Projected Gross-Pitaevskii equation for harmonically confined Bose gases at finite temperature

We extend the projected Gross-Pitaevskii equation formalism of Davis [Phys. Rev. Lett. 87, 160402 (2001)] to the experimentally relevant case of thermal Bose gases in harmonic potentials and outline a robust and accurate numerical scheme that can efficiently simulate this system. We apply this method to investigate the equilibrium properties of the harmonically trapped three-dimensional projected Gross-Pitaevskii equation at finite temperature and consider the dependence of condensate fraction, position, and momentum distributions and density fluctuations on temperature. We apply the scheme to simulate an evaporative cooling process in which the preferential removal of high-energy particles leads to the growth of a Bose-Einstein condensate. We show that a condensate fraction can be inferred during the dynamics even in this nonequilibrium situation.

Properties of the stochastic Gross-Pitaevskii equation: finite temperature Ehrenfest relations and the optimal plane wave representation

We present Ehrenfest relations for the high temperature stochastic Gross-Pitaevskii equation description of a trapped Bose gas, including the effect of growth noise and the energy cutoff. A condition for neglecting the cutoff terms in the Ehrenfest relations is found which is more stringent than the usual validity condition of the truncated Wigner or classical field method-that all modes are highly occupied. The condition requires a small overlap of the nonlinear interaction term with the lowest energy single particle state of the noncondensate band, and gives a means to constrain dynamical artefacts arising from the energy cutoff in numerical simulations. We apply the formalism to two simple test problems: (i) simulation of the Kohn mode oscillation for a trapped Bose gas at zero temperature, and (ii) computing the equilibrium properties of a finite temperature Bose gas within the classical field method. The examples indicate ways to control the effects of the cutoff, and that there is an optimal choice of plane wave basis for a given cutoff energy. This basis gives the best reproduction of the single particle spectrum, the condensate fraction and the position and momentum densities.

Openness and economic growth

The themes of this thesis are that international trade and foreign direct investment (FDI) are closely related and that they have varying impacts on economic growth in countries at different stages of development. The thesis consists of three empirical studies. The first one examines the causal relationship between FDI and trade in China. The empirical study is based on a panel of bilateral data for China and 19 home countries/regions over the period 1984-98. The specific feature of the study is that econometric techniques designed specially for panel data are applied to test for unit roots and causality. The results indicate a virtuous procedure of development for China. The growth of China’s imports causes growth in inward FDI from a home country/region, which in turn causes the growth of exports from China to the home country/region. The growth of exports causes the growth of imports. This virtuous procedure is the result of China’s policy of opening to the outside world. China has been encouraging export-oriented FDI and reducing trade barriers. Such policy instruments should be further encouraged in order to enhance economic growth. In the second study, an extended gravity model is constructed to identify the main causes of recent trade growth in OECD countries. The specific features include (a) the explicit introduction of R&D and FDI as two important explanatory variables into an augmented gravity equation; (b) the adoption of a panel data approach, and (c) the careful treatment of endogeneity. The main findings are that the levels and similarities of market size, domestic R&D stock and inward FDI stock are positively related to the volume of bilateral trade, while the geographical distance, exchange rate and relative factor endowments, has a negative impact. These findings lend support to new trade, FDI and economic growth theories. The third study evaluates the impact of openness on growth in different country groups. This research distinguishes itself from many existing studies in three aspects: first, both trade and FDI are included in the measurement of openness. Second, countries are divided' into three groups according to their development stages to compare the roles of FDI and trade in different groups. Third, the possible problems of endogeneity and multicollinearity of FDI and trade are carefully dealt with in a panel data setting. The main findings are that FDI and trade are both beneficial to a country's development. However, trade has positive effects on growth in all country groups but FDI has positive effects on growth only in the country groups which have had moderate development. The findings suggest FDI and trade may affect growth under different conditions.

(Table S1) Stable isotope record and growth rates of cultured Mytilus edulis

To study the effects of temperature, salinity, and life processes (growth rates, size, metabolic effects, and physiological/genetic effects) on newly precipitated bivalve carbonate, we quantified shell isotopic chemistry of adult and juvenile animals of the intertidal bivalve Mytilus edulis (Blue mussel) collected alive from western Greenland and the central Gulf of Maine and cultured them under controlled conditions. Data for juvenile and adult M. edulis bivalves cultured in this study, and previously by Wanamaker et al. (2006, doi:10.1029/2005GC001189), yielded statistically identical paleotemperature relationships. On the basis of these experiments we have developed a species-specific paleotemperature equation for the bivalve M. edulis [T °C = 16.28 (±0.10) - 4.57 (±0.15) {d18Oc VPBD - d18Ow VSMOW} + 0.06 (±0.06) {d18Oc VPBD - d18Ow VSMOW}**2; r**2 = 0.99; N = 323; p < 0.0001]. Compared to the Kim and O'Neil (1997) inorganic calcite equation, M. edulis deposits its shell in isotope equilibrium (d18Ocalcite) with ambient water. Carbon isotopes (d13Ccalcite) from sampled shells were substantially more negative than predicted values, indicating an uptake of metabolic carbon into shell carbonate, and d13Ccalcite disequilibrium increased with increasing salinity. Sampled shells of M. edulis showed no significant trends in d18Ocalcite based on size, cultured growth rates, or geographic collection location, suggesting that vital effects do not affect d18Ocalcite in M. edulis. The broad modern and paleogeographic distribution of this bivalve, its abundance during the Holocene, and the lack of an intraspecies physiologic isotope effect demonstrated here make it an ideal nearshore paleoceanographic proxy throughout much of the North Atlantic Ocean.

