Complexity and growth for polygonal billiards

We establish a relationship between the word complexity and the number of generalized diagonals for a polygonal billiard. We conclude that in the rational case the complexity function has cubic upper and lower bounds. In the tiling case the complexity has cubic asymptotic growth.Comment: 12 pages, 4 figure

The SLIM (Social learning for the integrated management and sustainable use of water at catchment scale) Final Report

Background: SLIM stands for 'Socuak Learning for the Integrated Management and Sustainable Use of Water at Catchment Scale'. It is a multi-country research project funded by the European Commission (DG RESEARCH - 5th Framework Programme for research and technological development, 1998-2002). Its main theme is the investigation of the socio-economic aspects of the sustainable use of water. Within this theme, its main focus of interest lies in understanding the application of social learning as a conceptual framework, an operational principle, a policy instrument and a process of systemic change

Formation of Giant Planets by Concurrent Accretion of Solids and Gas inside an Anti-Cyclonic Vortex

We study the formation of a giant gas planet by the core--accretion gas--capture process, with numerical simulations, under the assumption that the planetary core forms in the center of an anti-cyclonic vortex. The presence of the vortex concentrates particles of centimeter to meter size from the surrounding disk, and speeds up the core formation process. Assuming that a planet of Jupiter mass is forming at 5 AU from the star, the vortex enhancement results in considerably shorter formation times than are found in standard core--accretion gas--capture simulations. Also, formation of a gas giant is possible in a disk with mass comparable to that of the minimum mass solar nebula.Comment: 27 pages, 4 figures, ApJ in pres

Influence of band structure effects on domain-wall resistance in diluted ferromagnetic semiconductors

Intrinsic domain-wall resistance (DWR) in (Ga,Mn)As is studied theoretically and compared to experimental results. The recently developed model of spin transport in diluted ferromagnetic semiconductors [Van Dorpe et al., Phys. Rev. B 72, 205322 (2005)] is employed. The model combines the disorder-free Landauer-B\"uttiker formalism with the tight-binding description of the host band structure. The obtained results show how much the spherical 4x4 kp model [Nguyen, Shchelushkin, and Brataas, cond-mat/0601436] overestimates DWR in the adiabatic limit, and reveal the dependence of DWR on the magnetization profile and crystallographic orientation of the wall.Comment: 4 pages, 4 figures, submitted to Phys. Rev. B - Rapid Com

Surface Roughness Dominated Pinning Mechanism of Magnetic Vortices in Soft Ferromagnetic Films

Although pinning of domain walls in ferromagnets is ubiquitous, the absence of an appropriate characterization tool has limited the ability to correlate the physical and magnetic microstructures of ferromagnetic films with specific pinning mechanisms. Here, we show that the pinning of a magnetic vortex, the simplest possible domain structure in soft ferromagnets, is strongly correlated with surface roughness, and we make a quantitative comparison of the pinning energy and spatial range in films of various thickness. The results demonstrate that thickness fluctuations on the lateral length scale of the vortex core diameter, i.e. an effective roughness at a specific length scale, provides the dominant pinning mechanism. We argue that this mechanism will be important in virtually any soft ferromagnetic film.Comment: 4 figure

Rational invariants of even ternary forms under the orthogonal group

In this article we determine a generating set of rational invariants of minimal cardinality for the action of the orthogonal group $\mathrm{O}_3$ on the space $\mathbb{R}[x,y,z]_{2d}$ of ternary forms of even degree $2d$. The construction relies on two key ingredients: On one hand, the Slice Lemma allows us to reduce the problem to dermining the invariants for the action on a subspace of the finite subgroup $\mathrm{B}_3$ of signed permutations. On the other hand, our construction relies in a fundamental way on specific bases of harmonic polynomials. These bases provide maps with prescribed $\mathrm{B}_3$-equivariance properties. Our explicit construction of these bases should be relevant well beyond the scope of this paper. The expression of the $\mathrm{B}_3$-invariants can then be given in a compact form as the composition of two equivariant maps. Instead of providing (cumbersome) explicit expressions for the $\mathrm{O}_3$-invariants, we provide efficient algorithms for their evaluation and rewriting. We also use the constructed $\mathrm{B}_3$-invariants to determine the $\mathrm{O}_3$-orbit locus and provide an algorithm for the inverse problem of finding an element in $\mathbb{R}[x,y,z]_{2d}$ with prescribed values for its invariants. These are the computational issues relevant in brain imaging.Comment: v3 Changes: Reworked presentation of Neuroimaging application, refinement of Definition 3.1. To appear in "Foundations of Computational Mathematics

