Formulas and equations for finding scattering data from the Dirichlet-to-Neumann map with nonzero background potential

For the Schrodinger equation at fixed energy with a potential supported in a bounded domain we give formulas and equations for finding scattering data from the Dirichlet-to-Neumann map with nonzero background potential. For the case of zero background potential these results were obtained in [R.G.Novikov, Multidimensional inverse spectral problem for the equation -\Delta\psi+(v(x)-Eu(x))\psi=0, Funkt. Anal. i Ego Prilozhen 22(4), pp.11-22, (1988)]

Soil respiration in a northeastern US temperate forest: a 22‐year synthesis

To better understand how forest management, phenology, vegetation type, and actual and simulated climatic change affect seasonal and inter‐annual variations in soil respiration (Rs), we analyzed more than 100,000 individual measurements of soil respiration from 23 studies conducted over 22 years at the Harvard Forest in Petersham, Massachusetts, USA. We also used 24 site‐years of eddy‐covariance measurements from two Harvard Forest sites to examine the relationship between soil and ecosystem respiration (Re). Rs was highly variable at all spatial (respiration collar to forest stand) and temporal (minutes to years) scales of measurement. The response of Rs to experimental manipulations mimicking aspects of global change or aimed at partitioning Rs into component fluxes ranged from −70% to +52%. The response appears to arise from variations in substrate availability induced by changes in the size of soil C pools and of belowground C fluxes or in environmental conditions. In some cases (e.g., logging, warming), the effect of experimental manipulations on Rs was transient, but in other cases the time series were not long enough to rule out long‐term changes in respiration rates. Inter‐annual variations in weather and phenology induced variation among annual Rs estimates of a magnitude similar to that of other drivers of global change (i.e., invasive insects, forest management practices, N deposition). At both eddy‐covariance sites, aboveground respiration dominated Re early in the growing season, whereas belowground respiration dominated later. Unusual aboveground respiration patterns—high apparent rates of respiration during winter and very low rates in mid‐to‐late summer—at the Environmental Measurement Site suggest either bias in Rs and Re estimates caused by differences in the spatial scale of processes influencing fluxes, or that additional research on the hard‐to‐measure fluxes (e.g., wintertime Rs, unaccounted losses of CO2 from eddy covariance sites), daytime and nighttime canopy respiration and its impacts on estimates of Re, and independent measurements of flux partitioning (e.g., aboveground plant respiration, isotopic partitioning) may yield insight into the unusually high and low fluxes. Overall, however, this data‐rich analysis identifies important seasonal and experimental variations in Rs and Re and in the partitioning of Re above‐ vs. belowground

Infrared Observations of the Candidate LBV 1806-20 & Nearby Cluster Stars

We report near-infrared photometry, spectroscopy, and speckle imaging of the hot, luminous star we identify as candidate LBV 1806-20. We also present photometry and spectroscopy of 3 nearby stars, which are members of the same star cluster containing LBV 1806-20 and SGR 1806-20. The spectroscopy and photometry show that LBV 1806-20 is similar in many respects to the luminous ``Pistol Star'', albeit with some important differences. They also provide estimates of the effective temperature and reddening of LBV 1806-20, and confirm distance estimates, leading to a best estimate for the luminosity of this star of $> 5 \times 10^6 L_{\odot}$. The nearby cluster stars have spectral types and inferred absolute magnitudes which confirm the distance (and thus luminosity) estimate for LBV 1806-20. If we drop kinematic measurements of the distance ($15.1 ^{+1.8}_{-1.3}$ kpc), we have a lower limit on the distance of $>9.5$ kpc, and on the luminosity of $>2 \times 10^6 L_{\odot}$, based on the cluster stars. If we drop both the kinematic and cluster star indicators for distance, an ammonia absorption feature sets yet another lower limit to the distance of $>5.7$ kpc, with a corresponding luminosity estimate of $>7 \times 10^5 L_{\odot}$ for the candidate LBV 1806-20. Furthermore, based on very high angular-resolution speckle images, we determine that LBV 1806-20 is not a cluster of stars, but is rather a single star or binary system. Simple arguments based on the Eddington luminosity lead to an estimate of the total mass of LBV 1806-20 (single or binary) exceeding $190 M_{\odot}$. We discuss the possible uncertainties in these results, and their implications for the star formation history of this cluster.Comment: 36 pages, including 8 figures (Figures 1 and 7 in JPG format due to space); Accepted for publication in Ap

