Research Outputs

Permanent URI for this communityhttps://hdl.handle.net/20.500.14288/2

Browse

Filters

2010 - 20132

Advanced Search

Filter by

Settings

Sponsors: search.filters.sponsors.EUSubject: search.filters.subject.Mathematical physics

Search Results

Now showing 1 - 2 of 2
  • Thumbnail Image
    PublicationOpen Access
    Equilibrium polyelectrolyte bundles with different multivalent counterion concentrations
    (American Physical Society (APS), 2010) Holm, Christian; Department of Mechanical Engineering; Sayar, Mehmet; Faculty Member; Department of Mechanical Engineering; College of Engineering; 109820
    We present the results of molecular-dynamics simulations on the salt concentration dependence of the formation of polyelectrolyte bundles in thermodynamic equilibrium. Extending our results on salt-free systems we investigate here deficiency or excess of trivalent counterions in solution. Our results reveal that the trivalent counterion concentration significantly alters the bundle size and size distribution. The onset of bundle formation takes place at earlier Bjerrum length values with increasing trivalent counterion concentration. For the cases of 80%, 95%, and 100% charge compensation via trivalent counterions, the net charge of the bundles decreases with increasing size. We suggest that competition among two different mechanisms, counterion condensation and merger of bundles, leads to a nonmonotonic change in line-charge density with increasing Bjerrum length. The investigated case of having an abundance of trivalent counterions by 200% prohibits such a behavior. In this case, we find that the difference in effective line-charge density of different size bundles diminishes. In fact, the system displays an isoelectric point, where all bundles become charge neutral.
  • Thumbnail Image
    PublicationOpen Access
    Global solvability and blow up for the convective Cahn-Hilliard equations with concave potentials
    (American Institute of Physics (AIP) Publishing, 2013) Eden, A.; Zelik, S. V.; Department of Mathematics; Kalantarov, Varga; Faculty Member; Department of Mathematics; college of sciences; 117655
    We study initial boundary value problems for the unstable convective Cahn-Hilliard (CH) equation, i.e., the Cahn Hilliard equation whose energy integral is not bounded below. It is well-known that without the convective term, the solutions of the unstable CH equation ?t u + ? 4xu + ?2x(|u|pu) = 0 may blow up in ?nite time for anyp > 0. In contrast to that, we show that the presence of the convective term u?xuin the Cahn-Hilliard equation prevents blow up at least for 0 < p <49. We alsoshow that the blowing up solutions still exist if p is large enough (p ? 2). The related equations like Kolmogorov-Sivashinsky-Spiegel equation, sixth order convective Cahn-Hilliard equation, are also considered.