16 research outputs found
Polyelectrolytes in the presence of multivalent ions: gelation versus segregation
We analyze solutions of strongly charged chains bridged by linkers such as
multivalent ions. The gelation induced by the strong short range electrostatic
attractions is dramatically suppressed by the long range electrostatic
correlations due to the charge along the uncrosslinked monomers and ions. A
modified Debye-Huckel approach of crosslinked clusters of charged chains is
used to determined the mean field gelation transition self-consistently. Highly
dilute polyelectrolyte solutions tend to segregate macroscopically. Semidilute
solutions can form gels if the Bjerrum length and the distance between
neighboring charged monomers along the chain are both greater than the ion
size
Differential model for 2D turbulence
We present a phenomenological model for 2D turbulence in which the energy spectrum obeys a nonlinear fourth-order differential equation. This equation respects the scaling properties of the original Navier-Stokes equations, and it has both the -5/3 inverse-cascade and the -3 direct-cascade spectra. In addition, our model has Raleigh-Jeans thermodynamic distributions as exact steady state solutions. We use the model to derive a relation between the direct-cascade and the inverse-cascade Kolmogorov constants, which is in good qualitative agreement with the laboratory and numerical experiments. We discuss a steady state solution where both the enstrophy and the energy cascades are present simultaneously, and we discuss it in the context of the Nastrom-Gage spectrum observed in atmospheric turbulence. We also consider the effect of the bottom friction on the cascade solutions and show that it leads to an additional decrease and finite-wavenumber cutoffs of the respective cascade spectra, which agrees with the existing experimental and numerical results