The Stability of One-Step Schemes for First-Order Two-Point Boundary Value Problems

The stability of a finite difference scheme is related explicitly to the stability of the continuous problem being solved. At times, this gives materially better estimates for the stability constant than those obtained by the standard process of appealing to the stability of the numerical scheme for the associated initial value problem

CARBON BALANCE AND VEGETATION DYNAMICS IN AN OLD‐GROWTH AMAZONIAN FOREST

Amazon forests could be globally significant sinks or sources for atmospheric carbon dioxide, but carbon balance of these forests remains poorly quantified. We surveyed 19.75 ha along four 1‐km transects of well‐drained old‐growth upland forest in the Tapajós National Forest near Santarém, Pará, Brazil (2°51′ S, 54°58′ W) in order to assess carbon pool sizes, fluxes, and climatic controls on carbon balance. In 1999 there were, on average, 470 live trees per hectare with diameter at breast height (dbh) ≥10 cm. The mean (and 95% ci) aboveground live biomass was 143.7 ± 5.4 Mg C/ha, with an additional 48.0 ± 5.2 Mg C/ha of coarse woody debris (CWD). The increase of live wood biomass after two years was 1.40 ± 0.62 Mg C·ha−1·yr−1, the net result of growth (3.18 ± 0.20 Mg C·ha−1·yr−1 from mean bole increment of 0.36 cm/yr), recruitment of new trees (0.63 ± 0.09 Mg C·ha−1·yr−1, reflecting a notably high stem recruitment rate of 4.8 ± 0.9%), and mortality (−2.41 ± 0.53 Mg C·ha−1·yr−1 from stem death of 1.7% yr−1). The gain in live wood biomass was exceeded by respiration losses from CWD, resulting in an overall estimated net loss from total aboveground biomass of 1.9 ± 1.0 Mg C·ha−1·yr−1. The presence of large CWD pools, high recruitment rate, and net accumulation of small‐tree biomass, suggest that a period of high mortality preceded the initiation of this study, possibly triggered by the strong El Niño Southern Oscillation events of the 1990s. Transfer of carbon between live and dead biomass pools appears to have led to substantial increases in the pool of CWD, causing the observed net carbon release. The data show that biometric studies of tropical forests neglecting CWD are unlikely to accurately determine carbon balance. Furthermore, the hypothesized sequestration flux from CO2 fertilization (\u3c0.5 Mg C·ha−1·yr−1) would be comparatively small and masked for considerable periods by climate‐driven shifts in forest structure and associated carbon balance in tropical forests

Convergence to stable laws for multidimensional stochastic recursions: the case of regular matrices

Given a sequence $(M_{n},Q_{n})_{n\ge 1}$ of i.i.d.\ random variables with generic copy $(M,Q) \in GL(d, \R) \times \R^d$, we consider the random difference equation (RDE) $$R_{n}=M_{n}R_{n-1}+Q_{n},$$ $n\ge 1$, and assume the existence of $\kappa >0$ such that \lim_{n \to \infty}(\E{\norm{M_1 ... M_n}^\kappa})^{\frac{1}{n}} = 1 . We prove, under suitable assumptions, that the sequence $S_n = R_1 + ... + R_n$, appropriately normalized, converges in law to a multidimensional stable distribution with index $\kappa$. As a by-product, we show that the unique stationary solution $R$ of the RDE is regularly varying with index $\kappa$, and give a precise description of its tail measure. This extends the prior work http://arxiv.org/abs/1009.1728v3 .Comment: 15 page

Phase transition and correlation decay in Coupled Map Lattices

For a Coupled Map Lattice with a specific strong coupling emulating Stavskaya's probabilistic cellular automata, we prove the existence of a phase transition using a Peierls argument, and exponential convergence to the invariant measures for a wide class of initial states using a technique of decoupling originally developed for weak coupling. This implies the exponential decay, in space and in time, of the correlation functions of the invariant measures

Search for an exosphere in sodium and calcium in the transmission spectrum of exoplanet 55 Cancri e

