzmaim equation approach as well. 

The molecular constants that describe the stnicture of a molecule can be measured using many optical teclmiques described in section A3.5.1 as long as the resolution is sufficient to separate the rovibrational states [110. 111 and 112]. Absorption spectroscopy is difficult with ions in the gas phase, hence many ion species have been first studied by matrix isolation methods [113], in which the IR spectrum is observed for ions trapped witliin a frozen noble gas on a liquid-helium cooled surface. The measured frequencies may be shifted as much as 1 % from gas phase values because of the weak interaction witli the matrix. 

The physical situation of interest m a scattering problem is pictured in figure A3.11.3. We assume that the initial particle velocity v is comcident with the z axis and that the particle starts at z = -co, witli x = b = impact parameter, andy = 0. In this case, L = pvh. Subsequently, the particle moves in the v, z plane in a trajectory that might be as pictured in figure A3.11.4 (liere shown for a hard sphere potential). There is a point of closest approach, i.e., r = (iimer turning point for r motions) where... 

Figure A3.14.2. Characteristic features of a clock reaction, illustrated for the Landolt reaction, showing (a) variation of product concentration witii induction period followed by sharp reaction event (b) variation of overall reaction rate witli course of reaction.

Borokmans P, Dewel G, De Wit A and Walgraef D Turing bifuroations and pattern seleotion Chemical M/aves and Patterns eds R Kapral and K Showalter (Dordreoht Kluwer) eh 10, pp 323-63... 

Figure Bl.1.1. (a) Potential curves for two states with little or no difference in the equilibrium position of tire upper and lower states. A ttansition of O2, witli displacement only 0.02 A, is shown as an example. Data taken from [11]. Most of the mtensity is in the 0-0 vibrational band with a small intensity in the 1-0 band, (b) Potential curves for two states with a large difference in the equilibrium position of the two states. A ttansition in I2, with a displacement of 0.36 A, is shown as an example. Many vibrational peaks are observed.

The 70 years since these first observations have witnessed dramatic developments in Raman spectroscopy, particularly with the advent of lasers. By now, a large variety of Raman spectroscopies have appeared, each with its own acronym. They all share the conunon trait of using high energy ( optical ) light to probe small energy level spacings in matter. 

Rotational transition frequencies acquired in the THz region expand upon and complement those acquired in the microwave. Two types of molecules undergo rotational transitions that fall in the FIR molecules witli rotation about an axis having a small moment of inertia, and molecules in high-J states. FIR spectra of the first type of molecules are... 

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