Root segment

The third edition of "Properties of Gases and Liquids" by Reid et al. (1977) lists useful group contribution methods for predicting critical properties. Contributions to the second  [c.36]

The secondary reactions are series with respect to the chloromethane but parallel with respect to chlorine. A very large excess of methane (mole ratio of methane to chlorine on the order of 10 1) is used to suppress selectivity losses. The excess of methane has two effects. First, because it is only involved in the primary reaction, it encourages the primary reaction. Second, by diluting the product, chloromethane, it discourages the secondary reactions, which prefer a high concentration of chloromethane.  [c.40]

The monomers used are second generation petrochemical products. The polymethacrylates are in fact copolymers based on methyl methacrylate and up to C20 molecular weight alcohol methacrylate. The properties of the additive are controlled based on the molecular ratio of these different monomers and their molecular weight.  [c.356]

This stage can be divided in two sub-stages. The first sub-stage incorporates the damage developed during the initial quasi-static loading of the specimen to reach the maximum stress level and then unloading to the mean stress. This procedure is carried out in order to measure the initial stiffness of the specimen. The second sub-stage, which consists the main part of stage I, begins as soon as the fatigue amplitude is applied over the mean stress. This stage is characterised by the development of homogeneous non interactive damage, restricted to individual plies. Matrix cracking of the off-axis plies is the dominant damage mechanism. This mechanism continues being active until the Characteristic Damage State (CDS) is reached in all the off-axis plies. Small edge delaminations are also observed but these are limited and present only at the tips of the matrix cracks. Damage in this stage develops at a decreasing rate (Figure 6). This is due to the exhaustion of new damage sites and the slow growth of the existing ones.  [c.49]

The second system has been developed for interpretation of B-scan images from an ultrasonic rail-inspection system used by the Dutch Railways. The inspection is done using a set of ultrasonic transducers gliding over the rails on a water film. The signals from the transducers are assembled to form B-scan images. The images have to be analysed to determine if they contain any indications from defects. When the inspection system was first introduced the image interpretation was done entirely by the operator. In the currently operational system the image analysis is done by a Clips [Giarratano Riley, 1989] expert system. Because of the complexity of the images the recognition ratio is not very high. Research on ways to improve the recognition ratio has lead to the current prototype of a hybrid rule-based / CBR system for image interpretation. Figure 1 shows the components of the system - it contains three main stages pre-processing where the image is segmented into meaningful elements, rule-based classification, and case-based classification.  [c.102]

In fig. 2 an ideal profile across a pipe is simulated. The unsharpness of the exposure rounds the edges. To detect these edges normally a differentiation is used. Edges are extrema in the second derivative. But a twofold numerical differentiation reduces the signal to noise ratio (SNR) of experimental data considerably. To avoid this a special filter procedure is used as known from Computerised Tomography (CT) /4/. This filter based on Fast Fourier transforms (1 dimensional FFT s) calculates a function like a second derivative based on the first derivative of the profile P (r)  [c.519]

Therefore it is reasonable to prepare already the data acquisition for a three dimensional evaluation in cone-beam-technique by means of two-dimensional detectors. The system is already prepared to integrate a second detector- system for this purpose. An array of up to four flat panel detectors is foreseen. The detector- elements are based on amorphous silicon. Because of the high photon energy and the high dose rates special attention was necessary to protect the read-out electronics. Details of the detector arrangement and the software for reconstruction, visualisation and comparison between the CT results and CAD data are part of a separate paper during this conference [2].  [c.586]

In order to prepare the system for 3D-CT, it is not enough to integrate a second detector array. Besides this special attention has to be paid to the computer hardware, the synchronisation between object movement and the data read out as well as to the collimator of the LINAC. The collimator has been built with 4 tungsten blocks which can be moved individually m order to shape different sht sizes for 2D-CT as well as different cone angles for 3D-CT or digital radiography.  [c.586]

The second example shows results obtained with an angle beam probe for transverse waves in coarse grained grey cast iron. Two commercially available probes are compared the composite design SWK 60-2 and the standard design SWB 60-2. The reflector in this example is a side-drilled hole of 5 mm diameter. The A-scans displayed below in Fig. 5 and 6 show that the composite probe has a higher sensitivity by 12 dB and that the signal to noise ratio is improved by more than 6 dB.  [c.709]

This means an acquisition rate of 64 channels simultaneously, and 128 data channels as 2 frequencies are used. The acquisition speed is 140 points per second for each channel, meaning practically 6 to 12 points per rod mm. Since the method was developed 10 years ago, the processing and analysis time of this amount of information (20 Mbytes average) was long and difficult.  [c.1007]

