Partitioning the triangles of the cross polytope into surfaces

We present a constructive proof that there exists a decomposition of the 2-skeleton of the k-dimensional cross polytope $\beta^k$ into closed surfaces of genus $g \leq 1$, each with a transitive automorphism group given by the vertex transitive $\mathbb{Z}_{2k}$-action on $\beta^k$. Furthermore we show that for each $k \equiv 1,5(6)$ the 2-skeleton of the (k-1)-simplex is a union of highly symmetric tori and M\"obius strips.Comment: 13 pages, 1 figure. Minor update. Journal-ref: Beitr. Algebra Geom. / Contributions to Algebra and Geometry, 53(2):473-486, 201

Meiotic sex chromosome cohesion and autosomal synapsis are supported by Esco2.

In mitotic cells, establishment of sister chromatid cohesion requires acetylation of the cohesin subunit SMC3 (acSMC3) by ESCO1 and/or ESCO2. Meiotic cohesin plays additional but poorly understood roles in the formation of chromosome axial elements (AEs) and synaptonemal complexes. Here, we show that levels of ESCO2, acSMC3, and the pro-cohesion factor sororin increase on meiotic chromosomes as homologs synapse. These proteins are less abundant on the largely unsynapsed sex chromosomes, whose sister chromatid cohesion appears weaker throughout the meiotic prophase. Using three distinct conditional Esco2 knockout mouse strains, we demonstrate that ESCO2 is essential for male gametogenesis. Partial depletion of ESCO2 in prophase I spermatocytes delays chromosome synapsis and further weakens cohesion along sex chromosomes, which show extensive separation of AEs into single chromatids. Unsynapsed regions of autosomes are associated with the sex chromatin and also display split AEs. This study provides the first evidence for a specific role of ESCO2 in mammalian meiosis, identifies a particular ESCO2 dependence of sex chromosome cohesion and suggests support of autosomal synapsis by acSMC3-stabilized cohesion

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

Combinatorial 3-manifolds with transitive cyclic symmetry

In this article we give combinatorial criteria to decide whether a transitive cyclic combinatorial d-manifold can be generalized to an infinite family of such complexes, together with an explicit construction in the case that such a family exists. In addition, we substantially extend the classification of combinatorial 3-manifolds with transitive cyclic symmetry up to 22 vertices. Finally, a combination of these results is used to describe new infinite families of transitive cyclic combinatorial manifolds and in particular a family of neighborly combinatorial lens spaces of infinitely many distinct topological types.Comment: 24 pages, 5 figures. Journal-ref: Discrete and Computational Geometry, 51(2):394-426, 201

Simulation of cyclotron resonant scattering features: The effect of bulk velocity

X-ray binary systems consisting of a mass donating optical star and a highly magnetized neutron star, under the right circumstances, show quantum mechanical absorption features in the observed spectra called cyclotron resonant scattering features (CRSFs). We have developed a simulation to model CRSFs using Monte Carlo methods. We calculate Green's tables which can be used to imprint CRSFs to arbitrary X-ray continua. Our simulation keeps track of scattering parameters of individual photons, extends the number of variable parameters of previous works, and allows for more flexible geometries. Here we focus on the influence of bulk velocity of the accreted matter on the CRSF line shapes and positions

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

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

Formation of phase lags at the cyclotron energies in the pulse profiles of magnetized, accreting neutron stars

Context: Accretion-powered X-ray pulsars show highly energy-dependent and complex pulse-profile morphologies. Significant deviations from the average pulse profile can appear, in particular close to the cyclotron line energies. These deviations can be described as energy-dependent phase lags, that is, as energy-dependent shifts of main features in the pulse profile. Aims: Using a numerical study we explore the effect of cyclotron resonant scattering on observable, energy-resolved pulse profiles. Methods: We generated the observable emission as a function of spin phase, using Monte Carlo simulations for cyclotron resonant scattering and a numerical ray-tracing routine accounting for general relativistic light-bending effects on the intrinsic emission from the accretion columns. Results: We find strong changes in the pulse profile coincident with the cyclotron line energies. Features in the pulse profile vary strongly with respect to the average pulse profile with the observing geometry and shift and smear out in energy additionally when assuming a non-static plasma. Conclusions: We demonstrate how phase lags at the cyclotron energies arise as a consequence of the effects of angular redistribution of X-rays by cyclotron resonance scattering in a strong magnetic field combined with relativistic effects. We also show that phase lags are strongly dependent on the accretion geometry. These intrinsic effects will in principle allow us to constrain a system's accretion geometry.Comment: 4 pages, 4 figures; updated reference lis

Triangulations and Severi varieties

We consider the problem of constructing triangulations of projective planes over Hurwitz algebras with minimal numbers of vertices. We observe that the numbers of faces of each dimension must be equal to the dimensions of certain representations of the automorphism groups of the corresponding Severi varieties. We construct a complex involving these representations, which should be considered as a geometric version of the (putative) triangulations

Be-Phenomenon in Neutron Star X-ray Binaries

In this work we provide a brief insight into two aspects of Be/X-ray binaries, which are probably involved in production of X-ray outbursts: the evolution of the Be star disk, in particular of its size, and the binary geometry which drives gravitational interaction. Simultaneous X-ray and optical data will aid our investigation of the evolution of Be stars in binaries and the X-ray outburst mechanism