Long-wavelength fluctuations

All the above scaling relations have one common origin in the behavior of the correlation length of statistical fluctuations, in a finite system [140,141]. Namely, the most specific feature of the second-order transition is the divergence of at the transition point, as is described by Eq. (22). In the finite system, the development of long-wavelength fluctuations is suppressed by the system size limitation can be, at the most, of the same order as L. Taking this into account, we find from Eqs. (22) and (26) that... 

On the basis of general scaling arguments it can be shown that the stochastic evolution of a driven interface along a strip of width L is characterized by long wavelength fluctuations (w(L, t)) which have the following time and finite-size behavior [60]... 

The He-Ne laser has a stable, narrow-beam output at 632.8 nm in the red region. This type of laser typically has short term peak-to-peak fluctuation of less than 1%. Its long wavelength enables the studies of colorless materials and colored red-transmitting materials. The 632.8 nm line has a maximum output about 80 mW. 

Then the angles ground state. At low temperatures, cpr are small and the Gaussian approximation of long-wavelength fluctuations of the angular Fourier components >(k) permits the Hamiltonian of Eq. (2.2.1) to be written as ... 

For very large R the behavior of koo R) is determined by long wavelength density fluctuations, hence by the compressibility of the liquid. Precision small angle X-ray scattering measurements 17>, as well as extrapolations of hoo(s) to s = 0 for the data shown, are in agreement with predictions based on bulk thermodynamic data. 

The growth rate R(q), not to be confused with the Rayleigh factor R(q), Is always negative for metastable mixtures, as expected. For unstable mixtures, R(q) becomes positive for fluctuations of a sufficiently long wavelength that q < q, exhibits a maximum at... 

Theory for block copolymer rheology is still in its infancy. There are no models that can predict the rheological behaviour of a block copolymer from microscopic parameters. Fredrickson and Helfand (1988) considered fluctuation effects on the low frequency linear viscoelastic properties of block copolymers in the disordered melt near the ODT. They found that long-wavelength transverse momentum fluctuations couple only to compositional order parameter fluctua-... 

The vast array of experiments in the cuprates narrows the possible theories for the phenomena. One can be certain that the theories should have a QCP with a phase with a pseudogap ending at it. One can also be certain that in the long wavelength limit, the fluctuations about the QCP must have the form of Eq. (2) because that is what is observed [29],... 

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