If the spreading is into a limited surface area, as in a laboratory experiment, the film front rather quickly reaches the boundaries of the trough. The film pressure at this stage is low, and the now essentially uniform film more slowly increases in v to the final equilibrium value. The rate of this second-stage process is mainly determined by the rate of release of material from the source, for example a crystal, and the surface concentration F [46]. Franses and co-workers [47] found that the rate of dissolution of hexadecanol particles sprinkled at the water surface controlled the increase in surface pressure here the slight solubility of hexadecanol in the bulk plays a role.  [c.111]

The measurement of a from the experimental slope of the Tafel equation may help to decide between rate-determining steps in an electrode process. Thus in the reduction water to evolve H2 gas, if the slow step is the reaction of with the metal M to form surface hydrogen atoms, M—H, a is expected to be about If, on the other hand, the slow step is the surface combination of two hydrogen atoms to form H2, a second-order process, then a should be 2 (see Ref. 150).  [c.214]

The final equation obtained by Becker and Doting may be written down immediately by means of the following qualitative argument. Since the flux I is taken to be the same for any size nucleus, it follows that it is related to the rate of formation of a cluster of two molecules, that is, to Z, the gas kinetic collision frequency (collisions per cubic centimeter-second).  [c.331]

Since in chemisorption systems it is reasonable to suppose that the strong adsorbent-adsorbate interaction is associated with specific adsorption sites, a situation that may arise is that the adsorbate molecule occupies or blocks the occupancy of a second adjacent site. This means that each molecule effectively requires two adjacent sites. An analysis [106] suggests that in terms of the kinetic derivation of the Langmuir equation, the rate of adsorption should now be  [c.701]

It was pointed out that a bimolecular reaction can be accelerated by a catalyst just from a concentration effect. As an illustrative calculation, assume that A and B react in the gas phase with 1 1 stoichiometry and according to a bimolecular rate law, with the second-order rate constant k equal to 10 1 mol" see" at 0°C. Now, assuming that an equimolar mixture of the gases is condensed to a liquid film on a catalyst surface and the rate constant in the condensed liquid solution is taken to be the same as for the gas phase reaction, calculate the ratio of half times for reaction in the gas phase and on the catalyst surface at 0°C. Assume further that the density of the liquid phase is 1000 times that of the gas phase.  [c.740]

The first tenn conesponds to the average energy per electron in a free electron gas. The second tenn corresponds to the exchange energy per electron. The exchange energy is attractive and scales with the cube root of the average density. This fonn provides a clue as to what fonn the exchange energy might take in an interacting electron gas or non-unifonn electron gas.  [c.95]

Its ratio to the first temi can be seen to be (5 J / 5 Ef) E HT. Since E is proportional to the number of particles in the system A and Ej, is proportional to the number of particles in the composite system N + N, the ratio of the second-order temi to tire first-order temi is proportional to N N + N. Since the reservoir is assumed to be much bigger than the system, (i.e. N) this ratio is negligible, and the truncation of the  [c.397]

The energy conservation law also leads to an associated continuity equation for the total energy density. The total energy density contains both the kinetic energy density per unit volume and the internal energy density. The energy flux is made up of four temis a kinematic temi, the rates of work done by reversible pressure and dissipative viscous stress, and a dissipative heat flux. It is the dissipative heat flux that is assumed to be proportional to the temperature gradient and this linear transport law, Fourier s law, introduces as a proportionality coefficient, the coefficient of themial conductivity, k. From the resulting energy equation, one can obtain the equation for the rate of entropy balance in the system, which on account of the irreversibility and the arrow of time implied by the Second Law of Themiodynamics leads to the result drat each of the transport coefficients q, qj and k is a positive definite quantity. Using the mass conservation equation (A3.3.13). and themiodynamic relations which relate entropy change to changes in density and temperature, the entropy balance equation can be transfomied to the hydrodynamic equation for the local temperature T(  [c.722]

The are many ways to define the rate of a chemical reaction. The most general definition uses the rate of change of a themiodynamic state function. Following the second law of themiodynamics, for example, the change of entropy S with time t would be an appropriate definition under reaction conditions at constant energy U and volume V  [c.759]

The rate is given by tire second-order law (c = [CH ] or c = [A])  [c.768]

It is clear from figure A3.4.3 that the second-order law is well followed. Flowever, in particular for recombination reactions at low pressures, a transition to a third-order rate law (second order in the recombining species and first order in some collision partner) must be considered. If the non-reactive collision partner M is present in excess and its concentration [M] is time-independent, the rate law still is pseudo-second order with an effective second-order rate coefficient proportional to [Mj.  [c.769]

