Single occupancy probability

In the concentration wave (CW) theory [760] the distribution of atoms A in a binary A-B alloy is described by a single occupancy probability function n r). This is the probability to hnd the atom A (La) at the site r of the crystalline lattice. The conhgurational part of the free energy of solid-solution formation (per atom) includes the internal formation energy AU, the function n r), a concentration of particles La(A), the effective interatomic potentials between La atoms (A) and Sr atoms (B), for details see [754]. 

BCS occupation probabilities of the j neutron orbitals.Because of these v single-particle energy variations,a first correction to the unperturbed proton intruder configurations results as AEm = 2( ., )-2(c.,-e. )... 

Fig. 1. Single-quantum system approximated by a system of three levels with occupation probabilities pi interconnected by transition rates kij. A third level is taken into account in order to accommodate transitions to triplet or other dark states.

An example of such a simulation is shown in Fig. 3.13 where the evolution of the clusters with the mean occupation probability p on a square lattice is shown. The evolution of the single clusters n, all multi-clusters ns = X ins nii and all clusters na are depicted. The simulation was done on a 100 x 100 square lattice. 

Figure 3.13 Simulated normalised cluster numbers for a 100 x 100 square lattice. The evolution, with the mean occupation probability p, of the normalized cluster numbers of single and multi-clusters as well as the evolution of the total cluster density are plotted. The simulation of n, follows the analytical expression n, = p(l — p)4.

Fig. 16. Schematic of the occupation probabilities in phase II of TCTMB and DCTMB. From left to right molecules under study, three well potential, averaged quadrupolar interaction and asymmetry parameters measured from powders spectra, occupations probabilities calculated from single-crystal experiments.

As a representative primary explosive, we consider lead azide as a representative secondary, HMX. It is now possible to prepare single crystals of both materials and to measure their electronic properties. We shall consider in a preliminary way a few aspects of their electronic states and the occupational probability of these states, as described by the Fermi level, relevant to the decomposition of these materials. 

Equation (28-19) reveals that the total energy of a single molecule at equilibrium is obtained by weighting the energy of each available stationary state by the occupational probability of that state, which is given by the Boltzmann distribution. 

Spectroscopic factors together with occupation probabilities and magnetic moments are basic elements needed for the understanding of nuclear structure. The spectroscopic factor S is defined as the probability to reach a final single-particle (hole) state when a nucleon is added to (or removed from) the target nucleus (correspondingly 5+, 5+ or ). The mean field approximation is a... 

The omega mass is peaked at the nuclear surface, producing what sohd-state scientists would call surface states. In the nuclear case, this just corresponds to low-lying (i.e., near the Fermi surface) collective excitations associated with the physical surface. The combined effective masses and the potentials from which they are derived are shown in Fig. 3.19. The /c-mass suppresses the effective mass in the interior and the omega-mass produces a peak at the nuclear surface. Also extracted from this analysis are the occupation probabilities of single-particle levels, a subject that will be addressed in the next section when discussing singleparticle knockout reactions from nuclei far-removed from stability. 

Proton single-particle occupation probabilities in Ca circles), Ca squares), and Ca triangles) as deduced from a Dispersive Optical Model fit (Charity et al. 2007)... 

In order to formulate the excitation lifetime and the quantum yield in terms of transfer rates, we first introduce a master equation for the rate of change of occupation probabilities of chlorophylls. In the discussion below, a single excitation will be assumed to be localized at one of the chlorophylls and the effects of excitonic delocalization will be ignored. As a specific example we shall consider the case of excitation migration in cyanobacterial PSI ( ener et al, 2002b 2004). 

Fig. 10 Definition of the four rates of capture and emission of electrons and holes by a single trap level. These four rate equations are the basis of Shockley-Read-Hall statistics, which defines the occupation probability and the recombination rate via this trap...

We calculated the free energies of all the minima in order to determine the equilibrium probability distribution (see Section IV.C.2). We found that the several hundred lowest free energy minima have about the same free energy, and that no single minimum has an equilibrium occupation probability which exceeds 0.004. This is in stark contrast with unsolvated tetra-alanine, where the ground state had an equilibrium occupation probability of 0.748, and the lowest three potential energy states accounted for 0.936 of the total equilibrium probability. 

Electron transfer rates between adrenaline and related benzene diols and complexes of iron(III) with some substituted 1,10-phenanthrolines have been reported [67] in surfactant systems. In cationic systems the reactions take place in the aqueous phase and reaction rates are lower than they are in simple aqueous systems, but in anionic surfactant systems the reaction rates are enhanced, reactions probably taking place at the micellar interface. The rates of exit and entrance of aromatic compounds from and into micelles have recently been studied using phosphorescence decay measurements [68] exit rate constants of aromatic hydrocarbons are of the order of 10 to 10 s " S whereas values of 10 to 10 (moll ) s have been reported for intramicellar energy transfer processes. Release of aromatic phosphorescence probes from micelles followed by their deactivation in the aqueous phase is hence expected to be an important mode of deactivation of the triplet state [69]. Kinetic schemes for triplets that are partitioned between aqueous and micellar phases are considered for the cases of single occupancy and double occupancy of the micellar units. 

Once I had decided on a career in chemistry, I was determined rather single-mindedly to make a success of it. I sometimes think about what would have happened had I chosen a different occupation or field. Having a rather competitive nature, I could probably have done reasonably well in a number of other areas. Certainly for some fields you must be born with a special talent. Musical talent, artistic ability, business acumen, leadership ability, and vision can be further developed. 

In Fig. 7A is given the steady state scheme for two sites which defines each of the elemental rate constants and in Fig. 7B are the steady state equations for the rate of change with time of the probability, %, of each of the occupancy states of the channel oo, xo, ox and xx. C and Cx are the concentrations of the x ion on the left-and right-hand sides, respectively. The general expression for the current, ix, due to the ionic species, x, passing through a single channel is... 

Utilizing the above five experimentally derived rate constants and Eyring rate theory, the ten rate constants of Eq. 6 are all obtained. With the rate constants known, the probability of each occupancy state, /(ox) for example, can be calculated and finally the single channel current can be calculated as a function of molal activity of sodium ion. This is done for a 100 mV transmembrane potential in Fig. 9. It should be emphasized that Fig. 9 represents a calculation of single channel currents... 

Mineral Oil Hydraulic Fluids. Studies regarding cancer in humans or animals after inhalation exposure to mineral oil hydraulic fluids were limited to a single case-control study that examined associations between subjectively reported occupational exposure to petroleum-derived liquids and cancer at particular sites among 3,726 male cancer patients (Siemiatycki et al. 1987a). The study found no convincing associations between occupational exposure to hydraulic fluids and cancer at any site. This study is discussed in more detail in Section 2.2.3.8, because, while inhalation exposure was probable for the subject occupations, the authors reported that the exposure route was more often dermal contact. 

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