Average ground-state energy of finite Fermi systems

Semiclassical theories such as the Thomas-Fermi and Wigner-Kirkwood methods give a good description of the smooth average part of the total energy of a Fermi gas in some external potential when the chemical potential is varied. However, in systems with a fixed number of particles N, these methods overbind the actual average of the quantum energy as N is varied. We describe a theory that accounts for this effect. Numerical illustrations are discussed for fermions trapped in a harmonic oscillator potential and in a hard-wall cavity, and for self-consistent calculations of atomic nuclei. In the latter case, the influence of deformations on the average behavior of the energy is also considered.

Annual Average Daily Traffic on the Interstate System, 2010

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On the zeta-function regularization of a two-dimensional series of epsten-Hurwitz type

For a few years now, the study of quantum field theories in partially compactified space-time manifolds has acquired increasing importance in several domains of quantum physics. Let me just mention the issues of dimensional reduction and spontaneous compactification, and the multiple questions associated with the study of quantum field theories in the presence of boundaries (like the Casimir effect) and on curved space-time (manifolds with curvature and nontrivial topology), a step towards quantum gravity.

Comparing Basal Area Diameter Distributions Estimated by Tree Species and for the Entire Stock in a Mixed Stand

Summary

Multivariate analysis applied to the study of the relationship between soil and plant properties in a peach orchard

In the State of Rio Grande do Sul, the municipality of Pelotas is responsible for 90 % of peach production due to its suitable climate and soil conditions. However, there is the need for new studies that aim at improved fruit quality and increased yield. The aim of this study was to evaluate the relationship that exists between soil physical properties and properties in the peach plant in the years 2010 and 2011 by the technique of multivariate canonical correlation. The experiment was conducted in a peach orchard located in the municipality of Morro Redondo, RS, Brazil, where an experimental grid of 101 plants was established. In a trench dug beside each one of the 101 plants, soil samples were collected to determine silt, clay, and sand contents, soil density, total porosity, macroporosity, microporosity, and volumetric water content in the 0.00-0.10 and 0.10-0.20 m layers, as well as the depth of the A horizon. In each plant and in each year, the following properties were assessed: trunk diameter, fruit size and number of fruits per plant, average weight of the fruit per plant, fruit pulp firmness, Brix content, and yield from the orchard. Exploratory analysis of the data was undertaken by descriptive statistics, and the relationships between the physical properties of the soil and of the plant were assessed by canonical correlation analysis. The results showed that the clay and microporosity variables were those that exhibited the highest coefficients of canonical cross-loading with the plant properties in the soil layers assessed, and that the variable of mean weight of the fruit per plant was that which had the highest coefficients of canonical loading within the plant group for the two years assessed.

Linear least squares estimation of the first order moving average parameter

We propose an iterative procedure to minimize the sum of squares function which avoids the nonlinear nature of estimating the first order moving average parameter and provides a closed form of the estimator. The asymptotic properties of the method are discussed and the consistency of the linear least squares estimator is proved for the invertible case. We perform various Monte Carlo experiments in order to compare the sample properties of the linear least squares estimator with its nonlinear counterpart for the conditional and unconditional cases. Some examples are also discussed

A model of cellular dosimetry for macroscopic tumors in radiopharmaceutical therapy.

PURPOSE: In the radiopharmaceutical therapy approach to the fight against cancer, in particular when it comes to translating laboratory results to the clinical setting, modeling has served as an invaluable tool for guidance and for understanding the processes operating at the cellular level and how these relate to macroscopic observables. Tumor control probability (TCP) is the dosimetric end point quantity of choice which relates to experimental and clinical data: it requires knowledge of individual cellular absorbed doses since it depends on the assessment of the treatment's ability to kill each and every cell. Macroscopic tumors, seen in both clinical and experimental studies, contain too many cells to be modeled individually in Monte Carlo simulation; yet, in particular for low ratios of decays to cells, a cell-based model that does not smooth away statistical considerations associated with low activity is a necessity. The authors present here an adaptation of the simple sphere-based model from which cellular level dosimetry for macroscopic tumors and their end point quantities, such as TCP, may be extrapolated more reliably. METHODS: Ten homogenous spheres representing tumors of different sizes were constructed in GEANT4. The radionuclide 131I was randomly allowed to decay for each model size and for seven different ratios of number of decays to number of cells, N(r): 1000, 500, 200, 100, 50, 20, and 10 decays per cell. The deposited energy was collected in radial bins and divided by the bin mass to obtain the average bin absorbed dose. To simulate a cellular model, the number of cells present in each bin was calculated and an absorbed dose attributed to each cell equal to the bin average absorbed dose with a randomly determined adjustment based on a Gaussian probability distribution with a width equal to the statistical uncertainty consistent with the ratio of decays to cells, i.e., equal to Nr-1/2. From dose volume histograms the surviving fraction of cells, equivalent uniform dose (EUD), and TCP for the different scenarios were calculated. Comparably sized spherical models containing individual spherical cells (15 microm diameter) in hexagonal lattices were constructed, and Monte Carlo simulations were executed for all the same previous scenarios. The dosimetric quantities were calculated and compared to the adjusted simple sphere model results. The model was then applied to the Bortezomib-induced enzyme-targeted radiotherapy (BETR) strategy of targeting Epstein-Barr virus (EBV)-expressing cancers. RESULTS: The TCP values were comparable to within 2% between the adjusted simple sphere and full cellular models. Additionally, models were generated for a nonuniform distribution of activity, and results were compared between the adjusted spherical and cellular models with similar comparability. The TCP values from the experimental macroscopic tumor results were consistent with the experimental observations for BETR-treated 1 g EBV-expressing lymphoma tumors in mice. CONCLUSIONS: The adjusted spherical model presented here provides more accurate TCP values than simple spheres, on par with full cellular Monte Carlo simulations while maintaining the simplicity of the simple sphere model. This model provides a basis for complementing and understanding laboratory and clinical results pertaining to radiopharmaceutical therapy.

Intérêt de l'échographie du diamètre de l'enveloppe du nerf optique pour la détection non invasive de l'hypertension intracrânienne [Interest of optic nerve sheath diameter ultrasonography in dectecting non-invasively raised intracranial pressure].

Intracranial hypertension is an emergency suspected from clinical symptoms, imaging data and ophthalomologic signs. Intracranial hypertension is confirmed by invasive intracranial monitoring, which is the gold standard technique to measure intracranial pressure (ICP). Because of complications, hemorrhage or infection, non-invasive methods have been developed such as neuroimaging, transcranial Doppler sonography and optic nerve sheath diameter (ONSD) ultrasonography. We have reviewed ONSD technique that detects intracranial hypertension related volume variations of subarachnoid space along the retro bulbar segment of the optic nerve. Technique, indications and prospects are discussed.

Annual Average Daily Traffic on the Interstate System, 2012

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