Hamiltonian submanifolds of regular polytopes

We investigate polyhedral $2k$-manifolds as subcomplexes of the boundary complex of a regular polytope. We call such a subcomplex {\it $k$-Hamiltonian} if it contains the full $k$-skeleton of the polytope. Since the case of the cube is well known and since the case of a simplex was also previously studied (these are so-called {\it super-neighborly triangulations}) we focus on the case of the cross polytope and the sporadic regular 4-polytopes. By our results the existence of 1-Hamiltonian surfaces is now decided for all regular polytopes. Furthermore we investigate 2-Hamiltonian 4-manifolds in the $d$-dimensional cross polytope. These are the "regular cases" satisfying equality in Sparla's inequality. In particular, we present a new example with 16 vertices which is highly symmetric with an automorphism group of order 128. Topologically it is homeomorphic to a connected sum of 7 copies of $S^2 \times S^2$. By this example all regular cases of $n$ vertices with $n < 20$ or, equivalently, all cases of regular $d$-polytopes with $d\leq 9$ are now decided.Comment: 26 pages, 4 figure

What Can We Learn From Open Questions in Surveys? A Case Study on Non-Voting Reported in the 2013 German Longitudinal Election Study

Open survey questions are often used to evaluate closed questions. However, they can fulfil this function only if there is a strong link between answers to open questions and answers to related closed questions. Using reasons for non-voting reported in the German Longitudinal Election Study 2013, we investigated this link by examining whether the reported reasons for non-voting may be substantive reasons or ex-post legitimations. We tested five theoretically derived hypotheses about respondents who gave, or did not give, a specific reason. Results showed that (a) answers to open questions were indeed related to answers to closed questions and could be used in explanatory turnout models to predict voting behavior, and (b) the relationship between answers to open and closed questions and the predictive power of reasons given in response to the open questions were stronger in the post-election survey (reported behavior) than in the pre-election survey (intended behavior)

Perturbative behaviour of a vortex in a trapped Bose-Einstein condensate

We derive a set of equations that describe the shape and behaviour of a single perturbed vortex line in a Bose-Einstein condensate. Through the use of a matched asymptotic expansion and a unique coordinate transform a relation for a vortex's velocity, anywhere along the line, is found in terms of the trapping, rotation, and distortion of the line at that location. This relation is then used to find a set of differential equations that give the line's specific shape and motion. This work corrects a previous similar derivation by Anatoly A. Svidzinsky and Alexander L. Fetter [Phys. Rev. A \textbf{62}, 063617 (2000)], and enables a comparison with recent numerical results.Comment: 12 pages with 3 figure

From Golden Spirals to Constant Slope Surfaces

In this paper, we find all constant slope surfaces in the Euclidean 3-space, namely those surfaces for which the position vector of a point of the surface makes constant angle with the normal at the surface in that point. These surfaces could be thought as the bi-dimensional analogue of the generalized helices. Some pictures are drawn by using the parametric equations we found.Comment: 11 pages, 8 figure

Coupled CFD-CAA approach for rotating systems

We present a recently developed computational scheme for the numerical simulation of flow induced sound for rotating systems. Thereby, the flow is fully resolved in time by utilizing a DES (Detached Eddy Simulation) turbulance model and using an arbitrary mesh interface scheme for connecting rotating and stationary domains. The acoustic field is modeled by a perturbation ansatz resulting in a convective wave equation based on the acoustic scalar potential and the substational time derivative of the incompressible flow pressure as a source term. We use the Finite-Element (FE) method for solving the convective wave equation and apply a Nitsche type mortaring at the interface between rotating and stationary domains. The whole scheme is applied to the numerical computation of a side channel blower

Benutzerdefinierte Design-Matrizen in log-linearen Analysen: Realisierungsmöglichkeiten in den SPSS-Prozeduren GENLOG und LOGLINEAR

