Relaxation Of Fluctuations Research Articles

Brillouin Scattering Study of the Anisotropic Relaxation of the Polarization Fluctuation in Ferroelectric TGS

The polarization relaxation phenomena in the uniaxial ferroelectric TGS have been studied by the observation of the angular dependence of the Brillouin scattering spectra. Both the frequency shift and the full width of the Brillouin satellite show remarkable anisotropic anomalies most strongly at 44.94°C below the transition temperature T c =48.86°C. The experimental result is successfully interpreted from the viewpoint of the depolarization effect on the polarization fluctuation. The effect is characterized by the anisotropic relaxation time with only two parameters ; a relaxation time τ 0 for a transverse polarization fluctuation and a generalized Lorentz factor L . The values τ 0 =(0.93±0.09)×10 -11 sec and L ≃0.41 give a good description of the experimental result.

Observation of the relaxation of composition fluctuations in a binary liquid mixture

Light scattering was used to study the decay of concentration fluctuations in a critical mixture of isobutyric acid and water. The aim of the experiment was to study the dynamic interaction between composition and velocity in the mixture. At large wavenumber, the structure factor S ( k , t ) is observed to decay exponentially, with a relaxation rate somewhat smaller than the equilibrium value. At small k , however, there is a marked departure from the exponential relaxation one expects in the absence of coupling between composition and velocity. Also measured was the spinodal ring diameter, k m , as a function of the total scattered intensity, C tot ( t ) = (2 π ) −2 ∫ S ( k , t ) k 2 dk . A calculation of Ruiz, based on the above coupling effect, predicts a linear variation of In k m ( t ) with C tot ( t ) and such a linear variation is observed.

Decay of concentration fluctuations in liquid mixtures

Our previous work on the influence of hydrodynamic effects on the relaxation of concentration fluctuations in liquid mixtures is extended to include the effects of strong diffusion. The fluctuations migrate, as in the diffusionless case, towards the largest scales at a rate dictated by the instantaneous value of the fluctuation strength. Experimental tests of our theory are suggested and discussed.

Relaxation of nonequilibrium fluctuations in liquid mixtures above the consolute point

We study the relaxation of nonequilibrium concentration fluctuations in binary-liquid mixtures near but above the critical consolute temperature. We show that if the strength of the fluctuations is far enough above the thermal level, hydrodynamic effects cause these fluctuations to migrate towards the smallest wave numbers. They are dissipated only in an exceedingly long time at the largest available scale. The structure factor of the fluctuations obeys a scaling law similar to the one observed in experiments of spinodal decomposition. Experimental tests of our result are suggested and their possible relevance to the theory of spinodal decomposition briefly discussed.

Cross-correlation laser scattering

Cross-correlation between two detectors was applied to analyze laser light-scattering fluctuations. Laser scattering from random concentration fluctuations is spatially coherent over small angular areas that are inversely proportional in size to the dimension of the scattering volume. By cross-correlating scattering intensity fluctuations in different angles, the correlation due to relaxation of concentration fluctuations is practically eliminated, and correlations reflecting changes in the scattering from the individual particles can be enhanced. Rotational diffusion of assymetric particles, conformational relaxation of random coils, and association-dissociation dynamics are determined here using the above approach.

Relaxational dynamics of the Edwards-Anderson model and the mean-field theory of spin-glasses

