Hydrodynamic fluctuations

Forster D 1975 Hydrodynamic Fluctuations, Broken Symmetry, and Correlation Functions (New York Benjamin)... 

D. Forster, Hydrodynamic Fluctuations, Broken Symmetry and Correlation Functions, Benjamin, Reading, MA, 1975. 

The intensity of SHG for a poled (67 kV/cm) and crosslinked film of 22 in a longitudinal package is shown in Figure 8. The concave appearance of the signal across the gap is most likely caused by a field-induced modification of the film thickness, which can also be seen by optical microscopy. The thickness deviations appeared to be field-dependent and were absent in unpoled samples. The formation of this thickness gradient may be caused by flow as a consequence of hydrodynamic fluctuations stemming from ionic impurities. 

In a recent work [43], Martem Yanov and Grafov, envisaged also the effect of hydrodynamic fluctuations on the electrochemical current, proposing to call it a hydroelectrochemical impedance, with the same definitions as those given above (see Section 1.3). Their approach is basically the same as that described in Section 1.3 in that they consider the hydrodynamic and electrical perturbations from a unified position. More precisely, for the kinetic situation described in Section 4.2 they show that an equation such as Eq. (4-7), obtained in a simplified version (i.e. no convective diffusion and a qualitative analysis of the fluctuating flow field) can be written as... 

Forster D (1975) Hydrodynamic fluctuations, broken symmetries, and correlation functions. W.A. Benjamin, Massachusetts... 

Recently, Brillouin scattering has proved useful in this area for studying the frequency dependence of hypersonic (GHz zone) absorption and dispersion velocity in liquid sulphur dioxide [91] the effect of isotopes on hydrodynamic fluctuations in self-associated fluids [92] and the elastic properties of polyethylene glycol solutions in water, benzene and toluene [93]. 

C. Deslouis, O. Gil, and B. Tribollet, "Frequency Response of Electrochemical Sensors to Hydrodynamic Fluctuations," Journal of Fluid Mechanics, 215 (1990) 85-100. 

Keywords self-diffusion coefficient, thermal hydrodynamic fluctuations, dynamic viscosity, kinematic viscosity, Maxwellian relaxation time... 

In the general case, the thermal motion in liquids represents a combination of shifts of molecules with respect to their nearest surrounding and the collective drift in the field of thermal hydrodynamic fluctuations It is clear that an increase of the pressure is accompanied by the growth of the liquid density and, as a result, by essential increase of the relative role of the collective contriljution to the self-diffusion coefficient. Indeed, due to the geometric restrictions, the relative motion of molecules is reduced to oscillations in the cell formed by the nearest neighbors. At the same time, an increase in the density influences the vortical modes of the thermal motion of molecules to a much smaller extent (Fig. 1). Since the collective transport in liquid is related just to vortical (transversal) hydrodynamic modes " (see Fig. 2), one can conclude that the role of the collective drift in the self-diffusion increases as the pressure grows. 

Fox R F and Uhienbeck G E 1970 Contributions to non-equilibrium thermodynamics. I. Theory of hydrodynamical fluctuations Rhys. Fluids 13 1893... 

Hence this chapter is devoted to an investigation of hydrodynamic fluctuation theory. Much of what we use in this chapter is developed more formally in Chapter 11. In order to use hydrodynamic fluctuation theory it is necessary to discuss the derivation of the usual equations of fluid mechanics. Unfortunately this task would require the writing of a separate monograph. Space does not permit us to present a detailed account of the equations of fluid dynamics. We refer the reader to the excellent monograph on this subject by Landau and Lifshitz (1960), and will only highlight the important points here. 

Although originally designed for astrophysical problems [86], as shown in [120], SPH can also be used for modeling polymers in the macroscale. However, smoothed particle hydrodynamics does not include thermal fluctuations in the form of a random stress tensor and heat flux as in the Landau and Lifshitz theory of hydrodynamic fluctuations. Therefore, the validity of SPH to the study of complex fluids is problematic at scales where thermal fluctuations are important. 

In principle, generalized kinetic equations derived by microscopic analysis starting from (2.11) or suitable generalizations could be used to describe the evolution, including statistical and hydrodynamic fluctuations, of an arbitrary ufp aerosol system. However, such general treatment of an arbitrary aerosol system appears to be unlikely in the near future. 

Ortiz de Zarate, J.M., Sengers, J.V., 2006. Hydrodynamic Fluctuations in Fluids and Fluid Mixtures. Elsevier, Amsterdam. Shannon, C.E., Weaver, W., 1949. The Mathematical Theory of Conununication. University of Illinois Press. 

Koch, S.W., Desai, R.C., and Abraham, F.F. (1982) Spinodal decomposition of a one-component fluid a hydrodynamic fluctuation theory and comparison with computer simulation, Phys. Rev. A. 26, 1015. 

J. Swift and P. C. Hohenberg, Hydrodynamic fluctuations at the convective instability,... 

Deslouis C, Gil O, Tribollet B (1990) Frequency response of electrochemical sensors to hydrodynamic fluctuations. J Fluid Mech 215 85-100... 

J. M. Ortiz de Zarate and J. Sengers, Hydrodynamic Fluctuations in Fluid Mixtures, Elsevier, Amsterdam, 2006. 

V. M. Zaitsev and M. 1. Shliomis, Hydrodynamic fluctuations near the convection threshold, Soviet Phys. JETP, 32,866-870 (1971). 

A common problem in growth of solid solution crystals are striations, i.e. growth bands with varying concentrations. Striations are caused by temperature fluctuations, not by hydrodynamic fluctuations in a system of homogeneous temperature (Scheel and Swendsen [13], Scheel [14]). For the example of KTai Nb 03... 

On the other hand, in a pure liquid crystal system, liquid crystalline order, such as orientation order in nematic or layer order in smectic, is created under phase transition point, and the symmetry of the system is reduced. At the same time, new hydrodynamic fluctuation motions appear to be associated with new degrees of freedom. The modes of hydrodynamic fluctuations are characterized by a dispersion relation that can be obtained by solving the constitutive hydrodynamic equations of the system, giving the angular frequency wave number q of the fluctuations. It can be said that in a uniform alignment of the pure liquid crystal, the system universally satisfies the dispersion relation from the micrometer scale up to the length of the sample chamber, which means that the material keeps spatial homogeneity for the dynamics in pure system. 

Simulations of Gaussian chains, i.e, polymers with the bond potential (81), can be compared with analytical calculations based on the Zimm approach [6,107]. Note, however, that the simulations are not performed in the Zimm model. The Zimm approach relies on the preaveraging approximation of hydrodynamic interactions, whereas the simulations take into account the configurational dependence of the hydrodynamic interactions, and therefore hydrodynamic fluctuations. Hence, the comparison can serve as a test of the validity of the approximations employed in the Zimm approach. 

Comparing (75) with (44) we can read off the relations between the hydrodynamic fluctuations and the random noise. 

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