The identification of continuous, spatiotemporal systems

We present a method for the identification of continuous, spatiotemporal dynamics from experimental data. We use a model in the form of a partial differential equation and formulate an optimization problem for its estimation from data. The solution is found as a multivariate nonlinear regression problem using the ACE-algorithm. The procedure is successfully applied to data, obtained by simulation of the Swift-Hohenberg equation. There are no restrictions on the dimensionality of the investigated system, allowing for the analysis of high-dimensional chaotic as well as transient dynamics. The demands on the experimental data are discussed as well as the sensitivity of the method towards noise

Parametric, nonparametric and parametric modelling of a chaotic circuit time series

The determination of a differential equation underlying a measured time series is a frequently arising task in nonlinear time series analysis. In the validation of a proposed model one often faces the dilemma that it is hard to decide whether possible discrepancies between the time series and model output are caused by an inappropriate model or by bad estimates of parameters in a correct type of model, or both. We propose a combination of parametric modelling based on Bock's multiple shooting algorithm and nonparametric modelling based on optimal transformations as a strategy to test proposed models and if rejected suggest and test new ones. We exemplify this strategy on an experimental time series from a chaotic circuit where we obtain an extremely accurate reconstruction of the observed attractor.Comment: 19 pages, 8 Fig

Probing the evolving massive star population in Orion with kinematic and radioactive tracers

We assemble a census of the most massive stars in Orion, then use stellar isochrones to estimate their masses and ages, and use these results to establish the stellar content of Orion's individual OB associations. From this, our new population synthesis code is utilized to derive the history of the emission of UV radiation and kinetic energy of the material ejected by the massive stars, and also follow the ejection of the long-lived radioactive isotopes 26Al and 60Fe. In order to estimate the precision of our method, we compare and contrast three distinct representations of the massive stars. We compare the expected outputs with observations of 26Al gamma-ray signal and the extent of the Eridanus cavity. We find an integrated kinetic energy emitted by the massive stars of 1.8(+1.5-0.4)times 10^52 erg. This number is consistent with the energy thought to be required to create the Eridanus superbubble. We also find good agreement between our model and the observed 26Al signal, estimating a mass of 5.8(+2.7-2.5) times 10^-4 Msol of 26Al in the Orion region. Our population synthesis approach is demonstrated for the Orion region to reproduce three different kinds of observable outputs from massive stars in a consistent manner: Kinetic energy as manifested in ISM excavation, ionization as manifested in free-free emission, and nucleosynthesis ejecta as manifested in radioactivity gamma-rays. The good match between our model and the observables does not argue for considerable modifications of mass loss. If clumping effects turn out to be strong, other processes would need to be identified to compensate for their impact on massive-star outputs. Our population synthesis analysis jointly treats kinematic output and the return of radioactive isotopes, which proves a powerful extension of the methodology that constrains feedback from massive stars.Comment: Accepted for publication in A&A, 10 page

An LDEF 2 dust instrument for discrimination between orbital debris and natural particles in near-Earth space

The characteristics of a space dust instrument which would be ideally suited to carry out near-Earth dust measurements on a possible Long Duraction Exposure Facility reflight mission (LDEF 2) is discussed. As a model for the trajectory portion of the instrument proposed for LDEF 2, the characteristics of a SPAce DUSt instrument (SPADUS) currently under development for flight on the USA ARGOS mission to measure the flux, mass, velocity, and trajectory of near-Earth dust is summarized. Since natural (cosmic) dust and man-made dust particles (orbital debris) have different velocity and trajectory distributions, they are distinguished by means of the SPADUS velocity/trajectory information. The SPADUS measurements will cover the dust mass range approximately 5 x 10(exp -12) g (2 microns diameter) to approximately 1 x 10(exp -5) g (200 microns diameter), with an expected mean error in particle trajectory of approximately 7 deg (isotropic flux). Arrays of capture cell devices positioned behind the trajectory instrumentation would provide for Earth-based chemical and isotopic analysis of captured dust. The SPADUS measurement principles, characteristics, its role in the ARGOS mission, and its application to an LDEF 2 mission are summarized

Subgraphs with Restricted Degrees of their Vertices in Large Polyhedral Maps on Compact Two-manifolds

AbstractLet k≥ 2, be an integer and M be a closed two-manifold with Euler characteristic χ(M) ≤ 0. We prove that each polyhedral map G onM , which has at least (8 k2+ 6 k− 6)|χ (M)| vertices, contains a connected subgraph H of order k such that every vertex of this subgraph has, in G, the degree at most 4 k+ 4. Moreover, we show that the bound 4k+ 4 is best possible. Fabrici and Jendrol’ proved that for the sphere this bound is 10 ifk= 2 and 4 k+ 3 if k≥ 3. We also show that the same holds for the projective plane

Universal Behavior of the Resistance Noise across the Metal-Insulator Transition in Silicon Inversion Layers

Studies of low-frequency resistance noise show that the glassy freezing of the two-dimensional (2D) electron system in the vicinity of the metal-insulator transition occurs in all Si inversion layers. The size of the metallic glass phase, which separates the 2D metal and the (glassy) insulator, depends strongly on disorder, becoming extremely small in high-mobility samples. The behavior of the second spectrum, an important fourth-order noise statistic, indicates the presence of long-range correlations between fluctuators in the glassy phase, consistent with the hierarchical picture of glassy dynamics.Comment: revtex4; 4+ pages, 5 figure

Parallel Algorithm and Dynamic Exponent for Diffusion-limited Aggregation

A parallel algorithm for ``diffusion-limited aggregation'' (DLA) is described and analyzed from the perspective of computational complexity. The dynamic exponent z of the algorithm is defined with respect to the probabilistic parallel random-access machine (PRAM) model of parallel computation according to $T \sim L^{z}$, where L is the cluster size, T is the running time, and the algorithm uses a number of processors polynomial in L\@. It is argued that z=D-D_2/2, where D is the fractal dimension and D_2 is the second generalized dimension. Simulations of DLA are carried out to measure D_2 and to test scaling assumptions employed in the complexity analysis of the parallel algorithm. It is plausible that the parallel algorithm attains the minimum possible value of the dynamic exponent in which case z characterizes the intrinsic history dependence of DLA.Comment: 24 pages Revtex and 2 figures. A major improvement to the algorithm and smaller dynamic exponent in this versio