Langevin equations for the relaxation of spin fluctuations in a soft-spin version of the Edwards-Anderson model are used as a starting point for the study of the dynamic and static properties of spin-glasses. An exact uniform Lagrangian for the average dynamic correlation and response functions is derived for arbitrary range of random exchange, using a functional-integral method proposed by De Dominicis. The properties of the Lagrangian are studied in the mean-field limit which is realized by considering an infinite-ranged random exchange. In this limit, the dynamics are represented by a stochastic equation of motion of a single spin with self-consistent (bare) propagator and Gaussian noise. The low-frequency and the static properties of this equation are studied both above and below ${T}_{c}$. Approaching ${T}_{c}$ from above, spin fluctuations slow down with a relaxation time proportional to ${|T\ensuremath{-}{T}_{c}|}^{\ensuremath{-}1}$ whereas at ${T}_{c}$ the damping function vanishes as ${\ensuremath{\omega}}^{\frac{1}{2}}$. We derive a criterion for dynamic stability below ${T}_{c}$. It is shown that a stable solution necessarily violates the fluctuation-dissipation theorem below ${T}_{c}$. Consequently, the spin-glass order parameters are the time-persistent terms which appear in both the spin correlations and the local response. This is shown to invalidate the treatment of the spin-glass order parameters as purely static quantities. Instead, one has to specify the manner in which they relax in a finite system, along time scales which diverge in the thermodynamic limit. We show that the finite-time correlations decay algebraically with time as ${t}^{\ensuremath{-}\ensuremath{\nu}}$ at all temperatures below ${T}_{c}$, with a temperature-dependent exponent $\ensuremath{\nu}$. Near ${T}_{c}$, $\ensuremath{\nu}$ is given (in the Ising case) as $\ensuremath{\nu}(T)\ensuremath{\sim}\frac{1}{2}\ensuremath{-}{\ensuremath{\pi}}^{\ensuremath{-}1}(\frac{1\ensuremath{-}T}{{T}_{c}})+\ensuremath{\sigma}{(\frac{1\ensuremath{-}T}{{T}_{c}})}^{2}$. A tentative calculation of $\ensuremath{\nu}$ at $T=0$ K is presented. We briefly discuss the physical origin of the violation of the fluctuation-dissipation theorem.

The kinetics of relaxation of magnetization fluctuations near the phase transition from paramagnetic state to ferromagnetic state with domain structure

The equations of motion describing relaxation of magnetization fluctuations in the paramagnetic state for a uniaxial ferromagnet have been solved. In the Landau-Ginzburg functional the demagnetization energy has been taken into account. The finite dimensions of a sample have been considered. It has been shown, that a phase transition is generated by fluctuations containing information about the period of the domain structure at the phase transition point Tc∗. The obtained formulae describe Tc∗ and the period of the domain structure. The results can be used both for bulk materials and thin films.

Use of the single electrode voltage clamp to perform noise and relaxation studies of acetylcholine-activated channels in aplysia neurons

The single electrode voltage clamp has been used to perform fluctuation analysis (“noise” analysis) and relaxation experiments in order to study the average lifetime and conductance of ACh-activated sodium channels in Aplysia neurons. Measured values of average channel lifetime, which is ∼20 msec at −80 mV and 11°C, and elementary conductance, which is ∼8 pS, are consistent with previously published results using two electrode clamping. The frequency response of the clamp was evaluated to determine its capabilities and limitations for the study of membrane currents. Sinusoidal currents injected into a voltage-clamped model membrane to simulate the frequency components of membrane noise are accurately reproduced at frequencies up to 500 Hz. Following a voltage clamp command, the new membrane potential is established in less than 2 msec, and current relaxations recorded after that time can be used to determine average channel lifetime. Since the frequency response of the clamp is much greater than the average lifetime of ACh-activated channels in Aplysia neurons, the single electrode voltage clamp is comparable to conventional two-electrode systems for investigating the properties of these channels, and may also be useful in other systems in which the time course of membrane currents is much slower than the frequency response of the clamp.

Addendum to "Density fluctuations in liquid rubidium"

We performed molecular-dynamics simulations of liquid rubidium and the Lennard-Jones fluid at several densities and temperatures, and of a system whose pair potential is the repulsive core of the rubidium potential. In all cases, propagating density fluctuations occurred in the rubidiumlike systems at much shorter wavelengths than in the Lennard-Jones system. This indicates that the repulsive part of the pair potential is the dominant factor in determining the relaxation of short-wavelength density fluctuations.