If the dominant contributions /r,[M.] are approximately constant, this leads to pseudo second-order kinetics with an effective rate constant  [c.770]

A hierarchical system is the simplest type ofdatabase system. In this form, the var-iou.s data typc.s also called entities (sec figure 5-,3) arc as.signcd. systematically to various levels (Figure 5-5). The hierarchical system is represented as an upside-down tree with one root segment and ordered nodes. Each parent object can have one or more children (objects) but each child has only one parent. If an object should have more than one parent, this entity has to be placed a second time at another place in the database system.  [c.232]

If the objective function is considered two-dimensional, consisting of Equations (7-13) and (7-14) and the vector X includes only T and a, then the only change in the iteration is that the derivatives of with respect to composition are ignored in establishing the Newton-Raphson corrections to T and a. The new compositions can then be determined from Equations (7-8) and (7-9). Such a simplified procedure sacrifices little in convergence rate for vapor-liquid systems, where the contributions of compfosition-derivatives to changes in T and a are almost always smad 1. This approach requires only two evaluations of per iteration and still avoids creeping since it is essentially second-order in the limit as convergence is approached.  [c.117]

The achievable silver concentrations depend mainly on the regeneration rate of the fixer. The steady-state silver concentration in the first fixing step is inversely proportional to the regeneration rate. The dilution factor in the second step is equal to the ratio of the carry-over (e.g. 40 ml/m ) and the regeneration. An doubling of the regeneration rate will result in A of the original silver level in the rinsing section. A standard regeneration rate of 1200 ml/m will result in a decrease of the silver level by a factor of 20, compared to the standard situation. Contrarily to electrolysis, the daily production does not affect the silver content in the rinsing water, which makes cascade fixing a preferable technology in case of high daily productions (>15 m per processor per day).  [c.608]

This paper presents solutions of two different NDT problems which could not be solved using standard ultrasonic systems and methods. The first problem eoncems the eraek detection in the root of turbine blades in a specified critical zone. The second problem concerns an ultrasonie thiekness measurement for a case when the sound velocity varies along the object surface, thus not allowing to take a predetermined eonstant velocity into account.  [c.764]

Fig.7 shows the relation between the echo height F/B and the defect area s ratio Sr/So, when the ultrasonic wave is input from FCD500 side. This Sr/So is the ratio of the defect area Sr to the beam irradiational area So. Moreover, // X of (a) (b) (c) (d) are the value at the position where the echo height F/B is changed in Fig.5. And, the defect position of (i) (iv) in figure is shown the each position of Fig.3 respectively. Moreover, each curves are calculation values respectively, and this is described later. There has two case that F/T) of (a) (d) is changed by the defect position. The first case, F/B are increased as defect area s ratio Sr/So increases. The second case, F/B are increased after decrases as Sr/So increases. And defect area s ratio Sr/So to which F/B decreases is different according to the defect position Fig.7 shows the relation between the echo height F/B and the defect area s ratio Sr/So, when the ultrasonic wave is input from FCD500 side. This Sr/So is the ratio of the defect area Sr to the beam irradiational area So. Moreover, // X of (a) (b) (c) (d) are the value at the position where the echo height F/B is changed in Fig.5. And, the defect position of (i) (iv) in figure is shown the each position of Fig.3 respectively. Moreover, each curves are calculation values respectively, and this is described later. There has two case that F/T) of (a) (d) is changed by the defect position. The first case, F/B are increased as defect area s ratio Sr/So increases. The second case, F/B are increased after decrases as Sr/So increases. And defect area s ratio Sr/So to which F/B decreases is different according to the defect position
If the first plane is rotated through a full circle, the first radius of curvature will go through a minimum, and its value at this minimum is called the principal radius of curvature. The second principal radius of curvature is then that in the second plane, kept at right angles to the first. Because Fig. II-3 and Eq. II-7 are obtained by quite arbitrary orientation of the first plane, the radii R and R2 are not necessarily the principal radii of curvature. The pressure difference AP, cannot depend upon the manner in which and R2 are chosen, however, and it follows that the sum ( /R + l/f 2) is independent of how the first plane is oriented (although, of course, the second plane is always at right angles to it).  [c.6]