Soil respiration in a northeastern US temperate forest: a 22‐year synthesis

To better understand how forest management, phenology, vegetation type, and actual and simulated climatic change affect seasonal and inter‐annual variations in soil respiration (Rs), we analyzed more than 100,000 individual measurements of soil respiration from 23 studies conducted over 22 years at the Harvard Forest in Petersham, Massachusetts, USA. We also used 24 site‐years of eddy‐covariance measurements from two Harvard Forest sites to examine the relationship between soil and ecosystem respiration (Re). Rs was highly variable at all spatial (respiration collar to forest stand) and temporal (minutes to years) scales of measurement. The response of Rs to experimental manipulations mimicking aspects of global change or aimed at partitioning Rs into component fluxes ranged from −70% to +52%. The response appears to arise from variations in substrate availability induced by changes in the size of soil C pools and of belowground C fluxes or in environmental conditions. In some cases (e.g., logging, warming), the effect of experimental manipulations on Rs was transient, but in other cases the time series were not long enough to rule out long‐term changes in respiration rates. Inter‐annual variations in weather and phenology induced variation among annual Rs estimates of a magnitude similar to that of other drivers of global change (i.e., invasive insects, forest management practices, N deposition). At both eddy‐covariance sites, aboveground respiration dominated Re early in the growing season, whereas belowground respiration dominated later. Unusual aboveground respiration patterns—high apparent rates of respiration during winter and very low rates in mid‐to‐late summer—at the Environmental Measurement Site suggest either bias in Rs and Re estimates caused by differences in the spatial scale of processes influencing fluxes, or that additional research on the hard‐to‐measure fluxes (e.g., wintertime Rs, unaccounted losses of CO2 from eddy covariance sites), daytime and nighttime canopy respiration and its impacts on estimates of Re, and independent measurements of flux partitioning (e.g., aboveground plant respiration, isotopic partitioning) may yield insight into the unusually high and low fluxes. Overall, however, this data‐rich analysis identifies important seasonal and experimental variations in Rs and Re and in the partitioning of Re above‐ vs. belowground

Evaluating remote sensing of deciduous forest phenology at multiple spatial scales using PhenoCam imagery

Plant phenology regulates ecosystem services at local and global scales and is a sensitive indicator of global change. Estimates of phenophase transition dates, such as the start of spring or end of autumn, can be derived from sensor-based time series data at the near-surface and remote scales, but must be interpreted in terms of biologically relevant events. We use the PhenoCam archive of digital repeat photography to implement a consistent protocol for visual assessment of canopy phenology at 13 temperate deciduous forest sites throughout eastern North America, as well as to perform digital image analysis for time series-based estimates of phenology dates. We then compare these near-surface results to remote sensing metrics of phenology at the landscape scale, derived from the Moderate Resolution Imaging Spectroradiometer (MODIS) and Advanced Very High Resolution Radiometer (AVHRR) sensors. We present a new type of curve fit, using a generalized sigmoid, to estimate phenology dates. We quantify the statistical uncertainty of phenophase transition dates estimated using this method and show that the generalized sigmoid results in less statistical uncertainty than other curve-fitting methods. Additionally, we find that dates derived from analysis of high-frequency PhenoCam imagery have smaller uncertainties than remote sensing metrics of phenology, and that dates derived from the remotely-sensed enhanced vegetation index (EVI) have smaller uncertainty than those derived from the normalized difference vegetation index (NDVI). Near-surface time series estimates for the start of spring are found to closely match visual assessment of leaf out, as well as remote sensing-derived estimates of the start of spring. However late spring and autumn phenology exhibit larger differences between near-surface and remote scales. Differences in late spring phenology between near-surface and remote scales are found to correlate with a landscape metric of deciduous forest cover. These results quantify the effect of landscape heterogeneity when aggregating to the coarser spatial scales of remote sensing, and demonstrate the importance of accurate curve fitting and vegetation index selection when analyzing and interpreting phenology time series.Organismic and Evolutionary Biolog

