Removal density

The first term represents the rate of transitions to E from all other energies on collision. The second term is the rate at which collisions remove density from energy E and the third term is the rate at which density at energy E is removed by reaction, k E) being the microcanonical rate coefficient. 

Consider then a thermal reactor consisting of a spherical core of radius a and an infinite moderating reflector. For the present two-group model we label the fast neutrons in the core by the index i = I and those in the reflector by i = 3. Thermal neutrons in the core are labeled t = 2 and those in the reflector, i = 4. By definition, all fissions are caused by thermal neutrons (i = 2), and all neutrons born from fission appear in the fast group. We write the neutron-balance relation for this system in terms of the removal density (number of neutrons of group i removed per unit time per unit volume around r) i4 (r) = where 0,(r)... 

In general the removal densities A (r) are complicated functions, but in the present calculation we represent these by rough approximations based on the fundamental mode from the one-velocity model. In the... 

This is the only new quantity which appears in the set (8.231) and (8.232). In determining this function it is convenient to introduce the slow-neutron removal density in the reflector, Aa(t ) and a new kernel for slow neutrons, Q2(r r), which we define ... 

Note that this function is symmetric in r and r i.e., Q2(r r ) is the track length at r in the core produced by a unit source at r in the reflector. The removal density Aa t ) may be written in terms of Q2. Thus if (r) is the distribution of slow-neutron sources in the core, we can write... 

In the analysis which follows it will suffice to use an approximation to this series. Now the functions to be used in the expansion of the removal density in the reflector are nearly all the same shape in the limit of diffusion theory, these are in fact simple exponentials. Thus in first approximation we represent the n (r) by a single function ... 

Figure 5.37 depicts the basic set up of a wireline logging operation. A sonde is lowered downhole after the drill string has been removed. The sonde is connected via an insulated and reinforced electrical cable to a winch unit at the surface. At a speed of about 600m per hour the cable Is spooled upward and the sonde continuously records formation properties like natural gamma ray radiation, formation resistivity or formation density. The measured data is sent through the cable and is recorded and processed in a sophisticated logging unita the surface. Offshore, this unit will be located in a cabin, while on land it is truck mounted. In either situation data can be transmitted in real time via satellite to company headquarters if required. 

One can write acid-base equilibrium constants for the species in the inner compact layer and ion pair association constants for the outer compact layer. In these constants, the concentration or activity of an ion is related to that in the bulk by a term e p(-erp/kT), where yp is the potential appropriate to the layer [25]. The charge density in both layers is given by the algebraic sum of the ions present per unit area, which is related to the number of ions removed from solution by, for example, a pH titration. If the capacity of the layers can be estimated, one has a relationship between the charge density and potential and thence to the experimentally measurable zeta potential [26]. 

Another realistic approach is to constnict pseiidopotentials using density fiinctional tlieory. The implementation of the Kolm-Sham equations to condensed matter phases without the pseiidopotential approximation is not easy owing to the dramatic span in length scales of the wavefimction and the energy range of the eigenvalues. The pseiidopotential eliminates this problem by removing tlie core electrons from the problem and results in a much sunpler problem [27]. 

With the density fiinctional theory, the first step in the constmction of a pseudopotential is to consider the solution for an isolated atom [27]. If the atomic wavefiinctions are known, tire pseudo-wavefiinction can be constmcted by removing the nodal stmcture of the wavefiinction. For example, if one considers a valence... 

The density determination may be carried out at the temperature of the laboratory. The liquid should stand for at least one hour and a thermometer placed either in the liquid (if practicable) or in its immediate vicinity. It is usually better to conduct the measurement at a temperature of 20° or 25° throughout this volume a standard temperature of 20° will be adopted. To determine the density of a liquid at 20°, a clean, corked test-tube containing about 5 ml. of toe liquid is immersed for about three-quarters of its length in a water thermostat at 20° for about 2 hours. An empty test-tube and a shallow beaker (e.g., a Baco beaker) are also supported in the thermostat so that only the rims protrude above the surface of the water the pycnometer is supported by its capillary arms on the rim of the test-tube, and the small crucible is placed in the beaker, which is covered with a clock glass. When the liquid has acquired the temperature of the thermostat, the small crucible is removed, charged with the liquid, the pycnometer rapidly filled and adjusted to the mark. With practice, the whole operation can be completed in about half a minute. The error introduced if the temperature of the laboratory differs by as much as 10° from that of the thermostat does not exceed 1 mg. if the temperature of the laboratory is adjusted so that it does not differ by more than 1-2° from 20°, the error is negligible. The weight of the empty pycnometer and also filled with distilled (preferably conductivity) water at 20° should also be determined. The density of the liquid can then be computed. 

