A variational perturbation scheme for many-particle systems in the functional integral approach

A variational Perturbation theory based on the functional integral approach is formulated for many-particle systems. Using the variational action obtained through Jensen-Peierls' inequality, a perturbative expansion scheme for the thermodynamic potential is established. A modified Wick's theorem is obtained for the variational perturbation expansions. This theorem allows one to carry out systematic calculations of higher order terms without worrying about the double counting problem. A model numerical calculation was carried out on a nucleon gas system interacting through the Yukawa-type potential to test the efficiency of the present method.Comment: accepted for publication in Phys. Rev.

Thinning response in Alnus rubra and Arbutus menziesii : effects of spacing, light, and moisture

In western Oregon, hardwood trees occupy 20% of the timberland but account for less than 1% of the timber harvest. Information about how to manage them effectively is limited. The objective of this study was to examine: 1) effect of thinning on tree growth, plant moisture stress, and crown cover expansion and 2) the inter-relationships of these three factors. The study site for red alder was on the western slope of the central Oregon Coast Range. The trees were about 20 years old when thinned in 1986. The red alder experiment was designed as a completely randomized design and each treatment was replicated three times. The average stem densities per ha were 1466(100%), 535(36%), and 412(28%). The Pacific madrone study site was about 8 km west of Central Point in southwestern Oregon. Tree ages ranged from 40 to 45 years when thinning was done in 1984. Measurements continued for 5 years. The study was designed as a randomized block design and composed of three blocks. The average stem densities per ha were 2290(100%), 486(21%), and 272(12%). The data were analyzed for two groups of sample trees, average plot trees and crop trees. The average plot trees were random samples of each plot. The crop trees were dominant trees that would be left to harvest at the end of the rotation. The effect of thinning on soil moisture availability was evaluated by measuring predawn plant moisture stress (PMS) with a pressure chamber once in a summer. To determine the effect of thinning on light availability, five fisheye photographs of crown cover were taken per each plot and analyzed using an automated fisheye photograph analysis system. For tree basal area, red alder crop trees in the heavily thinned plot increased 66% (13.1 cm²) more than those in the control stand but average plot trees did not grow more. Tree growth of red alder was negatively correlated with stem density, but was not significantly correlated with plant moisture stress. For Pacific madrone, average plot trees in the heavily thinned stand increased 286% more than those in the control stand, while crop trees increased 589% (13.2 cm²) more. Tree growth of Pacific madrone was significantly correlated not only with stem density but also with plant moisture stress. However, it was not significantly correlated with crown cover. Plant moisture stress might be a reason for marked effects of thinning on Pacific madrone tree growth. Total height and merchantable height growth were not significantly different among the treatments for both species. For red alder, however, height growth of the heavily thinned plot was significantly less than that of the control plot. Total height and merchantable height growth were not significantly correlated with stem density or plant moisture stress. There were no significant differences in plant moisture stress among the treatments for red alder. For Pacific madrone, however, plant moisture stresses of the thinned plots were 37-42% lower than those of the control plot in the third and fifth year after thinning. The increases of stand basal area and volume were not significantly different among the treatments for both species. If the management objective is to increase growth of crop trees without losing stand productivity, it is recommended that the stands should be managed at a low density range (stand density index 300-360 for red alder, 200-290 for Pacific madrone)

Probability-Based Crack Width Estimation Model for Flexural Members of Underground RC Box Culverts

Crack control for slabs and beams in current design practices in Korea are based on the Frosch’s model, which is adapted in ACI 318. It is more difficult to have consistent quality control in underground construction sites, such as the RC box culverts used for electric power distribution built below the ground level. There are more discrepancies between the as-built dimensions and the design dimensions provided in drawings in these structures. Due to this variability in construction error, the crack widths measured in such structures have higher potential to have more differences than the calculated values. Although crack control is a serviceability concern, if the owner chooses to have a target crack width that needs better control, crack width estimations can be improved by considering such construction variability. The probability-based crack width model suggested in this study will allow minimizing the discrepancies between the measured and calculated crack widths and provide reliable estimations of crack widths. Typical size of slabs and beams ranging between 300 mm (12 in.) to 500 mm (20 in.) used in underground RC box culverts in Korea were tested under the four-point bending test program. The thicker specimens had smaller bar spacings which created more cracks with smaller crack widths. However, with smaller crack widths generated in these specimens, there were more errors between the measurements and calculated values. From site investigations in Korea, the thickness of slabs in underground box culverts varied the most among all parameters. As a result, the bottom concrete covers had the highest variability. Bottom concrete covers and bar spacings are the two most important parameters in concrete crack control. A probability-based crack width estimation model for flexural members was developed in this study to consider this construction variability. Monte Carlo simulations were performed to evaluate the probabilistic characteristics of the design surface crack widths with a target width of either 0.3 mm (12 mils) or 0.5 mm (20 mils). The probabilistic models of design variables included in the crack width estimation model were generated based on field-collected information from construction sites in Korea. Because the surface crack widths in RC flexural members are sensitive to the construction errors of concrete cover depths, and since there are differences between the assumed and actual stress distribution closer to the reinforcing bars, the probability of having surface cracks of 0.3 mm width (12 mils) is found to be quite high, such as 89% at the positive moment region (mid-span, bottom surface) of the top slab in RC box culverts and 45% for the negative moment region (support area, top surface) of the top slab with current design practice. In order to ensure crack widths to be smaller than the design target width, probability-based crack width factors are recommended in this study to improve estimations depending on the selected target reliability levels