On periodic solutions of 2-periodic Lyness difference equations

We study the existence of periodic solutions of the non--autonomous periodic Lyness' recurrence u_{n+2}=(a_n+u_{n+1})/u_n, where {a_n} is a cycle with positive values a,b and with positive initial conditions. It is known that for a=b=1 all the sequences generated by this recurrence are 5-periodic. We prove that for each pair (a,b) different from (1,1) there are infinitely many initial conditions giving rise to periodic sequences, and that the family of recurrences have almost all the even periods. If a is not equal to b, then any odd period, except 1, appears.Comment: 27 pages; 1 figur

The O VI Absorbers Toward PG0953+415: High Metallicity, Cosmic-Web Gas Far From Luminous Galaxies

The spectrum of the low-redshift QSO PG0953+415 shows two strong, intervening O VI absorption systems. To study the nature of these absorbers, we have used the Gemini Multiobject Spectrograph to conduct a deep spectroscopic galaxy redshift survey in the 5' x 5' field centered on the QSO. This survey is fully complete for r' < 19.7 and is 73% complete for r' < 21.0. We find three galaxies at the redshift of the higher-z O VI system (z = 0.14232) including a galaxy at projected distance rho = 155 kpc. We find no galaxies in the Gemini field at the redshift of the lower-z O VI absorber (z = 0.06807), which indicates that the nearest galaxy is more than 195 kpc away or has L < 0.04 L*. Previous shallower surveys covering a larger field have shown that the z = 0.06807 O VI absorber is affiliated with a group/filament of galaxies, but the nearest known galaxy has rho = 736 kpc. The z = 0.06807 absorber is notable for several reasons. The absorption profiles reveal simple kinematics indicative of quiescent material. The H I line widths and good alignment of the H I and metal lines favor photoionization and, moreover, the column density ratios imply a high metallicity: [M/H] = -0.3 +/- 0.12. The z = 0.14232 O VI system is more complex and less constrained but also indicates a relatively high metallicity. Using galaxy redshifts from SDSS, we show that both of the PG0953+415 O VI absorbers are located in large-scale filaments of the cosmic web. Evidently, some regions of the web filaments are highly metal enriched. We discuss the origin of the high-metallicity gas and suggest that the enrichment might have occurred long ago (at high z).Comment: Submitted for publication in the Astrophysical Journal Letters. Figs. 1 and 2 compressed for astro-ph. High-resolution version available at http://www.astro.umass.edu/~tripp/astro/qualitypreps/pg0953tripp.pd

Flow-induced Agitations Create a Granular Fluid

We fluidize a granular medium through localized stirring and probe the mechanical response of quiescent regions far away from the main flow. In these regions the material behaves like a liquid: high-density probes sink, low-density probes float at the depth given by Archimedes' law, and drag forces on moving probes scale linearly with the velocity. The fluid-like character of the material is set by agitations generated in the stirred region, suggesting a non-local rheology: the relation between applied stress and observed strain rate in one location depends on the strain rate in another location

Conditioning problems for invariant sets of expanding piecewise affine mappings: Application to loss of ergodicity in globally coupled maps

We propose a systematic approach to the construction of invariant union of polytopes (IUP) in expanding piecewise affine mappings. The goal is to characterize ergodic components in these systems. The approach relies on using empirical information embedded in trajectories in order to infer, and then to solve, a so-called conditioning problem for some generating collection of polytopes. A conditioning problem consists of a series of requirements on the polytopes' localisation and on the dynamical transitions between these elements. The core element of the approach is a reformulation of the problem as a set of piecewise linear inequalities for some matrices which encapsulate geometric constraints. In that way, the original topological puzzle is converted into a standard problem in computational geometry. This transformation involves an optimization procedure that ensures that both problems are equivalent, ie. no information is dropped when passing to the analytic formulation. As a proof of concept, the approach is applied to the construction of asymmetric IUP in piecewise expanding globally coupled maps, so that multiple ergodic components result. The resulting mathematical statements explain, complete and extend previous results in the literature, and in particular, they address the dynamics of cluster configurations. Comparison with the numerics reveals that, in all examples, our approach provides sharp existence conditions and accurate fits of the empirical ergodic components

Wave generation in unidirectional chains of idealized neural oscillators

We investigate the dynamics of unidirectional semi-infinite chains of type-I oscillators that are periodically forced at their root node, as an archetype of wave generation in neural networks. In previous studies, numerical simulations based on uniform forcing have revealed that trajectories approach a traveling wave in the far-downstream, large time limit. While this phenomenon seems typical, it is hardly anticipated because the system does not exhibit any of the crucial properties employed in available proofs of existence of traveling waves in lattice dynamical systems. Here, we give a full mathematical proof of generation under uniform forcing in a simple piecewise affine setting for which the dynamics can be solved explicitly. In particular, our analysis proves existence, global stability, and robustness with respect to perturbations of the forcing, of families of waves with arbitrary period/wave number in some range, for every value of the parameters in the system