Step 4. The steam-volatile neutral compounds. The solution (containing water-soluble neutral compounds obtained in Step 1 is usually very dilute. It is advisable to concentrate it by distillation until about one-third to one-half of the original volume is collected as distillate the process may be repeated if necessary and the progress of the concentration may be followed by determination of the densities of the distillates. It is frequently possible to salt out the neutral components from the concentrated distillate by saturating it with solid potassium carbonate. If a layer of neutral compound makes its appearance, remove it. Treat this upper layer (which usually contains much water) with solid anhydrous potassium carbonate if another aqueous layer forms, separate the upper organic layer and add more anhydrous potassium carbonate to it. Identify the neutral compound. 

LORG (localized orbital-local origin) technique for removing dependence on the coordinate system when computing NMR chemical shifts LSDA (local spin-density approximation) approximation used in more approximate DFT methods for open-shell systems LSER (linear solvent energy relationships) method for computing solvation energy... 

The condensation of aldehydes or ketones with secondary amines leads to "encunines via N-hemiacetals and immonium hydroxides, when the water is removed. In these conjugated systems electron density and nudeophilicity are largely transferred from the nitrogen to the a-carbon atom, and thus enamines are useful electroneutral d -reagents (G.A. Cook, 1969 S.F. Dyke, 1973). A bulky heterocyclic substituent supports regio- and stereoselective reactions. 

Experimental confirmation of the metal-nitrogen coordination of thiazole complexes was recently given by Pannell et al. (472), who studied the Cr(0), Mo(0), and W(0) pentacarbonyl complexes of thiazole (Th)M(CO)5. The infrared spectra are quite similar to those of the pyridine analogs the H-NMR resonance associated with 2- and 4-protons are sharper and possess fine structure, in contrast to the broad, featureless resonances of free thiazole ligands. This is expected since removal of electron density from nitrogen upon coordination reduces the N quad-rupole coupling constant that is responsible for the line broadening of the a protons. 

Cholesterol is biosynthesized in the liver trans ported throughout the body to be used in a va riety of ways and returned to the liver where it serves as the biosynthetic precursor to other steroids But cholesterol is a lipid and isn t soluble in water How can it move through the blood if it doesn t dis solve in if The answer is that it doesn t dissolve but IS instead carried through the blood and tissues as part of a lipoprotein (lipid + protein = lipoprotein) The proteins that carry cholesterol from the liver are called low density lipoproteins or LDLs those that return it to the liver are the high-density lipoproteins or HDLs If too much cholesterol is being transported by LDL or too little by HDL the extra cholesterol builds up on the walls of the arteries caus mg atherosclerosis A thorough physical examination nowadays measures not only total cholesterol con centration but also the distribution between LDL and HDL cholesterol An elevated level of LDL cholesterol IS a risk factor for heart disease LDL cholesterol is bad cholesterol HDLs on the other hand remove excess cholesterol and are protective HDL cholesterol IS good cholesterol... 

The total electron density contributed by all the electrons in any molecule is a property that can be visualized and it is possible to imagine an experiment in which it could be observed. It is when we try to break down this electron density into a contribution from each electron that problems arise. The methods employing hybrid orbitals or equivalent orbitals are useful in certain circumsfances such as in rationalizing properties of a localized part of fhe molecule. Flowever, fhe promotion of an electron from one orbifal fo anofher, in an electronic transition, or the complete removal of it, in an ionization process, both obey symmetry selection mles. For this reason the orbitals used to describe the difference befween eifher fwo electronic states of the molecule or an electronic state of the molecule and an electronic state of the positive ion must be MOs which belong to symmetry species of the point group to which the molecule belongs. Such orbitals are called symmetry orbitals and are the only type we shall consider here. 

Inertial impaction involves the removal of contaminants smaller than the pore size. Particles are impacted on the filter through inertia. In practice, because the differential densities of the particles and the fluids are very small, inertial impaction plays a relatively small role in Hquid filtration, but can play a major role in gas filtration. 

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