Computer simulations of the interactions of the (012) and (001) surfaces of jarosite with Al, Cd, Cu2+ and Zn

Jarosite is an important mineral on Earth, and possibly on Mars, where it controls the mobility of iron, sulfate and potentially toxic metals. Atomistic simulations have been used to study the incorporation of Al3+, and the M2+ impurities Cd, Cu and Zn, in the (0 1 2) and (0 0 1) surfaces of jarosite. The calculations show that the incorporation of Al on an Fe site is favorable on all surfaces in which terminal Fe ions are exposed, and especially on the (0 0 1) [Fe3(OH)3]6+ surface. Incorporation of Cd, Cu or Zn on a K site balanced by a K vacancy is predicted to stabilize the surfaces, but calculated endothermic solution energies and the high degree of distortion of the surfaces following incorporation suggest that these substitutions will be limited. The calculations also suggest that incorporation of Cd, Cu and Zn on an Fe site balanced by an OH vacancy, or by coupled substitution on both K and Fe sites, is unfavorable, although this might be compensated for by growth of a new layer of jarosite or goethite, as predicted for bulk jarosite. The results of the simulations show that surface structure will exert an influence on uptake of impurities in the order Cu > Cd > Zn, with the most favorable surfaces for incorporation being (0 1 2) [KFe(OH)4]0 and (0 0 1) [Fe3(OH)3]6+

Long-Time Asymptotics for the Camassa-Holm Equation

We apply the method of nonlinear steepest descent to compute the long-time asymptotics of the Camassa-Holm equation for decaying initial data, completing previous results by A. Boutet de Monvel and D. Shepelsky.Comment: 30 page

Hot Nucleons in Chiral Soliton Models

Chiral lagrangians as effective field theories of QCD are most suitable for the study of nucleons in a hot pion gas because they contain pions and also baryons as solitons of the same action. The semiclassical treatment of the soliton solutions must be augmented by pionic fluctuations which requires renormalisation to 1-loop, and finite temperatures do not introduce new ultraviolet divergencies and may easily be considered. Alternatively, a renormalisation scheme based on the renormalisation group equation at finite temperature comprises and extends the rigorous results of chiral perturbation theory and renders the low energy constants temperature-dependent which allows the construction of temperature-dependent solitons below the critical temperature. The temperature-dependence of the baryon energy and the pion-nucleon coupling is studied. There is no simple scaling law for the temperature-dependence of these quantities.Comment: 17 pages (RevTeX), 5 figure