Statistics of the Island-Around-Island Hierarchy in Hamiltonian Phase Space

The phase space of a typical Hamiltonian system contains both chaotic and regular orbits, mixed in a complex, fractal pattern. One oft-studied phenomenon is the algebraic decay of correlations and recurrence time distributions. For area-preserving maps, this has been attributed to the stickiness of boundary circles, which separate chaotic and regular components. Though such dynamics has been extensively studied, a full understanding depends on many fine details that typically are beyond experimental and numerical resolution. This calls for a statistical approach, the subject of the present work. We calculate the statistics of the boundary circle winding numbers, contrasting the distribution of the elements of their continued fractions to that for uniformly selected irrationals. Since phase space transport is of great interest for dynamics, we compute the distributions of fluxes through island chains. Analytical fits show that the "level" and "class" distributions are distinct, and evidence for their universality is given.Comment: 31 pages, 13 figure

Graphs of Transportation Polytopes

This paper discusses properties of the graphs of 2-way and 3-way transportation polytopes, in particular, their possible numbers of vertices and their diameters. Our main results include a quadratic bound on the diameter of axial 3-way transportation polytopes and a catalogue of non-degenerate transportation polytopes of small sizes. The catalogue disproves five conjectures about these polyhedra stated in the monograph by Yemelichev et al. (1984). It also allowed us to discover some new results. For example, we prove that the number of vertices of an $m\times n$ transportation polytope is a multiple of the greatest common divisor of $m$ and $n$.Comment: 29 pages, 7 figures. Final version. Improvements to the exposition of several lemmas and the upper bound in Theorem 1.1 is improved by a factor of tw

A comment on BCC crystalization in higher dimensions

The result that near the melting point three-dimensional crystals have an octahedronic structure is generalized to higher flat non compact dimensions

Some Comments on an MeV Cold Dark Matter Scenario

We discuss several aspects of astroparticle physics pertaining to a new model with MeV cold dark matter particles, which annihilate to electron-positron pairs in a manner yielding the correct CDM density required today, and explaining the enhanced electron-positron annihilation line from the center of the Galaxy. We note that the mass of the vector meson mediating the annihilations, should exceed the mass of CDM particle, and comment on possible enhancement due to CDM clustering, on the detectability of the new CDM, and on particle physics models incorporating this scenario.Comment: 13 pages, 2 figures. v2 - Added some remarks regarding a more stringent mass bound. References added, some typos corrected. v3 - Added a comment regarding the invalidity of perturbative calculation in the case of a very small coupling g'. Removed the comment regarding the smallness of the angular width of the 511 keV lin

Social Facts, Moral Regulation and Statistical Jurisdiction: A Critical Evaluation of Canadian Census Figures on Education

