Curvature estimates for submanifolds in warped products

We give estimates on the intrinsic and the extrinsic curvature of manifolds that are isometrically immersed as cylindrically bounded submanifolds of warped products. We also address extensions of the results in the case of submanifolds of the total space of a Riemannian submersion.Comment: 21 page

A nonlinear vehicle-structure interaction methodology with wheel-rail detachment and reattachment

. A vehicle-structure interaction methodology with a nonlinear contact formulation based on contact and target elements has been developed. To solve the dynamic equations of motion, an incremental formulation has been used due to the nonlinear nature of the contact mechanics, while a procedure based on the Lagrange multiplier method imposes the contact constraint equations when contact occurs. The system of nonlinear equations is solved by an efficient block factorization solver that reorders the system matrix and isolates the nonlinear terms that belong to the contact elements or to other nonlinear elements that may be incorporated in the model. Such procedure avoids multiple unnecessary factorizations of the linear terms during each Newton iteration, making the formulation efficient and computationally attractive. A numerical example has been carried out to validate the accuracy and efficiency of the present methodology. The obtained results have shown a good agreement with the results obtained with the commercial finite element software ANSY

Doped AB_2 Hubbard Chain: Spiral, Nagaoka and RVB States, Phase Separation and Luttinger Liquid Behavior

We present an extensive numerical study of the Hubbard model on the doped AB$_2$ chain, both in the weak coupling and the infinite-U limit. Due to the special unit cell topology, this system displays a rich variety of phases as function of hole doping ($\delta$) away from half-filling. Near half-filling, spiral states develop in the weak coupling regime, while Nagaoka itinerant ferromagnetism is observed in the infinite-U limit. For higher doping the system phase-separates before reaching a Mott insulating phase of short-range RVB states at $\delta=1/3$. Moreover, for $\delta>1/3$ we observe a crossover, which anticipates the Luttinger liquid behavior for $\delta > 2/3$.Comment: 11 pages, 13 figure

Coping Mechanisms in Graduate School: A Discipline Comparison

The current study aimed to provide an overview of graduate students’ stress and coping mechanisms. Per self-reported questionnaires, participants (N=95) rated their experiences with academic-related stressors, common coping mechanisms, and strain outcomes (somatic symptoms, insomnia, and burnout). This study found that task-related stressors were the most prevalent for graduate schoolwork. More specifically, graduate students in STEM, Arts & Humanities, and Social Sciences rated the amount and difficulty of the tasks (quantitative and qualitative properties of tasks) as the highest stressors in graduate school. The preferred coping strategies across all fields were planning and emotional coping. Additionally, students in STEM reported more significant organizational constraints and interpersonal conflict than graduate students in Arts & Humanities, and Social Sciences. Finally, students in Arts & Humanities reported more maladaptive coping mechanisms than students in the other two groups. These findings can guide program directors and administrators in informing initiatives to enhance graduate students’ well-being

Evidence for azimuthal variations of the oxygen abundance gradient tracing the spiral structure of the galaxy HCG91c

Context. The distribution of elements in galaxies forms an important diagnostic tool to characterize the system's formation and evolution. This tool is however complex to use in practice, as galaxies are subject to a range of simultaneous physical processes active from pc to kpc scales. This renders observations of the full optical extent of galaxies down to sub-kpc scales essential. Aims. Using the WiFeS integral field spectrograph, we previously detected abrupt and localized variations in the gas-phase oxygen abundance of the spiral galaxy HCG91c. Here, we follow-up on these observations to map HCG91c's disk out to ~2Re at a resolution of 600pc, and characterize the non-radial variations of the gas-phase oxygen abundance in the system. Methods. We obtained deep MUSE observations of the target under ~0.6 arcsec seeing conditions. We perform both a spaxel-based and aperture-based analysis of the data to map the spatial variations of 12+log(O/H) across the disk of the galaxy. Results. We confirm the presence of rapid variations of the oxygen abundance across the entire extent of the galaxy previously detected with WiFeS, for all azimuths and radii. The variations can be separated in two categories: a) localized and associated with individual HII regions, and b) extended over kpc scales, and occurring at the boundaries of the spiral structures in the galaxy. Conclusions. Our MUSE observations suggest that the enrichment of the interstellar medium in HGC91c has proceeded preferentially along spiral structures, and less efficiently across them. Our dataset highlights the importance of distinguishing individual star-forming regions down to scales of a few 100pc when using integral field spectrographs to spatially resolve the distribution of oxygen abundances in a given system, and accurately characterize azimuthal variations and intrinsic scatter.Comment: 12 pages, 11 figures, accepted for publication in A&A. Supplementary movie assocociated with Fig. 8 is available (until publication) at: http://www.sc.eso.org/~fvogt/supp_mat/HCG91c/O_gradient.mp

Ordering in the dilute weakly-anisotropic antiferromagnet Mn(0.35)Zn(0.65)F2

The highly diluted antiferromagnet Mn(0.35)Zn(0.65)F2 has been investigated by neutron scattering in zero field. The Bragg peaks observed below the Neel temperature TN (approximately 10.9 K) indicate stable antiferromagnetic long-range ordering at low temperature. The critical behavior is governed by random-exchange Ising model critical exponents (nu approximately 0.69 and gamma approximately 1.31), as reported for Mn(x)Zn(1-x)F2 with higher x and for the isostructural compound Fe(x)Zn(1-x)F2. However, in addition to the Bragg peaks, unusual scattering behavior appears for |q|>0 below a glassy temperature Tg approximately 7.0 K. The glassy region T<Tg corresponds to that of noticeable frequency dependence in earlier zero-field ac susceptibility measurements on this sample. These results indicate that long-range order coexists with short-range nonequilibrium clusters in this highly diluted magnet.Comment: 7 pages, 5 figure

Foliations and Chern-Heinz inequalities

We extend the Chern-Heinz inequalities about mean curvature and scalar curvature of graphs of $C^{2}$-functions to leaves of transversally oriented codimension one $C^{2}$-foliations of Riemannian manifolds. That extends partially Salavessa's work on mean curvature of graphs and generalize results of Barbosa-Kenmotsu-Oshikiri \cite{barbosa-kenmotsu-Oshikiri} and Barbosa-Gomes-Silveira \cite{barbosa-gomes-silveira} about foliations of 3-dimensional Riemannian manifolds by constant mean curvature surfaces. These Chern-Heinz inequalities for foliations can be applied to prove Haymann-Makai-Osserman inequality (lower bounds of the fundamental tones of bounded open subsets $\Omega \subset \mathbb{R}^{2}$ in terms of its inradius) for embedded tubular neighborhoods of simple curves of $\mathbb{R}^{n}$.Comment: This paper is an improvment of an earlier paper titled On Chern-Heinz Inequalities. 8 Pages, Late