Polynomial cubic differentials and convex polygons in the projective plane

We construct and study a natural homeomorphism between the moduli space of polynomial cubic differentials of degree d on the complex plane and the space of projective equivalence classes of oriented convex polygons with d+3 vertices. This map arises from the construction of a complete hyperbolic affine sphere with prescribed Pick differential, and can be seen as an analogue of the Labourie-Loftin parameterization of convex RP^2 structures on a compact surface by the bundle of holomorphic cubic differentials over Teichmuller space.Comment: 64 pages, 5 figures. v3: Minor revisions according to referee report. v2: Corrections in section 5 and related new material in appendix

Consumption of Single-Use Plastics by a Commercial Construction Firm: A Case Study

Most construction sites utilize single-use plastic bottles because they are easy to distribute and guarantee fresh, clean drinking water. The number of bottles consumed on a site is usually an unknown quantity and is not a waste center that is commonly focused on. This case study outlines a mid-sized construction company’s rate of consumption of single-use plastic bottles. This study details the specifics of the project including size, type, value, and number of workers onsite. The information was gained through working closely with an onsite contact in a management position. The range of focus has been narrowed to only the amount of labor provided by the general contractor, in order to focus the study to a single company, rather than an entire site. The rate of consumption and number of plastic bottles consumed over the project’s lifetime was studied. The final estimate found that this company’s projects consumed around 530,000 plastic bottles with a team of 72 onsite workers. The final number of plastic bottles consumed will be applied to companies with projects of similar scope, in order to gain more insight into the amount of single-use plastic waste contributed to the environment by the construction industry

Projective structures, grafting, and measured laminations

We show that grafting any fixed hyperbolic surface defines a homeomorphism from the space of measured laminations to Teichmuller space, complementing a result of Scannell-Wolf on grafting by a fixed lamination. This result is used to study the relationship between the complex-analytic and geometric coordinate systems for the space of complex projective (\CP^1) structures on a surface. We also study the rays in Teichmuller space associated to the grafting coordinates, obtaining estimates for extremal and hyperbolic length functions and their derivatives along these grafting rays.Comment: 31 pages, 4 figure

Becker's conjecture on Mahler functions

In 1994, Becker conjectured that if $F(z)$ is a $k$-regular power series, then there exists a $k$-regular rational function $R(z)$ such that $F(z)/R(z)$ satisfies a Mahler-type functional equation with polynomial coefficients where the initial coefficient satisfies $a_0(z)=1$. In this paper, we prove Becker's conjecture in the best-possible form; we show that the rational function $R(z)$ can be taken to be a polynomial $z^\gamma Q(z)$ for some explicit non-negative integer $\gamma$ and such that $1/Q(z)$ is $k$-regular.Comment: 19 page

Quantitative Decoding of Interactions in Tunable Nanomagnet Arrays Using First Order Reversal Curves

To develop a full understanding of interactions in nanomagnet arrays is a persistent challenge, critically impacting their technological acceptance. This paper reports the experimental, numerical and analytical investigation of interactions in arrays of Co nanoellipses using the first-order reversal curve (FORC) technique. A mean-field analysis has revealed the physical mechanisms giving rise to all of the observed features: a shift of the non-interacting FORC-ridge at the low-H$_c$ end off the local coercivity H$_c$ axis; a stretch of the FORC-ridge at the high-H$_c$ end without shifting it off the H$_c$ axis; and a formation of a tilted edge connected to the ridge at the low-H$_c$ end. Changing from flat to Gaussian coercivity distribution produces a negative feature, bends the ridge, and broadens the edge. Finally, nearest neighbor interactions segment the FORC-ridge. These results demonstrate that the FORC approach provides a comprehensive framework to qualitatively and quantitatively decode interactions in nanomagnet arrays.Comment: 19 pages, 4 figures. 9 page supplemental material including 3 figure

Business Cycles, Bifurcations and Chaos in a Neo-Classical Model with Investment Dynamics

This paper presents a non-equilibrium dynamic model (NEDyM) that introduces investment dynamics and non-equilibrium effects into a Solow growth model. NEDyM can reproduce several typical economic regimes and, for certain ranges of parameter values, exhibits endogenous business cycles with realistic characteristics. The cycles arise from the investment-profit instability and are constrained by the increase in labor costs and the inertia of production capacity. For other parameter ranges, the model exhibits chaotic behavior. These results show that complex variability in the economic system may be due to deterministic, intrinsic factors, even if the long-term equilibrium is neo-classical in nature

Needed Research on the Englishes of Appalachia

Information about the 79th annual meeting of the Southeastern Conference on Linguistics (SECOL) organized by Jennifer Cramer at the University of Kentucky on April 2012 in Lexington, Kentucky. Topics discussed at the meeting includes current state of research studies on linguistic processes in Appalachia, traditional dialectological and ethnographic. The meeting also featured panel experts including Bridget L. Anderson, Michael Montgomery and Walt Wolfram

The PdBI Arcsecond Whirlpool Survey (PAWS). I. A Cloud-Scale/Multi-Wavelength View of the Interstellar Medium in a Grand-Design Spiral Galaxy

The PdBI (Plateau de Bure Interferometer) Arcsecond Whirlpool Survey (PAWS) has mapped the molecular gas in the central ~9kpc of M51 in its 12CO(1-0) line emission at cloud-scale resolution of ~40pc using both IRAM telescopes. We utilize this dataset to quantitatively characterize the relation of molecular gas (or CO emission) to other tracers of the interstellar medium (ISM), star formation and stellar populations of varying ages. Using 2-dimensional maps, a polar cross-correlation technique and pixel-by-pixel diagrams, we find: (a) that (as expected) the distribution of the molecular gas can be linked to different components of the gravitational potential, (b) evidence for a physical link between CO line emission and radio continuum that seems not to be caused by massive stars, but rather depend on the gas density, (c) a close spatial relation between the PAH and molecular gas emission, but no predictive power of PAH emission for the molecular gas mass,(d) that the I-H color map is an excellent predictor of the distribution (and to a lesser degree the brightness) of CO emission, and (e) that the impact of massive (UV-intense) young star-forming regions on the bulk of the molecular gas in central ~9kpc can not be significant due to a complex spatial relation between molecular gas and star-forming regions that ranges from co-spatial to spatially offset to absent. The last point, in particular, highlights the importance of galactic environment -- and thus the underlying gravitational potential -- for the distribution of molecular gas and star formation.Comment: 52 pages, 14 figures, 2 tables, (several minor typos corrected) accepted by ApJ, high resolution version available, see http://www.mpia.de/PAWS/pub/paws_schinnerer.pdf ; for more information on PAWS, further papers and the data, see http://www.mpia.de/PAW