The maximum number of minimal codewords in an [n,k]−[n,k]-code

Upper and lower bounds are derived for the quantity in the title, which is tabulated for modest values of $n$ and $k.$ An application to graphs with many cycles is given.Comment: 6 pp. Submitte

From limit cycles to strange attractors

We define a quantitative notion of shear for limit cycles of flows. We prove that strange attractors and SRB measures emerge when systems exhibiting limit cycles with sufficient shear are subjected to periodic pulsatile drives. The strange attractors possess a number of precisely-defined dynamical properties that together imply chaos that is both sustained in time and physically observable.Comment: 27 page

Thermally-induced expansion in the 8 GeV/c π−\pi^- + 197^{197}Au reaction

Fragment kinetic energy spectra for reactions induced by 8.0 GeV/c $\rm{\pi^-}$ beams incident on a $\rm{^{197}}$Au target have been analyzed in order to deduce the possible existence and influence of thermal expansion. The average fragment kinetic energies are observed to increase systematically with fragment charge but are nearly independent of excitation energy. Comparison of the data with statistical multifragmentation models indicates the onset of extra collective thermal expansion near an excitation energy of E*/A $\rm{\approx}$ 5 MeV. However, this effect is weak relative to the radial expansion observed in heavy-ion-induced reactions, consistent with the interpretation that the latter expansion may be driven primarily by dynamical effects such as compression/decompression.Comment: 12 pages including 4 postscript figure

Uncertainty in hydrological modelling: a case study in the tern catchment, Shropshire, UK

This thesis explores a range of uncertainty issues within the commonly used hydrological modelling framework. It assesses the extent that choices made during model construction and calibration result in different model outputs and aims to assess whether it is possible to develop a modelling protocol better than the rest. Using the 876.36 km2 Tern catchment, Shropshire, UK, and the physically-based, distributed modelling code, MIKE SHE, the research draws on large volumes of secondary data and provides a comprehensive catchment review and conceptual model. Two hydrological models of differing spatial complexities are developed and subject to different parameterisations, sensitivity analyses, and calibration methods (manual and automatic). Results are assessed at different locations within the catchment. Six models developed with different protocols result in minimal intra-model uncertainty. Nash-Sutcliffe NSE varies between 0.69–0.79 for discharge at the catchment outlet. Differences between spatial representations are more apparent at internal gauging stations; despite this similar performing models are developed for both spatial representations. Multi-objective automatic calibration produces models which provide more balanced representation of observed data as shown by results of validation. However, it is not possible to statistically identify any of the modelling protocols as better than the rest. Results suggest the amount a particular statistic is used within the calibration will influence other performance statistics. Therefore an independent summary score measure is also developed to assess performance. Intra-model uncertainty is assessed for the six models for eight UKCIP02 climate change scenarios. Results suggest increases in intra-model uncertainty at a similar magnitude as potential impacts of climate change. The research suggests careful choices about the modelling protocol need to be addressed at the outset of any hydrological modelling, with attention given to the uncertainties that may result of decisions made by the modeller – especially if using models in impact studies

Spallation reactions. A successful interplay between modeling and applications

The spallation reactions are a type of nuclear reaction which occur in space by interaction of the cosmic rays with interstellar bodies. The first spallation reactions induced with an accelerator took place in 1947 at the Berkeley cyclotron (University of California) with 200 MeV deuterons and 400 MeV alpha beams. They highlighted the multiple emission of neutrons and charged particles and the production of a large number of residual nuclei far different from the target nuclei. The same year R. Serber describes the reaction in two steps: a first and fast one with high-energy particle emission leading to an excited remnant nucleus, and a second one, much slower, the de-excitation of the remnant. In 2010 IAEA organized a worskhop to present the results of the most widely used spallation codes within a benchmark of spallation models. If one of the goals was to understand the deficiencies, if any, in each code, one remarkable outcome points out the overall high-quality level of some models and so the great improvements achieved since Serber. Particle transport codes can then rely on such spallation models to treat the reactions between a light particle and an atomic nucleus with energies spanning from few tens of MeV up to some GeV. An overview of the spallation reactions modeling is presented in order to point out the incomparable contribution of models based on basic physics to numerous applications where such reactions occur. Validations or benchmarks, which are necessary steps in the improvement process, are also addressed, as well as the potential future domains of development. Spallation reactions modeling is a representative case of continuous studies aiming at understanding a reaction mechanism and which end up in a powerful tool.Comment: 59 pages, 54 figures, Revie