Neighborhoods of dominance

Pure searching Temporary mate guarding Monogamy monogamous mate guarding Neighborhoods of dominance... 

A 5 3.2 Formal derivation of the loop expansion To construct, the loop expansion we look for the extrema of S[(p] being guided by the idea that the functional integral is dominated by the neighborhood of the minimum of L [minimizing function is a constant... 

Following ideas of the extended Born approximation (Habashy et al., 1993), we recall that the Green s function G (r r o ) exhibits either singularity or a peak at the point where = r. Therefore, one can expect that the dominant contribution to the integral G [As Ap ] in equation (14.43) is from some neighborhood of the point Tj — r. In fact, we can expand A (r,cu) into a Taylor series about r = r ... 

As explained in Section 11, the partition function can be written as a onedimensional integral over the basin depth (Stillinger and Weber, 1982). In the thermodynamic hmit, the integral in Eq. (15) is dominated overwhelmingly by basin depths in the neighborhood of a particular, temperature-dependent value, which satisfies the extremum condition... 

In the laminar flow range Re < 10 the heat conduction dominates (which is periodically disturbed by the stirring device rotating past in the neighborhood of the wall) and the effect of density and viscosity disappears entirely. Then the following relationship applies for the heat transfer characteristic ... 

The constant Xc is the point at which ((/r(xi,xo)/t/xi)v,=xc = 0. We apply this result to a problem in which xq and xi on opposite sides of a high barrier so that both I E(xb) — V(xo) I and E(xb) — E(xi) are much larger than ksT. This implies that in the outer integral in (14.58) the dominant contribution comes fromx = Xb- The inner integral is then dx"I x" , and will not depend on Xc if the latter is placed anywhere on the other side of the well opposite to xb and far enough from the well bottom. This is so because in that case the inner integral is dominated by the neighborhood of the well bottom where Peq( ) has a sharp maximum. For the potential of Fig. 14.2 we can take Xc = — oo so that... 

For Eb 1 we can simplify this expression by noting that the integrands are heavily biased by the exponential factors the outer integral is dominated by the well bottom, E 0, where the frequency is (vo, while the inner integral is dominated by the neighborhood of = E. Therefore... 

If ionizing radiation (X-ray or particle radiation) directly hits a strand of DNA, most probably one of the DNA strands breaks. To obtain a double strand break by the same particle, one would need the second break in the neighborhood of the first one (otherwise repair enzymes would rebuild at least one of the first strands). On the other hand as the experimental number of double strand breaks versus dosage curves show, the linear term is dominant in their mathematical expression.170 This means that the double strand break is caused by a single particle (or by the secondary particles caused by it). On the other hand it is unprobable, from scattering theoretical considerations, that a particle will be scattered inelastically (after a strand break) with a very small space angle (the corresponding cross section is very small) so as to reach the second strand very near to the first one.171... 

In tellurium a boundary in the liquid state has been indicated by Deaton and Blum (22) which extends from the temperature at which tellurium begins to show metallic conduction at 1 atm (943°K) (41) to the neighborhood of the melting curve maximum (22) and is postulated to represent chain dissociation. Above this boundary metallic type behavior appears to dominate the conductivity (22). Controversy over this boundary is apparent also as Stishov (44) reports only semiconducting behavior, rather than metallic, in the liquid tellurium high pressure fields and states that the boundary intersects the liquidus beyond the maximum. 

The trends in phase behavior as a function of oil-phase ACN indicate an optimum point in the neighborhood of pentane or hexane. This behavior is a consequence of the enthalpic and entropic components of the solvent-surfactant tail interaction [25,43]. Alkanes heavier than hexane are hindered in their ability to penetrate between the surfactant tails, which makes the combinatorial (chain length compatibility) effect the dominant one for these solvents. Alkanes lighter than hexane penetrate between surfactant tails very easily, but their enthalpic interaction with the tails is weak. At pentane and hexane, the combinabon of enthalpic and entropic effects is balanced. This balance favors the formation of the 2 configuration in Winsor systems. In reverse micelle systems, the optimum solvent-surfactant tail interaction stabilizes the reverse micelles against phase separation driven by micelle-micelle interactions. Also, there is a minimum in the attractive intermicellar dispersion interaction [13]. Therefore W reaches a maximum. 

The above formulae give a representation of the whole neutron density due to a point source. The first part of the density N, i.e. iVi, is dominant at large distances from the source (except if aa/o is nearly one). The second part, N2, dominates in the neighborhood of the source. As Oa/cr approaches 1, the most probable exponential in N2 becomes the one with a cr <7. At the same time, the exponent /c of N2 also approaches cr <7. In this limiting case N and N2 have the same exponential. However, N contains the factor J/r, N2 the factor 1/r. Since I goes, at the same time, to zero, the total N becomes in this limiting case - as evident from physical considerations. 

This observation is quite noteworthy. It shows that by matching an antenna in the neighborhood of maximum power transfer (i.e., conjugate matching) we obtain an added benefit, namely a potential strong reduction of the ripples of the scan impedance even at a frequency where the surface waves are dominating. 

In order that this solution dominate the time-dependent problem for long times, it is necessary that there be no other solutions of Equation (10) in the neighborhood of A = 0. 

The first work described the fluorescence spectra and gave the qualitative assessment of fluorescence yields shown in Fig. 13. A qualitative diflerentiation among vibronic levels appeared. Nonradiative decay appeared to completely and uniformly dominate relaxation from levels lying above 2500 cm whereas fluorescence spectra could be observed from all levels below this region. Subsequent measurements with improved equipment have extended this limit to the neighborhood of 3000 cm but confirm the rapid decline in emission yields in the region 2000-3000 cm h Nonradiative channels quickly become dominant as excitation climbs the vibrational ladder. 

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