Dynamic light scattering studies of internal motions in DNA. II. Clean viral DNAs.

AbstractInternal Brownian motions of clean ϕ29 and λ‐DNAs have been studied using photon‐correlation techniques at both visible (λ0 = 632.8 nm) and uv (λ0 = 363.8 nm) wavelengths. The present dynamic light scattering data, which extend to K2 = 19 × 1010 cm−2, can in every case be satisfactorily simulated by a Rouse‐Zimm model polymer with an appropriate choice of the three model parameters. The effects of pH, salt concentration, single‐strand breaks, and molecular weight on those model parameters have also been investigated. Intact clean DNAs exhibit surprisingly little variation with pH from 7.85 to 10.25, with salt concentration from 0.01 NaCl to 5.4M NH4Cl, or with molecular weight or GC content. The single‐strand breaks have no effect at pH 9.46, but produce dramatic changes in the model parameters at pH 10.0 and 10.25, indicating the introduction of titratable joints at those pHs. The failure of either single‐strand breaks or a large change in GC content to alter the model parameters in the neutral pH range is a strong indication that local denaturation is not required for those flexions and torsions that dominate the relaxation of fluctuations in the scattered light. The Langevin relaxation time for the slowest internal mode of a particular Rouse‐Zimm model derived from the dynamic light scattering data is compared with pertinent literature data extrapolated to the same molecular weight. The present algorithm for determining model parameters from the light‐scattering Dapp vs K2 curve actually yields a Langevin time in fairly good agreement with the literature value. For unknown reasons the light‐scattering D0 values generally exceed those obtained from the molecular weight and sedimentation coefficient by about 20%.

Concentration fluctuation process in ethanol–water mixture

Shear and longitudinal relaxation data are reported for aqueous solution of 23 mole % ethanol. Measurement of shear impedance in the temperature range +20 to −40 °C and frequency range 8.6–740 MHz indicates a composite spectra of double or triple relaxation. Longitudinal data are measured by Brillouin scattering and pulse techniques in a frequency range from 20 MHz to 6 GHz. Complicated processes involved are interpreted in terms of additive contributions to longitudinal moduli, comprising (1) structural viscoelastic relaxation of the spectra employed in shear data; (2) a relaxation of concentration fluctuation with a modified form of Romanov and Solovyev.

Molecular dynamics of viscous liquids. A comparison of dielectric and Kerr-effect relaxation for tritolyl phosphate, ortho-terphenyl and their mixtures

Low frequency dielectric (10–2 to 105 Hz) and Kerr-effect (10–5 to 102 s) relaxation behaviour of pure liquid tritolylphosphate, super-cooled o-terphenyl and three tritolylphosphate +o-terphenyl mixtures have been examined. The Kerr-effect rise and decay transients for each of these systems at a given temperature, are characterized by the same relaxation time τK,r and τK,d respectively. For both pure liquids τK,r and τK,d are essentially the same as the dielectric relaxation time τD, and the dielectric loss curves and Kerr-effect transients are adequately described by the William–Watts empirical relaxation function. These results suggest that reorientational motions in highly viscous liquids do not occur by rotational diffusion, but that they are entirely consistent with a “fluctuation relaxation” mechanism, and they are discussed in terms of the Ivanov and Anderson models of rotational Brownian motion. For some o-terphenyl + tritolylphosphate mixtures τK,r=τK,d > τD and possible explanations of this result are considered.

Fluctuation, relaxation, and extensivity of macrovariables in nonequilibrium systems

The extensive property of a macrovariable is proved for a quantal system whose Hamiltonian depends on time and for a stochastic system whose temporal evolution operator depends on time. These generalized situations are concerned with bulk-contact open systems. The extensive property, fluctuation, and nonlinear relaxation are investigated explicitly by calculating rigorously generating functions in exactly soluble models such as the linear stochastic model and linearXY model. The relation between the nonlinear critical slowing down and linear critical slowing down is also discussed.

