New periodic orbits and basins for families of resonant normal forms

A special class of periodic orbits of parameter dependent families of truncated resonant normal forms is constructed. Their existence is shown for arbitrarily large periods. Explicit analytical criteria are derived for constructing the complete basin of attraction of an invariant circle for normal forms for which the eigenvalue of the linearized mapping is not a multiple root of unity. Persistence of these basins is shown for small perturbations of the parameters. Hence, the existence of bounded orbits for all times established, generically

A new finite difference scheme adapted to the one-dimensional Schrodinger equation

We present a new discretisation scheme for the Schrödinger equation based on analytic solutions to local linearisations. The scheme generates the normalised eigenfunctions and eigenvalues simultaneously and is exact for piecewise constant potentials and effective masses. Highly accurate results can be obtained with a small number of mesh points and a robust and flexible algorithm using continuation techniques is derived. An application to the Hartree approximation for SiGe heterojunctions is discussed in which we solve the coupled Schrödinger-Poisson model problem selfconsistently

Turbulente menging

Het mengen van onderling niet-oplosbare vloeistoffen geeft aanlei- ding tot complexe stromingsverschijnselen. Hiervan bestaan tal van voorbeelden uit de chemische, farmaceutische en cosmetische in- dustrie. Maar ook in diverse biologische processen of, dichter bij huis, tijdens voedselbereiding in de keuken is een goede menging vaak essentieel. Menging in een turbulente stroming verloopt aanzienlijk sneller dan zogenaamde ‘laminaire’ menging en staat mede hierdoor sterk in de belangstelling. Bernard Geurts, hoogleraar Dynamics of Complex Fluids aan de Faculteit der Toegepaste Wiskunde van de Universiteit Twente, beschrijft hoe dergelijke processen gesimuleerd en gemodelleerd kunnen worden. In het bijzonder gaat hij in op de vraag hoe de primaire dynamische verschijnselen kunnen worden behouden bij een meer globale en daarmee minder rekenintensieve aanpak

Complexes of block copolymers in solution: a graph-theoretical approach

We determine the statistical properties of block copolymers in solution. These complexes are assumed to have the topological structure of connected graphs with “nonnested” loops and cycles. The generating function method is used to determine the number of topologically different complexes containing a given number of block copolymers. It is shown that at sufficiently high concentration the system undergoes a transition to a gel phase. Furthermore, the average number of polymers per complex is calculated. Finally, the relative increase in viscosity is found under the assumption that the complexes can be treated as porous spheres