[Abridged] The aim of this work is to search for an absorption signal from exospheric sodium (Na) and singly ionized calcium (Ca$^+$) in the optical transmission spectrum of the hot rocky super-Earth 55 Cancri e. Although the current best-fitting models to the planet mass and radius require a possible atmospheric component, uncertainties in the radius exist, making it possible that 55 Cancri e could be a hot rocky planet without an atmosphere. High resolution (R$\sim$110000) time-series spectra of five transits of 55 Cancri e, obtained with three different telescopes (UVES/VLT, HARPS/ESO 3.6m & HARPS-N/TNG) were analysed. Targeting the sodium D lines and the calcium H and K lines, the potential planet exospheric signal was filtered out from the much stronger stellar and telluric signals, making use of the change of the radial component of the orbital velocity of the planet over the transit from -57 to +57 km/sec. Combining all five transit data sets, we detect a signal potentially associated with sodium in the planet exosphere at a statistical significance level of 3$\sigma$. Combining the four HARPS transits that cover the calcium H and K lines, we also find a potential signal from ionized calcium (4.1 $\sigma$). Interestingly, this latter signal originates from just one of the transit measurements - with a 4.9$\sigma$ detection at this epoch. Unfortunately, due to the low significance of the measured sodium signal and the potentially variable Ca$^+$ signal, we estimate the p-values of these signals to be too high (corresponding to <4$\sigma$) to claim unambiguous exospheric detections. By comparing the observed signals with artificial signals injected early in the analysis, the absorption by Na and Ca$^+$ are estimated to be at a level of approximately 2.3$\times 10^{-3}$ and 7.0$\times 10^{-2}$ respectively, relative to the stellar spectrum.Comment: 15 pages, 8 figures, submission updated after English language editing, submission updated to correct a mistaken cross-reference noticed in A&A proo

The "Symplectic Camel Principle" and Semiclassical Mechanics

Gromov's nonsqueezing theorem, aka the property of the symplectic camel, leads to a very simple semiclassical quantiuzation scheme by imposing that the only "physically admissible" semiclassical phase space states are those whose symplectic capacity (in a sense to be precised) is nh + (1/2)h where h is Planck's constant. We the construct semiclassical waveforms on Lagrangian submanifolds using the properties of the Leray-Maslov index, which allows us to define the argument of the square root of a de Rham form.Comment: no figures. to appear in J. Phys. Math A. (2002

High Resolution Observations using Adaptive Optics: Achievements and Future Needs

Over the last few years, several interesting observations were obtained with the help of solar Adaptive Optics (AO). In this paper, few observations made using the solar AO are enlightened and briefly discussed. A list of disadvantages with the current AO system are presented. With telescopes larger than 1.5m are expected during the next decade, there is a need to develop the existing AO technologies for large aperture telescopes. Some aspects of this development are highlighted. Finally, the recent AO developments in India are also presented

Striation and convection in penumbral filaments

Observations with the 1-m Swedish Solar Telescope of the flows seen in penumbral filaments are presented. Time sequences of bright filaments show overturning motions strikingly similar to those seen along the walls of small isolated structures in the active regions. The filaments show outward propagating striations with inclination angles suggesting that they are aligned with the local magnetic field. We interpret it as the equivalent of the striations seen in the walls of small isolated magnetic structures. Their origin is then a corrugation of the boundary between an overturning convective flow inside the filament and the magnetic field wrapping around it. The outward propagation is a combination of a pattern motion due to the downflow observed along the sides of bright filaments, and the Evershed flow. The observed short wavelength of the striation argues against the existence of a dynamically significant horizontal field inside the bright filaments. Its intensity contrast is explained by the same physical effect that causes the dark cores of filaments, light bridges and `canals'. In this way striation represents an important clue to the physics of penumbral structure and its relation with other magnetic structures on the solar surface. We put this in perspective with results from the recent 3-D radiative hydrodynamic simulations.Comment: Accepted for publication in A&

Proposal For A Quantum Hall Pump

A device is proposed that is similar in spirit to the electron turnstile except that it operates within a quantum Hall fluid. In the integer quantum Hall regime, this device pumps an integer number of electrons per cycle. In the fractional regime, it pumps an integer number of fractionally charged quasiparticles per cycle. It is proposed that such a device can make an accurate measurement of the charge of the quantum Hall effect quasiparticles.Comment: 4 pages, LaTeX, 4 figures include

Direct imaging of a massive dust cloud around R Coronae Borealis

We present recent polarimetric images of the highly variable star R CrB using ExPo and archival WFPC2 images from the HST. We observed R CrB during its current dramatic minimum where it decreased more than 9 mag due to the formation of an obscuring dust cloud. Since the dust cloud is only in the line-of-sight, it mimics a coronograph allowing the imaging of the star's circumstellar environment. Our polarimetric observations surprisingly show another scattering dust cloud at approximately 1.3" or 2000 AU from the star. We find that to obtain a decrease in the stellar light of 9 mag and with 30% of the light being reemitted at infrared wavelengths (from R CrB's SED) the grains in R CrB's circumstellar environment must have a very low albedo of approximately 0.07%. We show that the properties of the dust clouds formed around R CrB are best fitted using a combination of two distinct populations of grains size. The first are the extremely small 5 nm grains, formed in the low density continuous wind, and the second population of large grains (~0.14 {\mu}m) which are found in the ejected dust clouds. The observed scattering cloud, not only contains such large grains, but is exceptionally massive compared to the average cloud.Comment: 8 pages, 7 figures published in A&