Gaussian distribution transitions

Gaussian approximation, heat flow, 60 Gaussian distribution, transition state trajectory, white noise, 206-207 Gaussian-Markov process, linear... 

The mean field treatment of such a model has been presented by Forgacs et al. [172]. They have considered the particular problem of the effects of surface heterogeneity on the order of wetting transition. Using the replica trick and assuming a Gaussian distribution of 8 Vq with the variance A (A/kT < 1), they found that the prewetting transition critical point is a function of A and... 

Abstract. Quantum chaos at finite-temperature is studied using a simple paradigm, two-dimensional coupled nonlinear oscillator. As an approach for the treatment of the finite-temperature a real-time finite-temperature field theory, thermofield dynamics, is used. It is found that increasing the temperature leads to a smooth transition from Poissonian to Gaussian distribution in nearest neighbor level spacing distribution. 

The essential difference between the two transition probability densities lies in the fact that for the gaussian distribution pw r, ) the different moments E[Xm], m = 1, 2,. . . , n, exist, while for the Cauchy distribution pc(j, x) they do not exist. The Levy distributions characterized by p(t, k) = exp -a k qT) with 0< <2U 127 128 play a prominent role in the theory of relaxation processes.129 133... 

This expression shows that the field-dependence of the transition rate is given by the distribution function of local fields. Below, we analyze the results in terms of two limiting distributions, a Gaussian distribution and a Lorentzian one. 

In Figure 7 we present the free energy for an asymmetric Gaussian distribution (a = 1.4) as a function of distance for various values of the Hamaker constant (with all the other parameters unchanged). For H > 3.825 x 10-21 J, a stable minimum is obtained at a finite distance. For H < 3.825 x 10 21 J, the stable minimum is at infinite distance however, for 3.825 x 10-21c7 > H > 3.45 x 10-21 J, a local (unstable) minimum is still obtained at finite distance. For H = 3.825 x 10-21 J, a critical unbinding transition occurs, since the minima at finite and infinite distances become equal. However, these two minima are separated by a potential barrier, with a maximum height of 1.68 x 10 7 J/m2, located at a separation distance of 90 A. The results remained qualitatively the same for any combination of the interaction parameters. 

Weiss, M., A note on the role of generalized inverse Gaussian distributions of circulatory transit times in pharmacokinetics, Journal of Mathematical Biology, Vol. 20, 1984, pp. 95-102. 

Fig. 8.6 Features of the double-pulse technique Model on the influence of the transition moment between nucleation pulse and growth pulse in the course of the double-pulse deposition on the Gaussian particle distribution formed after the nucleation pulse [29] (a) Gaussian particle distribution of N nuclei with radii r > tcr (T)i) for different over potentials of the first pulse ( t ib << t iAl)- The hatched area of the Gaussian distribution corresponds to the number of stable particles with radii r > rcr (tje). whereas the white area of particles of under critical size is amputated as these particles dissolve, (b) Representation of the result of the particle cut off, small (dark) particles dissolve but larger particles (white) survive under the lower overvoltage of the growth pulse.(c) If a small particle lies in the diffusion zone of a larger particle the under saturation can favor the dissolution of the smaller ones...

The small random crystal strains can be quantified and this is also given in Table 5. It was found that the sttain can be described by a Gaussian distribution characterised by a mean value, 8, of zero and a half width of 8a = 2cm . The analysis also differed from that of previous workers in both the hyperfine values and the requirement of a nuclear quadrupole term. The transitions within the lowest excited singlet could also be observed directly [31]. It can be concluded that the Cu(ll)/MgO system can be described as an almost pure dynamic Jahn-Teller case. 

Figure 2.15. Effect of a distribution of interactions on the second-order quadrupole powder lineshape of the central transition in detail with the mean interaction Xq = 2 MHz and -ri = 0 at a Larmor frequency of 80 MHz showing A. no distribution, B. a Gaussian distribution of isotropic chemical shifts with FWHM = 0.17 A, C. a Gaussian distribution of the quadrupole interaction of 340A and D. both the chemical shift and quadrupole interactions distributed, (A = 2344Hz).

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