A variational approach to necklaces formation in polyelectrolytes

By means of a variational approach we study the conditions under which a polyelectrolyte in a bad solvent will undergo a transition from a rod-like structure to a ``necklace'' structure in which the chain collapses into a series of globules joined by stretched chain segments.Comment: 6 pages, 4 figures (unfortunately big). Requires revtex, eps

Sparse inversion of Stokes profiles. I. Two-dimensional Milne-Eddington inversions

Inversion codes are numerical tools used for the inference of physical properties from the observations. Despite their success, the quality of current spectropolarimetric observations and those expected in the near future presents a challenge to current inversion codes. The pixel-by-pixel strategy of inverting spectropolarimetric data that we currently utilize needs to be surpassed and improved. The inverted physical parameters have to take into account the spatial correlation that is present in the data and that contains valuable physical information. We utilize the concept of sparsity or compressibility to develop an new generation of inversion codes for the Stokes parameters. The inversion code uses numerical optimization techniques based on the idea of proximal algorithms to impose sparsity. In so doing, we allow for the first time to exploit the presence of spatial correlation on the maps of physical parameters. Sparsity also regularizes the solution by reducing the number of unknowns. We compare the results of the new inversion code with pixel-by-pixel inversions, demonstrating the increase in robustness of the solution. We also show how the method can easily compensate for the effect of the telescope point spread function, producing solutions with an enhanced contrast.Comment: 13 pages, 8 figures, accepted for publication in A&

Collapse of Flexible Polyelectrolytes in Multivalent Salt Solutions

The collapse of flexible polyelectrolytes in a solution of multivalent counterions is studied by means of a two state model. The states correspond to rod-like and spherically collapsed conformations respectively. We focus on the very dilute monomer concentration regime where the collapse transition is found to occur when the charge of the multivalent salt is comparable (but smaller) to that of the monomers. The main contribution to the free energy of the collapsed conformation is linear in the number of monomers $N$, since the internal state of the collapsed polymer approaches that of an amorphous ionic solid. The free energy of the rod-like state grows as $N\ln N$, due to the electrostatic energy associated with that shape. We show that practically all multivalent counterions added to the system are condensed into the polymer chain, even before the collapse.Comment: LaTeX-revtex, psfig file, 4 figure