Registry No. (C18) (maleic anhydride) (alternating copolymer, lithium salt), 113109-85-6; (C16)(maleic anhydride) (alternating copolymer, lithium salt), 115678-69-8; (C14)(maleic anhydride) (alternating copolymer, lithium salt), 115678-71-2; (C12)(maleic anhydride) (alternating copolymer, lithium salt), 115678-73-4; (C10)(maleic anhydride) (alternating copolymer, lithium salt), 115792-89-7; (C8) (maleic anhydride) (alternating copolymer, lithium salt), 115678-74-5.

A microscopic statistical theory of a symmetrical polyelectrolyte complex (PEC) is developed. PEC is shown to form a polymer globule. The equilibrium density of PEC, the width of a PEC surface layer, and the surface tension of PEC are calculated as a function of salt concentration. Description of PEC as a polymer globule enables us to simplify theoretical treatment of the phenomenon of phase separation in polyelectrolyte solutions (complex coacervation). Numerous experimental facts concerning complex coacervation are easily explained within this approach. Complex coacervation is considered as precipitation of polymer globules owing to minimization of surface energy. The theory is based on the Lifshitz-Grosberg theory of polymer globules and our previous work concerning the equation of state of polyelectrolyte solutions. It is limited to the case of polyions with the low linear density of charge, which is most clear from the theoretical point of view and is also of practical and, in particular, of biological interest.

Statistical properties of the subgrid-scale stress tensor, the local energy flux and filtered velocity gradients are analysed in numerical simulations of forced three-dimensional homogeneous turbulence. High Reynolds numbers are achieved by using hyperviscous dissipation. It is found that in the inertial range the subgrid-scale stress tensor and the local energy flux allow simple parametrization based on a tensor eddy viscosity. This parametrization underlines the role that negative skewness of filtered velocity gradients plays in the local energy transfer. It is found that the local energy flux only weakly correlates with the locally averaged energy dissipation rate. This fact reflects basic difficulties of large-eddy simulations of turbulence, namely the possibility of predicting the locally averaged energy dissipation rate through inertial-range quantities such as the local energy flux is limited. Statistical properties of subgrid-scale velocity gradients are systematically studied in an attempt to reveal the mechanism of local energy transfer.

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High-resolution numerical simulations (with up to 2515~ modes) are performed for three-dimensional flow driven by the large-scale constant force f y = F cos(x) in a periodic box of size L = 2n (Kolmogorov flow). High Reynolds number is attained by solving the Navier-Stokes equations with hyperviscosity (-l)h+lk' ( h = 8). It is shown that the mean velocity profile of Kolmogorov flow is nearly independent of Reynolds number and has the 'laminar' form Y, = Vcos(x) with a nearly constant eddy viscosity. Nevertheless, the flow is highly turbulent and intermittent even at large scales. The turbulent intensities, energy dissipation rate and various terms in the energy balance equation have the simple coordinate dependence a + b cos(2x) (with a,b constants). This makes Kolmogorov flow a good model to explore the applicability of turbulence transport approximations in open time-dependent flows. It turns out that the standard expression for egective (eddy) viscosity used in K-8 transport models overpredicts the effective viscosity in regions of high shear rate and should be modified to account for the non-equilibrium character of the flow. Also at large scales the flow is anisotropic but for large Reynolds number the flow is isotropic at small scales. The important problem of local isotropy is systematically studied by measuring longitudinal and transverse components of the energy spectra and crosscorrelation spectra of velocities and velocity-pressure-gradient spectra. Cross-spectra which should vanish in the case of isotropic turbulence decay only algebraically but somewhat faster than corresponding isotropic correlations. It is verified that the pressure plays a crucial role in making the flow locally isotropic. It is demonstrated that anisotropic large-scale flow may be considered locally isotropic at scales which are approximately ten times smaller than the scale of the flow.