From source to sink in central Gondwana: Exhumation of the Precambrian basement rocks of Tanzania and sediment accumulation in the adjacent Congo basin

Apatite fission track (AFT) and (U-Th)/He (AHe) thermochronometry data are reported and used to unravel the exhumation history of crystalline basement rocks from the elevated (&gt;1000 m above sea level) but low-relief Tanzanian Craton. Coeval episodes of sedimentation documented within adjacent Paleozoic to Mesozoic basins of southern Tanzania and the Congo basin of the Democratic Republic of Congo indicate that most of the cooling in the basement rocks in Tanzania was linked to erosion. Basement samples were from an exploration borehole located within the craton and up to 2200 m below surface. Surface samples were also analyzed. AFT dates range between 317 ± 33 Ma and 188 ± 44 Ma. Alpha (Ft)-corrected AHe dates are between 433 ± 24 Ma and 154 ± 20 Ma. Modeling of the data reveals two important periods of cooling within the craton: one during the Carboniferous-Triassic (340–220 Ma) and a later, less well constrained episode, during the late Cretaceous. The later exhumation is well detected proximal to the East African Rift (70 Ma). Thermal histories combined with the estimated geothermal gradient of 9°C/km constrained by the AFT and AHe data from the craton and a mean surface temperature of 20°C indicate removal of up to 9 ± 2 km of overburden since the end of Paleozoic. The correlation of erosion of the craton and sedimentation and subsidence within the Congo basin in the Paleozoic may indicate regional flexural geodynamics of the lithosphere due to lithosphere buckling induced by far-field compressional tectonic processes and thereafter through deep mantle upwelling and epeirogeny tectonic processes

Southern African summer-rainfall variability, and its teleconnections, on interannual to interdecadal timescales in CMIP5 models

23 pagesInternational audienceThis study provides the first assessment of CMIP5 model performances in simulating southern Africa (SA) rainfall variability in austral summer (Nov–Feb), and its teleconnections with large-scale climate variability at different timescales. Observed SA rainfall varies at three major timescales: interannual (2–8 years), quasi-decadal (8–13 years; QDV) and interdecadal (15–28 years; IDV). These rainfall fluctuations are, respectively, associated with El Niño Southern Oscillation (ENSO), the Interdecadal Pacific Oscillation (IPO) and the Pacific Decadal Oscillation (PDO), interacting with climate anomalies in the South Atlantic and South Indian Ocean. CMIP5 models produce their own variability, but perform better in simulating interannual rainfall variability, while QDV and IDV are largely underestimated. These limitations can be partly explained by spatial shifts in core regions of SA rainfall variability in the models. Most models reproduce the impact of La Niña on rainfall at the interannual scale in SA, in spite of limitations in the representation of ENSO. Realistic links between negative IPO are found in some models at the QDV scale, but very poor performances are found at the IDV scale. Strong limitations, i.e. loss or reversal of these teleconnections, are also noted in some simulations. Such model errors, however, do not systematically impact the skill of simulated rainfall variability. This is because biased SST variability in the South Atlantic and South Indian Oceans strongly impact model skills by modulating the impact of Pacific modes of variability. Using probabilistic multi-scale clustering, model uncertainties in SST variability are primarily driven by differences from one model to another, or comparable models (sharing similar physics), at the global scale. At the regional scale, i.e. SA rainfall variability and associated teleconnections, while differences in model physics remain a large source of uncertainty, the contribution of internal climate variability is increasing. This is particularly true at the QDV and IDV scales, where the individual simulations from the same model tend to differentiate, and the sampling error increase

Flicker as a tool for characterizing planets through Asterodensity Profiling

Variability in the time series brightness of a star on a timescale of 8 hours, known as 'flicker', has been previously demonstrated to serve as a proxy for the surface gravity of a star by Bastien et al. (2013). Although surface gravity is crucial for stellar classification, it is the mean stellar density which is most useful when studying transiting exoplanets, due to its direct impact on the transit light curve shape. Indeed, an accurate and independent measure of the stellar density can be leveraged to infer subtle properties of a transiting system, such as the companion's orbital eccentricity via asterodensity profiling. We here calibrate flicker to the mean stellar density of 439 Kepler targets with asteroseismology, allowing us to derive a new empirical relation given by $\log_{10}(\rho_{\star}\,[\mathrm{kg}\,\mathrm{m}^{-3}]) = 5.413 - 1.850 \log_{10}(F_8\,[\mathrm{ppm}])$. The calibration is valid for stars with $4500$K$<T_{\mathrm{eff}}<6500$K, $K_P<14$ and flicker estimates corresponding to stars with $3.25<\log g_{\star}<4.43$. Our relation has a model error in the stellar density of 31.7% and so has $\sim8$ times lower precision than that from asteroseismology but is applicable to a sample $\sim40$ times greater. Flicker therefore provides an empirical method to enable asterodensity profiling on hundreds of planetary candidates from present and future missions.Comment: 6 pages, 3 figures, 1 table. Accepted to ApJ Letters. Code available at https://www.cfa.harvard.edu/~dkipping/flicker.htm