Homotopy Method for the Large, Sparse, Real Nonsymmetric Eigenvalue Problem

A homotopy method to compute the eigenpairs, i.e., the eigenvectors and eigenvalues, of a given real matrix A1 is presented. From the eigenpairs of some real matrix A0, the eigenpairs of A(t) ≡ (1 − t)A0 + tA1 are followed at successive "times" from t = 0 to t = 1 using continuation. At t = 1, the eigenpairs of the desired matrix A1 are found. The following phenomena are present when following the eigenpairs of a general nonsymmetric matrix: • bifurcation, • ill conditioning due to nonorthogonal eigenvectors, • jumping of eigenpaths. These can present considerable computational difficulties. Since each eigenpair can be followed independently, this algorithm is ideal for concurrent computers. The homotopy method has the potential to compete with other algorithms for computing a few eigenvalues of large, sparse matrices. It may be a useful tool for determining the stability of a solution of a PDE. Some numerical results will be presented

Structure formation in electromagnetically driven granular media

We report structure formation in submonolayers of magnetic microparticles subjected to periodic electrostatic and magnetic excitations. Depending on the excitation parameters, we observe the formation of a rich variety of structures: clusters, rings, chains, and networks. The growth dynamics and shapes of the structures are strongly dependent on the amplitude and frequency of the external magnetic field. We find that for pure ac magnetic driving at low densities of particles, the low-frequency magnetic excitation favors clusters while high frequency excitation favors chains and net-like structures. An abrupt phase transition from chains to a network phase was observed for a high density of particles.Comment: 4 pages, 5 figure

Abrupt Transition from a Free, Repulsive to a Condensed, Attractive DNA Phase, Induced by Multivalent Polyamine Cations

We have investigated the energetics of DNA condensation by multivalent polyamine cations. Solution small angle x-ray scattering was used to monitor interactions between short 25 base pair dsDNA strands in the free supernatant DNA phase that coexists with the condensed DNA phase. Interestingly, when tetravalent spermine is used, significant inter-DNA repulsion is observed in the free phase, in contrast with the presumed inter-DNA attraction in the coexisting condensed phase. DNA condensation thus appears to be a discrete, first-order-like, transition from a repulsive gaseous to an attractive condensed solid phase, in accord with the reported all-or-none condensation of giant DNA. We further quantify the electrostatic repulsive potentials in the free DNA phase and estimate the number of additional spermine cations that bind to DNA upon condensation

Morphology of the red rectangle proto-planetary nebula

Poster no. 94Using the 3D morpho-kinematic modeling software SHAPE, we have created a model of the Red Rectangle that naturally reproduces many exotic morphological features including the notorious "ladder rungs". © 2012 International Astronomical Union.published_or_final_versionThe IAU Symposium No. 283: 'Planetary Nebulae: an Eye to the Future', Puerto de la Cruz, Tenerife, Spain, 25-29 July 2011. In International Astronomical Union Proceedings, 2012, v. 7 n. S283, p. 410-41

Post Asymptotic Giant Branch Bipolar Reflection Nebulae: Result of Dynamical Ejection or Selective Illumination?

published_or_final_versio

Fate of the Peak Effect in a Type-II Superconductor: Multicriticality in the Bragg-Glass Transition

We have used small-angle-neutron-scattering (SANS) and ac magnetic susceptibility to investigate the global magnetic field H vs temperature T phase diagram of a single crystal Nb in which a first-order transition of Bragg-glass melting (disordering), a peak effect, and surface superconductivity are all observable. It was found that the disappearance of the peak effect is directly related to a multicritical behavior in the Bragg-glass transition. Four characteristic phase boundary lines have been identified on the H-T plane: a first-order line at high fields, a mean-field-like continuous transition line at low fields, and two continuous transition line associated with the onset of surface and bulk superconductivity. All four lines are found to meet at a multicritical point.Comment: 4 figure

Measuring Inter-DNA Potentials in Solution

Interactions between short strands of DNA can be tuned from repulsive to attractive by varying solution conditions and have been quantified using small angle x-ray scattering techniques. The effective DNA interaction charge was extracted by fitting the scattering profiles with the generalized one-component method and inter-DNA Yukawa pair potentials. A significant charge is measured at low to moderate monovalent counterion concentrations, resulting in strong inter-DNA repulsion. The charge and repulsion diminish rapidly upon the addition of divalent counterions. An intriguing short range attraction is observed at surprisingly low divalent cation concentrations, ~16 mM Mg2+. Quantitative measurements of inter- DNA potentials are essential for improving models of fundamental interactions in biological systems

Inter-DNA Attraction Mediated by Divalent Counterions

Can nonspecifically bound divalent counterions induce attraction between DNA strands? Here, we present experimental evidence demonstrating attraction between short DNA strands mediated by Mg2 ions. Solution small angle x-ray scattering data collected as a function of DNA concentration enable model independent extraction of the second virial coefficient. As the [Mg2] increases, this coefficient turns from positive to negative reflecting the transition from repulsive to attractive inter-DNA interaction. This surprising observation is corroborated by independent light scattering experiments. The dependence of the observed attraction on experimental parameters including DNA length provides valuable clues to its origin