'Der Anwendung log-linearer Modelle in der Sozialforschung steht oft die Vorstellung entgegen, daß diese Modelle recht kompliziert und daher kaum zu interpretieren seien. Das Verständnis für log-lineare Analysen wird erleichtert, wenn die Verwandtschaft zur multiplen Regression mit nominalskalierten Prädikaten gesehen wird. Gleichzeitig kann so auch die Bedeutung der sogenannten Design-Matrix nahegebracht werden. Die volle Flexibilität log-linearer Modelle wird nämlich erst durch die Formulierung benutzerdefinierter Design-Matritzen erreicht. Anhand von Beispieldaten aus dem ALLBUS 1996 wird gezeigt, wie sich bei Anwendung der SPSS-Prozeduren GENLOG oder LOGLINEAR loglineare Analysen mit benutzerdefinierten Design-Matritzen realisieren lassen.' (Autorenreferat)'Applications of long-linear modelling are sometimes prevented by the impression that this technique is not user-friendly. Nevertheless, log-linear modelling is nothing more than multiple regression of the logarithms of cell counts on categorical predictors. Within this view the importance of the design matrix is easy to understand. The specification of user-defined design matrices within log-linear models allows for very flexible analyses of categorical data. It is shown how such analyses can be done using the SPSS procedures GENLOG or LOGLINEAR. An empirical example is given based on data from the ALLBUS 1996.' (author's abstract)

Mixing Effects in the Crystallization of Supercooled Quantum Binary Liquids

By means of Raman spectroscopy of liquid microjets we have investigated the crystallization process of supercooled quantum liquid mixtures composed of parahydrogen (pH$_2$) diluted with small amounts of up to 5\% of either neon or orthodeuterium (oD$_2$), and of oD$_2$ diluted with either Ne or pH$_2$. We show that the introduction of Ne impurities affects the crystallization kinetics in both the pH$_2$-Ne and oD$_2$-Ne mixtures in terms of a significant reduction of the crystal growth rate, similarly to what found in our previous work on supercooled pH$_2$-oD$_2$ liquid mixtures [M. K\"uhnel et {\it al.}, Phys. Rev. B \textbf{89}, 180506(R) (2014)]. Our experimental results, in combination with path-integral simulations of the supercooled liquid mixtures, suggest in particular a correlation between the measured growth rates and the ratio of the effective particle sizes originating from quantum delocalization effects. We further show that the crystalline structure of the mixture is also affected to a large extent by the presence of the Ne impurities, which likely initiate the freezing process through the formation of Ne crystallites.Comment: 19 pages, 7 figures, submitted to J. Chem. Phy

Topological Modes in Dual Lattice Models

Lattice gauge theory with gauge group $Z_{P}$ is reconsidered in four dimensions on a simplicial complex $K$. One finds that the dual theory, formulated on the dual block complex $\hat{K}$, contains topological modes which are in correspondence with the cohomology group $H^{2}(\hat{K},Z_{P})$, in addition to the usual dynamical link variables. This is a general phenomenon in all models with single plaquette based actions; the action of the dual theory becomes twisted with a field representing the above cohomology class. A similar observation is made about the dual version of the three dimensional Ising model. The importance of distinct topological sectors is confirmed numerically in the two dimensional Ising model where they are parameterized by $H^{1}(\hat{K},Z_{2})$.Comment: 10 pages, DIAS 94-3

Ist Politikverdrossenheit eine notwendige Bedingung für die Wahl der Republikaner? Eine Anmerkung zur Kontroverse zwischen Jagodzinski/ Klein und Schumann/ Hardt