After a brief general consideration of the census, state-formation and moral regulation, together with the use and abuse of this form of 'numbering the people', two major illustrative examples are provided which expose the problematic nature of seemingly objective censal data: illiteracy and ethnicity in the Canadian Censuses of 1921 and 1981 particularly. The bulk of the paper consists of an examination of the trends in ethnicity and gender in relation to varying measures of educational achievement in the Canadian Census 1921 through 1981. The summarised findings are that two of the three founding peoples' ('British' and 'French') are located in the middle range, whilst the third ('Native peoples') is located at the bottom; all other ethnic groups are more polarised. This is a consistent pattern across the sixty years surveyed, although it is often (in popular and academic writing) treated as a 'new phenomenon'. With regard to gender, the paper qualifies the popular myth that the education system is now less gender ascriptive than it was previously: wherever females have been better than males, the males have tended to close the gap or even reverse the situation; wherever males have been better than females, the gap has closed slowly, if at all. This confirms the recent study by Pineo and Goyder, based on the 1981 census alone, that "the Canadian educational system acts more ascriptively upon women than on men." For all the problems of Census data, the article argues that it can be used to discern aggregate trends over time which qualify many contemporary myths.Un bref examen du recensement en général, de la composition du pays et des règles morales, ainsi qu'une étude de l'usage normal et abusif de cette manière de "compter le peuple" ont permis de mettre en évidence deux principaux problems que cachent des données de recensement apparemment objectives. Il s'agit de l'analphabétisme et de l'appartenance ethnique dans les recensements canadiens de 1921 et 1981 en particulier. Dans l'ensemble, l'article traite des tendances ethniques et par sexe par rapport aux diverses réalisations dans le domaine de l'éducation révélées par Recensement Canada de 1921 à 1981. En résumé, on conclut que deux des trois peuples "fondateurs" (les Anglais et les Français) se situent dans la moyenne alors que le troisième (les Améridiens) est au bas de l'échelle. Ce modèle s'est répété constamment pendant les soixante années étudiées, bien que souvent (dans les publications communes et savantes) on qualifie ce phénomène de "nouveau". En ce qui concerne le sexe des étudiants, l'article !nuance! le mythe populaire qui veut que le système d'éducation favorise moins un certain sexe qu'il ne le faisait auparavant. Lorsque les femmes réussissent mieux que les hommes, les hommes ont tendance à rattraper le retard ou même à renverser la situation ; par contre, lorsque les hommes réussissent mieux que les femmes, l'écart se comble lentement, si jamais il se comble. Cette observation confirme les résultats de l'étude menée par Pineo et Goyder, basée sur le recensement de 1981, qui montre que le "système d'éducation canadien a un effet plus statique sur les femmes que pour les hommes". Devant tous les problèmes que présentent les données de recensement, l'article soutient qu'on peut les utiliser pour discerner les tendances générales dans le temps qui s'appliquent également à bien des mythes contemporains

Benchmark and Framework for Encouraging Research on Multi-Threaded Testing Tools

A problem that has been getting prominence in testing is that of looking for intermittent bugs. Multi-threaded code is becoming very common, mostly on the server side. As there is no silver bullet solution, research focuses on a variety of partial solutions. In this paper (invited by PADTAD 2003) we outline a proposed project to facilitate research. The project goals are as follows. The first goal is to create a benchmark that can be used to evaluate different solutions. The benchmark, apart from containing programs with documented bugs, will include other artifacts, such as traces, that are useful for evaluating some of the technologies. The second goal is to create a set of tools with open API s that can be used to check ideas without building a large system. For example an instrumentor will be available, that could be used to test temporal noise making heuristics. The third goal is to create a focus for the research in this area around which a community of people who try to solve similar problems with different techniques, could congregate

Time-independent approximations for periodically driven systems with friction

The classical dynamics of a particle that is driven by a rapidly oscillating potential (with frequency $\omega$) is studied. The motion is separated into a slow part and a fast part that oscillates around the slow part. The motion of the slow part is found to be described by a time-independent equation that is derived as an expansion in orders of $\omega^{-1}$ (in this paper terms to the order $\omega^{-3}$ are calculated explicitly). This time-independent equation is used to calculate the attracting fixed points and their basins of attraction. The results are found to be in excellent agreement with numerical solutions of the original time-dependent problem.Comment: 5 pages, 4 figures. Revised version. Minor change

Implications of Hyperon Pairing for Cooling of Neutron Stars

The implications of hyperon pairing for the thermal evolution of neutron stars containing hyperons are investigated. The outcome of cooling simulations are compared for neutron star models composed only of nucleons and leptons, models including hyperons, and models including pairing of hyperons. We show that lambda and neutron pairing suppresses all possible fast neutrino emission processes in not too massive neutron stars. The inclusion of lambda pairing yields better agreement with X-ray observations of pulsars. Particularly, the surface temperatures deduced from X-ray observations within the hydrogen atmosphere model are more consistent with the thermal history of neutron stars containing hyperons, if the critical temperature for the onset of lambda and nucleon pairing is not too small.Comment: 7 pages, 3 figures. To be published in ApJL. The postscript and additional tables can be found at http://www.physik.uni-muenchen.de/sektion/suessmann/astro/cool/schaab.089