Dynamics of a Polymer in the Presence of Permeable Membranes

We study the diffusion of a linear polymer in the presence of permeable membranes without excluded volume interactions, using scaling theory and Monte Carlo simulations. We find that the average time it takes for a chain with polymerization index~$N$ to cross a single isolated membrane varies with~$N$ as~% $N^{5/2}$, giving its permeability proportional to~$N^2$. When the membranes are stacked with uniform spacing~$d$ in the unit of the monomer size, the dynamics of a polymer is shown to have three different regimes. In the limit of small~\mbox{$d \ll N^{1/2}$}, the chain diffuses through reptation and \mbox{$D\sim N^{-2}$}. When $d$ is comparable to~$N^{1/2}$ the diffusion coefficients parallel and perpendicular to the membranes become different from each other. While the diffusion becomes Rouse-like, i.e.~\mbox{$D\sim N^{-1}$}, in the parallel direction, the motion in the perpendicular direction is still hindered by the two-dimensional networks. The diffusion eventually becomes isotropic and Rouse-like for large~\mbox{$d \gg N$}.Comment: 20 pages including figures, LaTeX v2.09 and psfig v1.

Quasilinear approach of the cumulative whistler instability in fast solar winds: Constraints of electron temperature anisotropy

Context. Solar outflows are a considerable source of free energy which accumulates in multiple forms like beaming (or drifting) components and/or temperature anisotropies. However, kinetic anisotropies of plasma particles do not grow indefinitely and particle-particle collisions are not efficient enough to explain the observed limits of these anisotropies. Instead, the self-generated wave instabilities can efficiently act to constrain kinetic anisotropies, but the existing approaches are simplified and do not provide satisfactory explanations. Thus, small deviations from isotropy shown by the electron temperature ($T$) in fast solar winds are not explained yet. Aims. This paper provides an advanced quasilinear description of the whistler instability driven by the anisotropic electrons in conditions typical for the fast solar winds. The enhanced whistler-like fluctuations may constrain the upper limits of temperature anisotropy $A \equiv T_\perp /T_\parallel > 1$, where $\perp, \parallel$ are defined with respect to the magnetic field direction. Methods. Studied are the self-generated whistler instabilities, cumulatively driven by the temperature anisotropy and the relative (counter)drift of the electron populations, e.g., core and halo electrons. Recent studies have shown that quasi-stable states are not bounded by the linear instability thresholds but an extended quasilinear approach is necessary to describe them in this case. Results. Marginal conditions of stability are obtained from a quasilinear theory of the cumulative whistler instability, and approach the quasi-stable states of electron populations reported by the observations.The instability saturation is determined by the relaxation of both the temperature anisotropy and the relative drift of electron populations.Comment: Accepted for publication in A&