Markov analysis of stochastic resonance in a periodically driven integrate-fire neuron

We model the dynamics of the leaky integrate-fire neuron under periodic stimulation as a Markov process with respect to the stimulus phase. This avoids the unrealistic assumption of a stimulus reset after each spike made in earlier work and thus solves the long-standing reset problem. The neuron exhibits stochastic resonance, both with respect to input noise intensity and stimulus frequency. The latter resonance arises by matching the stimulus frequency to the refractory time of the neuron. The Markov approach can be generalized to other periodically driven stochastic processes containing a reset mechanism.Comment: 23 pages, 10 figure

Ensembles of Gustatory Cortical Neurons Anticipate and Discriminate Between Tastants in a Single Lick

The gustatory cortex (GC) processes chemosensory and somatosensory information and is involved in learning and anticipation. Previously we found that a subpopulation of GC neurons responded to tastants in a single lick (Stapleton et al., 2006). Here we extend this investigation to determine if small ensembles of GC neurons, obtained while rats received blocks of tastants on a fixed ratio schedule (FR5), can discriminate between tastants and their concentrations after a single 50 μL delivery. In the FR5 schedule subjects received tastants every fifth (reinforced) lick and the intervening licks were unreinforced. The ensemble firing patterns were analyzed with a Bayesian generalized linear model whose parameters included the firing rates and temporal patterns of the spike trains. We found that when both the temporal and rate parameters were included, 12 of 13 ensembles correctly identified single tastant deliveries. We also found that the activity during the unreinforced licks contained signals regarding the identity of the upcoming tastant, which suggests that GC neurons contain anticipatory information about the next tastant delivery. To support this finding we performed experiments in which tastant delivery was randomized within each block and found that the neural activity following the unreinforced licks did not predict the upcoming tastant. Collectively, these results suggest that after a single lick ensembles of GC neurons can discriminate between tastants, that they may utilize both temporal and rate information, and when the tastant delivery is repetitive ensembles contain information about the identity of the upcoming tastant delivery

Plasma flows during the ablation stage of an over-massed pulsed-power-driven exploding planar wire array

We characterize the plasma flows generated during the ablation stage of an over-massed exploding planar wire array, fielded on the COBRA pulsed-power facility (1 MA peak current, 250 ns rise time). The planar wire array is designed to provide a driving magnetic field (80-100 T) and current per wire distribution (about 60 kA), similar to that in a 10 MA cylindrical exploding wire array fielded on the Z machine. Over-massing the arrays enables continuous plasma ablation over the duration of the experiment. The requirement to over-mass on the Z machine necessitates wires with diameters of 75-100 $\mu$m, which are thicker than wires usually fielded on wire array experiments. To test ablation with thicker wires, we perform a parametric study by varying the initial wire diameter between 33-100 $\mu$m. The largest wire diameter (100 $\mu$m) array exhibits early closure of the AK gap, while the gap remains open during the duration of the experiment for wire diameters between 33-75 $\mu$m. Laser plasma interferometry and time-gated XUV imaging are used to probe the plasma flows ablating from the wires. The plasma flows from the wires converge to generate a pinch, which appears as a fast-moving ($V \approx {100}$ kms$^{-1}$) column of increased plasma density ($\bar{n}_e \approx 2 \times 10^{18}$ cm$^{-3}$) and strong XUV emission. Finally, we compare the results with three-dimensional resistive-magnetohydrodynamic (MHD) simulations performed using the code GORGON, the results of which reproduce the dynamics of the experiment reasonably well.Comment: 14 pages; 14 figure