Saha Equation Normalized to Total Atomic Number

The Saha equation describes the relative number density of consecutive ionization levels of a given atomic species under conditions of thermodynamic equilibrium in an ionized gas. Because the number density in the denominator may be very small, special steps must be taken to ensure numerical stability. In this paper we recast the equation into a form in which each ionization fraction is normalized by the total number density of the atomic species, analogous to the Boltzmann equation describing the distribution of excitation states for a given ion

The General Relativistic Instability of Massive Stars

Binding energy of massive polytrope and general relativistic instability of massive star

Post-Band Merge Utilities Applied to Spitzer Pleiades Data

Band merging extracted point sources observed in multiple wavelength bands is generally done purely on the basis of positional information in order to avoid photometric biases. Automated merge decisions can be more optimal with better position estimation and more realistic modeling of positional estimation errors. Unfortunately, extraction software often does not provide the most accurate positional information possible, and so post-band merge utilities have been developed and implemented to refine both the source positions and the error modeling. Subsequent band merging of the refined detections improves the completeness and reliability of the multi-band source catalog. Application to Spitzer Space Telescope mapping observations of the Pleiades star cluster demonstrates some aspects of the improved band merging

Considerations When Sampling Spruce Budworm Egg Masses on Balsam Fir in the Lake States: Low to Extreme Population Levels

Nineteen balsam fir trees, Abies balsamea, from five spruce-fir stands in Michigan\u27s Upper Peninsula, were used to study egg mass densities and distributions. Ten were used to study the effects of branch size on mass density estimates. The foliage surface area and the number of new egg masses spruce budworm, Choristoneura fumiferana, were determined for each branch, and the top of each tree and (or) the branch segment of interest. We determined the effects of the bias and the variance of the estimator, of sampling different parts of the tree, and of sampling different size branches. Points that should be considered when estimating spruce budworm egg mass densities on balsam fir were identified. Generally, sampling whole branches from the mid-crown gave the most precise and accurate estimates of tree egg mass density

Spruce Budworm Egg Mass Density on Balsam Fir: Low to Extreme Population Levels (Lepidoptera: Tortricidae)

A study was initiated in Michigan\u27s Upper Peninsula to develop improved foliage sampling methods for spruce budworm, Choristoneura fumiferana (Clemens), egg masses. Four balsam fir, Abies balsamea, trees were chosen from each of four stands in 1979, and four balsam fir trees were chosen from one stand in 1980. The number of new egg masses, foliage surface area, and crown and quadrant classes of each branch were determined for all trees. Egg mass density for each part of the tree was determined by dividing total number of egg masses by total surfaee area. The 20 trees were divided into five groups with forecasted budworm damage varying from low to extreme. On the average the egg mass density (egg mass/lOOO cm2) of the lower-crown was 58% lower than the egg mass density of the entire tree; the mid-crown had 18% higher cgg mass density than the entire tree, the upper-crown had 63% higher density than the entire tree, and the tree top had 69% higher density than the entire tree. There was no strong trend to the small absolute differences in density among the four quadrants. Sampling at mid-crown may lead to over- or underestimation of tree egg mass density. The seriousness of such errors would depend on the bias and where the sample is taken vertically in the mid-crown

Cauldron subsidence and subglacial floods

Ice cauldrons are depressions which form at the surface of ice sheets when an underlying subglacial lake empties. Notable examples of such cauldrons occur on the surface of the Vatnajökull ice cap in Iceland, and in particular are formed when subglacial volcanic eruptions occur. More generally, cauldrons will form when a subglacial lake empties during a jökulhlaup. The rate of subsidence of the ice surface is related to the rate at which the subglacial water empties from the lake. We use a viscous version of classical beam theory applied to the ice sheet to determine the relation between the subsidence rate and flood discharge, and we use the results to make inferences concerning ring fracture spacings in cauldrons, the consequent effect on flood discharge dynamics, and the likely nature of subsidence events in the Antarctic Ice Sheet

Regression Equations and Table for Estimating Numbers of Eggs in Jack Pine Budworm (Lepidoptera: Tortricidae) Egg Masses in Michigan

Three simple linear regression equations were developed to estimate the numbers of eggs in jack pine budworm, Choristoneura pinus pinus, egg masses in Michigan. One equation was developed for each of 2-row, 2-row +, and 3-row egg masses. A table of estimated numbers of eggs per egg mass is given for each of the three row types for egg mass lengths from 1 to 25 nun

Considerations When Sampling Spruce Budworm Egg Masses on Balsam Fir and White Spruce in the Lake States: Low Population Levels

One cluster each of balsam fir, Abies balsamea, and white spruce, Picea glauca, trees was chosen from each of five stands of spruce-fir in Michigan\u27s Upper Peninsula. The foliage surface area and the number of new egg masses of the spruce budworm, Choristoneura fumiferana, were determined for each branch and the top of each tree. The effects, in terms of the bias and the variance of the estimator, of sampling in different parts of the tree and with various size branches were determined. Factors that the sampler should consider in developing sampling plans to estimate spruce bud worm egg mass densities in mixed spruce-fir stands were identified. Egg mass density and its per branch variance may be considerably higher in white spruce than in balsam fir. Sampling whole feasible branches at mid-crown yielded, in general, the most precise and accurate estimates of tree egg mass density