We compute a first approximation to the value of the capillary constant a by means of Eq. II-IO (fl = rh). TTte ratio r/a is then obtained and the corresponding value of r/b is determined firom Eq. 11-19 or 11-20 in the present case, = 1.201 x 0.0550 = 0.660 hence, r/a = 0.0550/0.2570 = 0.2140. From Eq. 11-19, r/fc is then 0.9850. Since b is the value of and of R2 at the bottom of the meniscus, the equation -bh is exact. From the value of r/b, we obtain a first approximation to b, that is, b = 0.0550/0.9850 = 0.05584. This value of b gives a second approximation to a from = b h = 0.05584 x 1.201 = 0.06706. A second round of approximations is not needed in this case but would be carried out by computing r/a2 then from Eq. 11-19, r/b2, and  [c.15]

Mobility of this second kind is illustrated in Fig. XVIII-14, which shows NO molecules diffusing around on terraces with intervals of being trapped at steps. Surface diffusion can be seen in field emission microscopy (FEM) and can be measured by observing the growth rate of patches or fluctuations in emission from a small area [136,138] (see Section V111-2C), field ion microscopy [138], Auger and work function measurements, and laser-induced desorption  [c.709]

If the desorption rate is second-order, as is often the case for hydrogen on a metal surface, so that appears in Eq. XVIII-1, an equation analogous to Eq. XVIII-3 can be derived by the Redhead procedure. Derive this equation. In a particular case, H2 on Cu3Pt(III) surface, A was taken to be 1 x 10 cm /atom, the maximum desorption rate was at 225 K, 6 at the maximum was 0.5. Monolayer coverage was 4.2 x 10 atoms/cm, and = 5.5 K/sec. Calculate the desorption enthalpy (from Ref. 110).  [c.739]

We now make two coimections with topics discussed earlier. First, at the begiiming of this section we defined 1/Jj as the rate constant for population decay and 1/J2 as the rate constant for coherence decay. Equation (A1.6.63) shows that for spontaneous emission MT = y, while 1/J2 = y/2 comparing with equation (A1.6.60) we see that for spontaneous emission, 1/J2 = 0- Second, note that y is the rate constant for population transfer due to spontaneous emission it is identical to the Einstein A coefficient which we defined in equation (Al.6.3).  [c.234]

The second-order rate law for bimolecular reactions is empirically well confinned. Figure A3.4.3 shows the example of methyl radical recombination (equation (A3.4.36)) in a graphical representation following equation (A3.4.38) [22, 23 and 24]. For this example the bimolecular rate constant is  [c.769]

The effective rate law correctly describes the pressure dependence of unimolecular reaction rates at least qualitatively. This is illustrated in figure A3,4,9. In the lunit of high pressures, i.e. large [M], becomes independent of [M] yielding the high-pressure rate constant of an effective first-order rate law. At very low pressures, product fonnation becomes much faster than deactivation. A j now depends linearly on [M]. This corresponds to an effective second-order rate law with the pseudo first-order rate constant Aq  [c.788]

The results of pressure-dependent measurements for tran.s -stilbene m supercritical n-pentane [46] ( figure A3.6.5) and the prediction from the model described by equation ( A3.6.29). using experimentally detemiined microcanonical rate coefficients in jet-cooled tran.s-stilbene to calculate k, show two marked discrepancies between model calculation and measurement (1) experimental values of/rare an order of magnitude higher already at low pressure and (2) the decrease of k due to friction is much less pronounced than predicted. As interpretations for the first observation, several ideas have been put forward that will not be fiirther discussed here, such as a decrease of the effective potential barrier height due to electrostatic solute-solvent interactions enhanced by cluster fomiation at relatively low pressures [72, 73], or incomplete intramolecular vibrational energy redistribution in the isolated molecule [74, 75, 76, 77, 78, 79 and ], or Franck-Condon cooling in the excitation process [79, ]. The second effect, the weak viscosity dependence, which was first observed in solvent series experiments in liquid solution [M, and M], has also led to controversial interpretations (i) the macroscopic solvent viscosity is an inadequate measure for microscopic friction acting along the reaction patii [84, M], (ii) the multidimensional character of the barrier crossing process leads to a fractional power dependence of /r on l/q [M, M, 87], (iii) as tlie reaction is very fast, one has to take into account the finite response time of the solvent, i.e. consider frequency-dependent friction [81, ] and (iv) the effective barrier  [c.820]

See pages that mention the term Root segment : [c.299]    [c.1152]    [c.227]    [c.198]    [c.283]    [c.288]    [c.65]    [c.722]    [c.6]    [c.682]    [c.730]    [c.244]    [c.701]    [c.720]    [c.768]   
Chemoinformatics (2003) -- [ c.232 ]