Hyperspectral sensing to detect the impact of herbicide drift on cotton growth and yield

Yield loss in crops is often associated with plant disease or external factors such as environment, water supply and nutrient availability. Improper agricultural practices can also introduce risks into the equation. Herbicide drift can be a combination of improper practices and environmental conditions which can create a potential yield loss. As traditional assessment of plant damage is often imprecise and time consuming, the ability of remote and proximal sensing techniques to monitor various bio-chemical alterations in the plant may offer a faster, non-destructive and reliable approach to predict yield loss caused by herbicide drift. This paper examines the prediction capabilities of partial least squares regression (PLS-R) models for estimating yield. Models were constructed with hyperspectral data of a cotton crop sprayed with three simulated doses of the phenoxy herbicide 2,4-D at three different growth stages. Fibre quality, photosynthesis, conductance, and two main hormones, indole acetic acid (IAA) and abscisic acid (ABA) were also analysed. Except for fibre quality and ABA, Spearman correlations have shown that these variables were highly affected by the chemical. Four PLS-R models for predicting yield were developed according to four timings of data collection: 2, 7, 14 and 28 days after the exposure (DAE). As indicated by the model performance, the analysis revealed that 7 DAE was the best time for data collection purposes (RMSEP = 2.6 and R2 = 0.88), followed by 28 DAE (RMSEP = 3.2 and R2 = 0.84). In summary, the results of this study show that it is possible to accurately predict yield after a simulated herbicide drift of 2,4-D on a cotton crop, through the analysis of hyperspectral data, thereby providing a reliable, effective and non-destructive alternative based on the internal response of the cotton leaves.

Growth and body nutrient deposition of two broiler commercial genetic lines

The objective of this work was to study growth and body nutrient deposition profiles of male and female Cobb and Ross broilers using Gompertz equations. A total number of 1,920 one- to 56-day-old broilers were used. A randomized experimental design in a factorial arrangement (2 strains x 2 sex), with 4 replicates of 120 birds each, was applied. Diets were formulated to supply the nutrient requirements recommended by the genetic companies. A sample of birds was weekly weighed and sacrificed after 24 hours fasting. Carcasses were de-feathered and weighed again. The parameters of the Gompertz equation for body weight and its components (water, ashes, protein, and fat) were estimated. An interaction (p<0.05) between sex and breed was observed for mature weight (Wm) (kg), growth rate (b) (daily) and time at maximum growth rate (t*) (day) of body weight, and body water and ash. Cobb was presented earlier growth and body protein and ash deposition. Ross strain was superior in body water deposition.

Damage and fracture algorithm using the screened Poisson equation and local remeshing

We propose a crack propagation algorithm which is independent of particular constitutive laws and specific element technology. It consists of a localization limiter in the form of the screened Poisson equation with local mesh refinement. This combination allows the cap- turing of strain localization with good resolution, even in the absence of a sufficiently fine initial mesh. In addition, crack paths are implicitly defined from the localized region, cir- cumventing the need for a specific direction criterion. Observed phenomena such as mul- tiple crack growth and shielding emerge naturally from the algorithm. In contrast with alternative regularization algorithms, curved cracks are correctly represented. A staggered scheme for standard equilibrium and screened equations is used. Element subdivision is based on edge split operations using a given constitutive quantity (either damage or void fraction). To assess the robustness and accuracy of this algorithm, we use both quasi-brittle benchmarks and ductile tests.

Detailed analysis of a conservative difference approximation for the time fractional diffusion equation

Diffusion equations that use time fractional derivatives are attractive because they describe a wealth of problems involving non-Markovian Random walks. The time fractional diffusion equation (TFDE) is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order α ∈ (0, 1). Developing numerical methods for solving fractional partial differential equations is a new research field and the theoretical analysis of the numerical methods associated with them is not fully developed. In this paper an explicit conservative difference approximation (ECDA) for TFDE is proposed. We give a detailed analysis for this ECDA and generate discrete models of random walk suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation. The stability and convergence of the ECDA for TFDE in a bounded domain are discussed. Finally, some numerical examples are presented to show the application of the present technique.