Interaction length

When g = 1 the extensivity of the entropy can be used to derive the Boltzmann entropy equation 5 = fc In W in the microcanonical ensemble. When g 1, it is the odd property that the generalization of the entropy Sq is not extensive that leads to the peculiar form of the probability distribution. The non-extensivity of Sq has led to speculation that Tsallis statistics may be applicable to gravitational systems where interaction length scales comparable to the system size violate the assumptions underlying Gibbs-Boltzmann statistics. [4]... 

The possibility to carefully tune the XB strength of a given halocarbon by modifying the substituents on the carbon skeleton is also confirmed experimentally. As expected, the stronger an XB, the shorter the interaction length (see onwards). The N I-C interaction length in the infinite chain given by 1,4-BPY with 1,4-diiodobenzene (1,4-DIB) is 3.032 A and the N I... 

The attractive nature of XB causes D- -X distances shorter than the sum of van der Waals radii of involved atoms the stronger the interaction, the shorter the D- -X interaction lengths. Consistent with the rationalization of XB as an electron donation from D to the antibonding X-Y orbital [59], XB formation results in an elongation of the X-Y covalent bond. The D- -X interaction length is usually a more sensitive probe for XB strength than the X - Y covalent bond elongation (Table 3). 

The third step (ANefj—>Ap) can be optimized by taking a large interaction length and a low wavelength, see (2), but there are trade offs with the desires of limited chip area and limited scattering and absorption losses respectively. 

In a crystalline medium, the parametric gain (2) T2 is propor-tionnal to d2 Ip n-3 and the oscillation condition r2A2>aA where a is the signal residual absorption (dramatically increased by any crystalline defect), d the efficient phase-matched nonlinear susceptibility, n an average refractive index, Ip the pump intensity (limited by the optical damage threshold) and A the effective interaction length (also limited by any source of crystalline disorientation). 

The theoretical analysis for this form of coupling shows that the SH conversion efficiency is proportional to the interaction length rather than the square of the interaction length as for the guided wave SHG. Also, in this case the overlap integral is small resulting in lower conversion efficiencies than the guided wave interaction. 

When a chemical or biochemical reaction takes place in the sensor area, only the light that travels through this arm will experience a change in its effective refractive index. At the sensor output, the intensity (I) of the light coming from both arms will interfere, showing a sinusoidal variation that depends on the difference of the effective refractive indexes of the sensor (Neff,s) and reference arms (Neff,R) and on the interaction length (L) ... 

The authors deduce the decay length (X) from the slope and the first interaction length or onset of repulsion (2Lq) defined as the distance at which the magnitude of force is 2 10 A. One of the main findings of this study is that the force profiles are strongly dependent upon the sequence of adsorption of polymer and surfactant and three cases are envisaged. 

Rgure 2.18. Decay length and first interaction length (2Lo) values deduced from the force curves in Fig. 2.17 (cases II and III), as a function of surfactant concentrations. Solid lines are a visual guide. (Adapted from [75].)... 

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