'In ihrer Kritik an einer Arbeit von Jagodzinski und Klein (1997) vertreten Schumann und Hardt (1998) die Auffassung, daß es keinen Interaktionseffekt zwischen Rechtsextremismus und Politikverdrossenheit bei der Erklärung der Wahl der Republikaner gäbe und Politikverdrossenheit insgesamt keine große Rolle spiele. Zur Prüfung dieser Frage wird nach einer kurzen Erläuterung des Konzepts der statistischen Interaktion als zusätzliche Datenquelle der ALLBUS 1996 herangezogen. Die ALLBUS-Daten bestätigen im wesentlichen die Ergebnisse von Jagodzinski und Klein. Die Wahrscheinlichkeit, bei der Bundestagswahl 1994 die Republikaner gewählt zu haben, erhöhte sich signifikant, wenn neben einer rechtsextremen Einstellung zusätzlich Politikverdrossenheit vorliegt. Dieser Effekt tritt noch deutlicher auf wenn anstelle der Wahlrückerinnerung die aktuelle Wahlabsicht betrachtet wird.' (Autorenreferat)'In the immediately prior article, Schumann and Hardt (1998) have criticized the earlier conclusions of Jagodzinski and Klein (1997) which stated that being discontent in politics is an important predictor of voting for the Republikaner party in Germany. In an attempt to adjudicate between these two positions, this paper replicates the earlier Jagodzinski-Klein analysis using more recent, 1996, ALLBUS data. The results confirm the hypothesis of Jagodzinski and Klein, Individuals who vote for the Republikanerparty are significantly more likely to be both right wing and discontented with German politics.' (author's abstract)

Können Mischverteilungsmodelle das Problem heterogener Daten lösen?

'Datenheterogenität liegt vor, wenn die Untersuchungseinheiten in einer Stichprobe nicht als Realisationen aus einer gemeinsamen Verteilung aufgefaßt werden können. Wird Heterogenität ignoriert, besteht die Gefahr von Fehlschlüssen. Die Berücksichtigung von Heterogenität durch die Spezifikation zusätzlicher exogener Variablen oder durch Gruppenvergleiche setzt voraus, daß Informationen darüber vorliegen, nie sich die Untersuchungseinheiten zu homogenen Subgruppen zusammenfassen lassen. In Mischverteilungsmodellen ist diese Kenntnis dagegen nicht nötig. Zwar wird auch hier vorausgesetzt daß sich eine Population aus Subpopulationen zusammensetzt. Die Zugehörigkeit der Fälle einer Stichprobe zu diesen als latente Klassen bezeichneten Subpopulationen muß aber nicht bekannt sein. Ein Nachteil dieser größeren Flexibilität von Mischverteilungsmodellen besteht darin, daß es schwierig sein kann, eine eindeutige Lösung zu finden. Trotz dieser Schwierigkeit sind Mischverteilungsmodelle eine fruchtbare Ergänzung des Angebots an statistischen Analysemodellen. Dies wird an einem Anwendungsbeispiel demonstriert bei dem anhand von Daten der ISSP-Umfrage 1993 der Zusammenhang zwischen der wahrgenommenen Umweltgefährdung durch Autos und der Befürwortung von politischen Maßnahmen zur Verkehrsreduktion untersucht wird. Die Schätzungen von Mischverteilungsmodellen mit dem Programm Mplus von Muthen führen hierzu einer Lösung mit zwei latenten Klassen, die sich in der Bewertung der Umweltgefährdung und der Zustimmung zu Maßnahmen zur Verkehrsreduktion deutlich unterscheiden.' (Autorenreferat)'Data are heterogeneous if units are not sampled from a unique population with common probability distribution. As a consequence inferences may become invalid. Heterogeneity can be controlled by specification of additional exogenous variables or simultaneous analysis of subgroups. In both approaches, a heterogeneous sample is divided in homogenous subgroups. Similarly, in latent variable mixture models the total population is divided in subpopulations that are called latent classes. But in contrast to the classical method of group comparisons, it is not necessary to know the membership of a case to a subpopulation. Therefore, latent variable mixture models are more flexible. On the other hand, it becomes more difficult to estimate a mixture model. In this paper, the application of latent variable mixture models and problems of application are demonstrated using data from the ISSP survey 1993. In this example the relation is investigated between perception of environmental risks caused by car traffic and support of policies to reduce car traffic. The estimation of a mixed model using Muthin's program Mplus results in a solution with two latent classes with different views on environmental risks and policies.' (author's abstract)