Adiabatic core

While the agreement of the measured and calculated Ba+ quadrupole polarizabilities is not very good, compared to an analysis based on adiabatic core polarization the agreement in Table 17.3 is superb. The adiabatic core polarization model leads to ad = 146flo and aq = —5800. The ground state of Ba+ cannot have a negative quadrupole polarizability. Taken together, the Ca and Ba experiments show clearly that the nonadiabatic effects in core polarization in the alkaline earth atoms are important and may be calculated with some accuracy. 

In most, but not all circumstances, the core gas temperature, T, is the natural reference temperature for the compressed gas because the highest temperature at the end of compression is responsible for the development of spontaneous ignition in the shortest time [88, 95]. Exceptionally, when the compression heats the reactants to temperatures that correspond to the region of ntc for that particular mixture, combustion may be initiated in the cooler boundary layer region. That is, gases which, at the end of compression, are colder than those in the adiabatic core control the duration of the ignition delay. This was demonstrated by Schreiber and coworkers by the simulation of alkane combustion, using various reduced kinetic schemes, in computational fluid dynamic calculations [102-104]. 

Nonadiabatic polarization effects have been observed in both Ca and An analysis of the Ba A/ intervals using the adiabatic core... 

An adiabatic core (Arteoli et al., 2010) is a fuel cycle strategy able to convert an input feed of either natural or depleted uranium (NU or DU, respectively) into energy, with FP and actinide reprocessing losses as the only output stream. This allows the full closure of the fuel cycle within the reactor (thus the term adiabatic, because of its having no significant exchange with the environment) with transuranics remaining at equilibrium in the core, as shown in Table 6.3, which depicts the results of an analysis carried out for the ELSY reactor. 

After bypassing the trigger in (28.65), on one hand the crystal remains in the adiabatic state, but on the other the electrons from the last occupied (conducting) band are not part of the rigid system any more, they are quasi free and interact with the lattice only via the electron-phonon interaction without the backward influence on the lattice symmetry and nuclear displacements. The whole system is divided in two subsystems, the adiabatic core consisting of nuclei and electron valence bands, and the quasi free conducting electrons. 

Since quantum field many body techniques are not directly transferable into quantum chemistry dealing with small molecular systems, they are not fully transferable into the solid-state physics dealing with great systems (crystals) either. As it was explained in detail in this work, only the COM many-body formulation is applicable in non-adiabatic cases. For non-adiabatic crystals the state of conductivity and superconductivity are two possible solutions of the extended Born-Handy formula. This is a quite different view from that using only the classical many body (without COM). The non-adiabatic treatment of crystals leads always to the splitting into two subsystems. In the case of conductors the first subsystem is the adiabatic core consisting of nuclei and all valence bands, and the second subsystem is the fluid of quasi-free conducting electrons. The explanation of conductors on the basis of a COM true many-body treatment is not so simple as in the case of the... 

Note 2 Since no system can be heal adiabatic in practice there is a ce.rtain amount of heat dissipation from the impregnated windings to the stator core and housing. This heat dissipation is considered as 15% of the total heat generated as in lEC 60079-7. 

Another instability mode of interest is due to the flow regime itself. For example, it is well known that the slug flow regime is periodic and that its occurrence in an adiabatic riser can drive a dynamic oscillation (Wallis and Hearsley, 1961). In a BWR system, one must guard against this type of instability in components such as steam separation standpipes. The design of the BWR steam separator complex is normally given a full-scale, out-of-core proof test to demonstrate that both static and dynamic performance are stable. 

PMS stars with M < 0.35 M0 have a simple structure - they are fully convective balls of gas all the way to the ZAMS. As the star contracts along its Hayashi track the core heats up, but the temperature gradient stays very close to adiabatic except in the surface layers. Li begins to burn in p, a reactions when the core temperature, Tc reaches c 3x 106 K and, because the reaction is so temperature sensitive (oc Tc16-19 at typical PMS densities) and convective mixing so very rapid, all the Li is burned in a small fraction of the Kelvin-Helmholtz timescale (see Fig. 1). 

At sufficiently high densities (e.g. cores of upper main-sequence stars), the > sign virtually becomes an equality (adiabatic stratification), but at lower densities (e.g. envelopes of the Sun and cooler stars) an exact calculation is very difficult and in most models a crude approximation based on mixing-length theory is used. In a situation where the chemical composition changes with depth, Eq. (5.24) (known as the Schwarzschild criterion) needs to be replaced by more complicated considerations. 

We have tacitly assumed that the photoemission event occurs sufficiently slowly to ensure that the escaping electron feels the relaxation of the core-ionized atom. This is what we call the adiabatic limit. All relaxation effects on the energetic ground state of the core-ionized atom are accounted for in the kinetic energy of the photoelectron (but not the decay via Auger or fluorescence processes to a ground state ion, which occurs on a slower time scale). At the other extreme, the sudden limit , the photoelectron is emitted immediately after the absorption of the photon before the core-ionized atom relaxes. This is often accompanied by shake-up, shake-off and plasmon loss processes, which give additional peaks in the spectrum. 

Figure 2. Simplified picture of atom-atom collisional ionization with crossing distance r. Heavy solid lines represent trajectories of neutral systems. At the first crossing (r= rj some fraction (1 - PJ of trajectories make adiabatic transitions and are represented by dashed lines (ion pairs). Those making diabatic transitions remain neutral and continue their flight relatively unaffected. Each of these trajectories then encounters r = r<- again, and again each trajectory can make an adiabatic or diabatic transition, resulting in ion pairs or neutrals depending on the trajectory. The ultimate production of ions requires one transition to be diabatic and one to be adiabatic, in either order. The inner circle represents the repulsive core.

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