Gardner's deformations of the N=2 supersymmetric a=4-KdV equation

We prove that P.Mathieu's Open problem on constructing Gardner's deformation for the N=2 supersymmetric a=4-Korteweg-de Vries equation has no supersymmetry invariant solutions, whenever it is assumed that they retract to Gardner's deformation of the scalar KdV equation under the component reduction. At the same time, we propose a two-step scheme for the recursive production of the integrals of motion for the N=2, a=4-SKdV. First, we find a new Gardner's deformation of the Kaup-Boussinesq equation, which is contained in the bosonic limit of the super-hierarchy. This yields the recurrence relation between the Hamiltonians of the limit, whence we determine the bosonic super-Hamiltonians of the full N=2, a=4-SKdV hierarchy. Our method is applicable towards the solution of Gardner's deformation problems for other supersymmetric KdV-type systems.Comment: Extended version of the talks given by A.V.K. at 8th International conference `Symmetry in Nonlinear Mathematical Physics' (June 20-27, 2009, Kiev, Ukraine) and 9th International workshop `Supersymmetry and Quantum Symmetries' (July 29 - August 3, 2009, JINR, Dubna, Russia); 22 page

Modelling of epitaxial film growth with a Ehrlich-Schwoebel barrier dependent on the step height

The formation of mounded surfaces in epitaxial growth is attributed to the presence of barriers against interlayer diffusion in the terrace edges, known as Ehrlich-Schwoebel (ES) barriers. We investigate a model for epitaxial growth using a ES barrier explicitly dependent on the step height. Our model has an intrinsic topological step barrier even in the absence of an explicit ES barrier. We show that mounded morphologies can be obtained even for a small barrier while a self-affine growth, consistent with the Villain-Lai-Das Sarma equation, is observed in absence of an explicit step barrier. The mounded surfaces are described by a super-roughness dynamical scaling characterized by locally smooth (faceted) surfaces and a global roughness exponent $\alpha>1$. The thin film limit is featured by surfaces with self-assembled three-dimensional structures having an aspect ratio (height/width) that may increase or decrease with temperature depending on the strength of step barrier.Comment: To appear in J. Phys. Cond. Matter; 3 movies as supplementary materia

Hydraulische invloed van structurele ingrepen tegen de verzanding van het Zwin

The specific fauna and flora of the natural reserve "Het Zwin" are generated by the seawater that streams in and out of the channels of the reserve at each tide. This water transports sand and mud, that are deposited in the channels and on the inundated surfaces. This way the chanels and saltmarshes are silting up gradually.The international Belgian-Dutch Commission of the Zwin has decided to stop the silting up and to maintain the Zwin as a salty tidal area.In 1987 a technical committee was established to deliberate on the mesures that had to be taken. In 1989 the main channel was deepened and a sandtrap introduced.This article represents mainly the calculations on mathematical model by Flanders Hydraulics to estimate the influence of different proposed solutions.Alternative managements are examined concerning their effect on the ecological values, the landscape and the recreational values of the Zwin.The international Commission of the Zwin has approuved a project in phases, where alternatives are combined to maintain and fortify the natural values of the Zwin

Dielectronic recombination data for dynamic finite-density plasmas VII. The neon isoelectronic sequence

Dielectronic recombination (DR) and radiative recombination (RR) data for neon-like ions forming sodium-like systems has been calculated as part of the assembly of a DR database necessary for modelling of dynamic and/or finite-density plasmas (Badnell et al. 2003). Dielectronic recombination coefficients for neon-like ions from Na+ to Zn20+, as well as Kr26+, Mo32+, Cd38+, and Xe44+, are presented and the results discussed

Dielectronic recombination data for dynamic finite-density plasmas II. The oxygen isoelectronic sequence

Dielectronic recombination (DR) and radiative recombination (RR) data for oxygen-like ions forming fluorine-like ions have been calculated as part of the assembly of a level-resolved DR and RR database necessary for modelling of dynamic finite-density plasmas (Badnell et al. 2003). Total DR and RR rate coefficients for F+ to Zn22+ are presented and the results discussed. By comparison between perturbative and R-matrix results, we find that RR/DR interference effects are negligible even for the lowest-charged F+ member. We also find that the 2→2 low-temperature DR (no change in the principal quantum number of the core electrons) does not scale smoothly with nuclear charge Z due to resonances straddling the ionization limit, thereby making explicit calculations for each ion necessary. These RR and DR data are suitable for modelling of solar and cosmic plasmas under conditions of collisional ionization equilibrium, photoionization equilibrium, and non-equilibrium ionization

Life at high Deborah number

In many biological systems, microorganisms swim through complex polymeric fluids, and usually deform the medium at a rate faster than the inverse fluid relaxation time. We address the basic properties of such life at high Deborah number analytically by considering the small-amplitude swimming of a body in an arbitrary complex fluid. Using asymptotic analysis and differential geometry, we show that for a given swimming gait, the time-averaged leading-order swimming kinematics of the body can be expressed as an integral equation on the solution to a series of simpler Newtonian problems. We then use our results to demonstrate that Purcell's scallop theorem, which states that time-reversible body motion cannot be used for locomotion in a Newtonian fluid, breaks down in polymeric fluid environments