Scaling relations for magnetic nanoparticles

A detailed investigation of the scaling relations recently proposed by [J. d'Albuquerque e Castro, D. Altbir, J. C. Retamal, and P. Vargas, Phys. Rev. Lett. 88, 237202 (2002)] to study the magnetic properties of nanoparticles is presented. Analytical expressions for the total energy of three characteristic internal configurations of the particles are obtained, in terms of which the behavior of the magnetic phase diagram for those particles upon scaling of the exchange interaction is discussed. The exponent $\eta$ in scaling relations is shown to be dependent on the geometry of the vortex core, and results for specific cases are presented.Comment: 6 pages, 4 figure

Angular-dependence of magnetization switching for a multi-domain dot: experiment and simulation

We have measured the in-plane angular variation of nucleation and annihilation fields of a multi-domain magnetic single dot with a microsquid. The dots are Fe/Mo(110) self-assembled in UHV, with sub-micron size and a hexagonal shape. The angular variations were quantitatively reproduced by micromagnetic simulations. Discontinuities in the variations are observed, and shown to result from bifurcations related to the interplay of the non-uniform magnetization state with the shape of the dot.Comment: 4 pages, 4 figures, for submission as a regular articl

Dynamics of magnetic domain wall motion after nucleation: Dependence on the wall energy

The dynamics of magnetic domain wall motion in the FeNi layer of a FeNi/Al2O3/Co trilayer has been investigated by a combination of x-ray magnetic circular dichroism, photoelectron emission microscopy, and a stroboscopic pump-probe technique. The nucleation of domains and subsequent expansion by domain wall motion in the FeNi layer during nanosecond-long magnetic field pulses was observed in the viscous regime up to the Walker limit field. We attribute an observed delay of domain expansion to the influence of the domain wall energy that acts against the domain expansion and that plays an important role when domains are small.Comment: Accepted for publication in Physical Review Letter

Forbidden oxygen lines at various nucleocentric distances in comets

To study the formation of the [OI] lines - i.e., 5577 A (the green line), 6300 A and 6364 A (the two red lines) - in the coma of comets and to determine the parent species of the oxygen atoms using the green to red-doublet emission intensity ratio (G/R ratio) and the lines velocity widths. We acquired at the ESO VLT high-resolution spectroscopic observations of comets C/2002 T7 (LINEAR), 73P-C/Schwassmann-Wachmann 3, 8P/Tuttle, and, 103P/Hartley 2 when they were close to the Earth (< 0.6 au). Using the observed spectra, we determined the intensities and the widths of the three [OI] lines. We have spatially extracted the spectra in order to achieve the best possible resolution of about 1-2", i.e., nucleocentric projected distances of 100 to 400 km depending on the geocentric distance of the comet. We have decontaminated the [OI] green line from C2 lines blends. It is found that the observed G/R ratio on all four comets varies as a function of nucleocentric projected distance. This is mainly due to the collisional quenching of O(1S) and O(1D) by water molecules in the inner coma. The observed green emission line width is about 2.5 km/s and decreases as the distance from the nucleus increases which can be explained by the varying contribution of CO2 to the O(1S) production in the innermost coma. The photodissociation of CO2 molecules seems to produce O(1S) closer to the nucleus while the water molecule forms all the O(1S) and O(1D) atoms beyond 1000 km. Thus we conclude that the main parent species producing O(1S) and O(1D) in the inner coma is not always the same. The observations have been interpreted in the framework of the coupled-chemistry-emission model of Bhardwaj & Raghuram (2012) and the upper limits of CO2 relative abundances are derived from the observed G/R ratios. Measuring the [OI] lines could indeed provide a new way to determine the CO2 relative abundance in comets.Comment: accepted for publication in A&A, the abstract is shortene