Consideration of dielectric relaxation and the Kerr-effect relaxation in relation to the reorientational motions of molecules

Relations between field-free orientational time-correlation functions and dielectric and Kerr-effect responses to step-on and step-off electric fields are considered. Whereas the dielectric and Kerr-effect decay transients are simply related to 〈P1(u, t)〉 and 〈P2(u, t)〉, where u= cos θ, the rise transients are not, in general, related to these quantities; assumptions and specific reorientation mechanisms are required in order to understand the rise transients. The dielectric and Kerr-effect relaxations are considered for the models of rotational diffusion and “fluctuation relaxation”. Experimental data for poly-n-butylisocyanate in solution and tritolyl phosphate are discussed in terms of the theory and mechanisms for motion.

Influence of discharge fluctuations on the spectral structure of intermodal laser beats at a frequencyc/2L

The results are reported of an experimental investigation of the structure of intermodal beats at a frequency c/2L due to two types of fluctuation (relaxation and losses) of the discharge current.

On the nature of spin-lattice relaxation in nematic MBBA

The measurements of the frequency dependence of the proton T 1 in nematic MBBA have been extended to 270 MHz, and the results have been compared with the predictions of the order fluctuation and self-diffusion relaxation theories. Both the frequency and the temperature dependences of T 1 are shown to be characteristic of a mechanism controlled by molecular self-diffusion.

Laser light scattering studies of poly(L‐lysine HBr) in aqueous solutions

AbstractA simple theory for the relaxation of concentration fluctuations in polyelectrolyte solutions is presented, and particular results for the high‐salt and no‐salt limiting cases are discussed.Autocorrelation functions for the fluctuating intensity of scattered light from dilute aqueous solutions of poly(L‐lysine HBr) (PLL‐HBr) with and without added salt have been observed over a wide range of pH. The observed autocorrelation functions are in general very satisfactorily represented by single exponentials except at high pH (>10.5), where considerable aggregation is manifested. Solutions of PLL HBr without added salt exhibit extraordinary behavior, evident at low pH, involving a species with a very slowly decaying autocorrelation function. Though this species is readily annealed to a more ordinary individual free‐molecule form by cycling the pH to 9.5 or higher and back, the resulting molecules are found to require unusually long times to reach internal configuration equilibrium under low pH conditions. Solutions of PLL‐HBr in 0.2M NaBr and 0.1M NaCl are apparently free of similar extraordinary effects and show the normal isothermal helix–coil transition accompanied by a 15–30% rise in the diffusion coefficient to a maximum at pH 10.5, which is interpreted in terms of a change in molecular dimension of an interrupted helix.The predicted K2 dependence of the reciprocal relaxation time and enhancement of the apparent diffusion coefficient of the polyelectrolyte in the absence of salt is confirmed.

The effect of electric charge on the diffusion of macromolecules

We have determined the time for the relaxation of concentration fluctuations in solutions of bovine serum albumin as a function of the protein charge and the ionic strength of the solution. The relaxation rates for fluctuations whose wavelengths were of the order of the wavelength of light were determined from the temporal correlations in the intensity of the light scattered from the fluctuations. The experimental results are compared with the theory of M. J. Stephen. While the theory provides a qualitative understanding of the results, the restrictions inherent in the Debye-Hückel approximation prevent a quantitative agreement between the theory and the experimental data.

Nonlinear coupling and relaxation of fluctuations and the central peak

A simple model Hamiltonian for a structural phase transition is discussed. It is shown that using the modecular field approximation one obtains a nonlinear coupling of the order parameter and entropy fluctuations. This results in a central peak in the order parameter fluctuation spectrum. The width of the central peak is proportional to the entropy relaxation rate.

Relaxation of fluctuations in the shape of a random-coil polymer chain

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