Speed-space

This function gives the neutron density in the energy space E, It can be directly related to the density in the speed space [given by (3.37)] by selecting the speed interval dv which corresponds to the energy interval dE. Clearly, if we specify that dv is to correspond to dE, then the number of neutrons per unit volume around r must be the same whether we describe it in terms of the energy variable E or in terms of the speed... 

This equation corresponds to the relation (3.42) and states that the total track length per unit volume per unit time around r at time t is conserved in going from speed space to energy space. If we introduce the Jacobian dv/dE, it is easily shown that (again omitting r and /)... 

It should be noted that these distributions are defined in terms of velocity space which is not to be confused with speed space. The distributions in velocity space are more detailed than those in speed space inasmuch as they specify not only the neutron speed but also its direction of motion. The transformation from the velocity function to the corresponding speed function is readily obtained by integration. Thus in the case of the neutron distribution (4.197) we compute the corresponding function in speed space by integrating (4.197) over all directions of motion Q. If we define... 

This result may be written in an alternative form by separating the integration over velocity space into an integration over speed space and an integration over all directions of neutron motion Q. Then, for example,... 

We find then that the computation of the thermal-neutron group cross sections may be carried out by integrating the measured cross-section data weighted by the neutron distribution in speed space (4.200) over the range 0 < v < . It would appear that the details of the computation introduce some ambiguity from a physical viewpoint since the integration... 

In tlie previous section we showed tliat because tlie stmcture space is very sparse tliere have to be many sequences tliat map onto tlie countable number of basins in tlie stmcture space. The kinetics here shows tliat not all tlie sequences, even for highly designable stmctures, are kinetically competent. Consequently, the biological requirements of stability and speed of folding severely restrict tlie number of evolved sequences for a given fold. This very important result is schematically shown in figure C2.5.4. 

Almost all chemical information systems work with tlicir own special type of connection table. They often use various formats distinguishing between internal and external connection tables. In most cases, the internal connection tables arc redundant, thus allowing maximum flexibility and increasing the speed of data processing. The external connection tables are usually non-redundant in order to save disk space. Although a connection table can be cprcsented in many different ways, the core remains the same the list of atoms and the list of bonds. Thus, the conversion of one connection table format into another is usually a fairly straightforward task. 

Energy minimisation and normal mode analysis have an important role to play in the study of the solid state. Algorithms similar to those discussed above are employed but an extra feature of such systems, at least when they form a perfect lattice, is that it is can be possible to exploit the space group symmetry of the lattice to speed up the calculations. It is also important to properly take the interactions with atoms in neighbouring cells into account. 

In molecular distillation, the permanent gas pressure is so low (less than 0 001 mm. of mercury) that it has very little influence upon the speed of the distillation. The distillation velocity at such low pressures is determined by the speed at which the vapour from the liquid being distilled can flow through the enclosed space connecting the still and condenser under the driving force of its own saturation pressure. If the distance from the surface of the evaporating liquid to the condenser is less than (or of the order of) the mean free path of a molecule of distillate vapour in the residual gas at the same density and pressure, most of the molecules which leave the surface will not return. The mean free path of air at various pressures is as follows —... 

Beryllium is used as an alloying agent in producing beryllium copper, which is extensively used for springs, electrical contacts, spot-welding electrodes, and non-sparking tools. It is applied as a structural material for high-speed aircraft, missiles, spacecraft, and communication satellites. Other uses include windshield frame, brake discs, support beams, and other structural components of the space shuttle. 

There are several issues to consider when using ECP basis sets. The core potential may represent all but the outermost electrons. In other ECP sets, the outermost electrons and the last filled shell will be in the valence orbital space. Having more electrons in the core will speed the calculation, but results are more accurate if the —1 shell is outside of the core potential. Some ECP sets are designated as shape-consistent sets, which means that the shape of the atomic orbitals in the valence region matches that for all electron basis sets. ECP sets are usually named with an acronym that stands for the authors names or the location where it was developed. Some common core potential basis sets are listed below. The number of primitives given are those describing the valence region. 

The end or front of the plasma flame impinges onto a metal plate (the cone or sampler or sampling cone), which has a small hole in its center (Figure 14.2). The region on the other side of the cone from the flame is under vacuum, so the ions and neutrals passing from the atmospheric-pressure hot flame into a vacuum space are accelerated to supersonic speeds and cooled as rapid expansion occurs. A supersonic jet of gas passes toward a second metal plate (the skimmer) containing a hole smaller than the one in the sampler, where ions pass into the mass analyzer. The sampler and skimmer form an interface between the plasma flame and the mass analyzer. A light... 

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