Microcanonical temperature for a classical field: Application to Bose-Einstein condensation

We show that the projected Gross-Pitaevskii equation (PGPE) can be mapped exactly onto Hamilton's equations of motion for classical position and momentum variables. Making use of this mapping, we adapt techniques developed in statistical mechanics to calculate the temperature and chemical potential of a classical Bose field in the microcanonical ensemble. We apply the method to simulations of the PGPE, which can be used to represent the highly occupied modes of Bose condensed gases at finite temperature. The method is rigorous, valid beyond the realms of perturbation theory, and agrees with an earlier method of temperature measurement for the same system. Using this method we show that the critical temperature for condensation in a homogeneous Bose gas on a lattice with a uv cutoff increases with the interaction strength. We discuss how to determine the temperature shift for the Bose gas in the continuum limit using this type of calculation, and obtain a result in agreement with more sophisticated Monte Carlo simulations. We also consider the behavior of the specific heat.

The interaction of nitrogen application and temperature during reproductive stage on spikelet sterility in field-grown rice

Increased grain yield in response to high rates of application of nitrogen (N) fertiliser is often limited by increased spikelet sterility, particularly under low temperature conditions in the New South Wales ( NSW) rice industry. In 3 field experiments, different N rates were applied for different sowing dates to investigate the interaction between N rate and temperature during microspore development on spikelet sterility and grain yield. In one experiment the effect of water depth on spikelet sterility was also investigated. Engorged pollen production, spikelet sterility, and yield and its components were recorded. Application of N affected a few different processes that lead into spikelet sterility. Application of N at both pre-flood (PF) and panicle initiation ( PI) significantly reduced the number of engorged pollen grains per anther, which was negatively correlated with spikelet sterility. Application of N and low temperature during microspore development with the absence of deep water also decreased pollen engorgement efficiency ( the percentage of pollen grains that were engorged). Application of N further increased spikelet density, which, in turn, increased both spikelet sterility and grain yield. The combined effect of spikelet density and low temperature during microspore development explained the 44% of variation in the number of engorged pollen grains per anther. Grain yield was decreased by low temperature during microspore development in the shallow water when N was applied. Spikelet sterility as a result of late sowing was strongly correlated with minimum temperature during flowering. It is concluded that N application reduced pollen number per anther as a result of increased spikelet density, and this made the spikelets more susceptible to low temperature, causing increased spikelet sterility.

Calculation of the microcanonical temperature for the classical Bose field

The ergodic hypothesis asserts that a classical mechanical system will in time visit every available configuration in phase space. Thus, for an ergodic system, an ensemble average of a thermodynamic quantity can equally well be calculated by a time average over a sufficiently long period of dynamical evolution. In this paper, we describe in detail how to calculate the temperature and chemical potential from the dynamics of a microcanonical classical field, using the particular example of the classical modes of a Bose-condensed gas. The accurate determination of these thermodynamics quantities is essential in measuring the shift of the critical temperature of a Bose gas due to nonperturbative many-body effects.

The electric field effect on spin injection in tunneling regime

Using the quantum tunneling theory, we investigate the spin-dependent transport properties of the ferromagnetic metal/Schottky barrier/semiconductor heterojunction under the influence of an external electric field. It is shown that increasing the electric field, similar to increasing the electron density in semiconductor, will result in a slight enhancement of spin injection in tunneling regime, and this enhancement is significantly weakened when the tunneling Schottky barrier becomes stronger. Temperature effect on spin injection is also discussed. (C) 2003 Elsevier B.V. All rights reserved.

[0 0 1] zone-axis bright-field diffraction contrast from coherent Ge(Si) islands on Si(0 0 1): Dedicated to Professor Fang-hua Li on the occasion of her 70th birthday

Coherent Ge(Si)/Si(001) quantum dot islands grown by solid source molecular beam epitaxy at a growth temperature of 700degreesC were investigated using transmission electron microscopy working at 300 kV. The [001] zone-axis bright-field diffraction contrast images of the islands show strong periodicity with the change of the TEM sample substrate thickness and the period is equal to the effective extinction distance of the transmitted beam. Simulated images based on finite element models of the displacement field and using multi-beam dynamical diffraction theory show a high degree of agreement. Studies for a range of electron energies show the power of the technique for investigating composition segregation in quantum dot islands. (C) 2003 Elsevier B.V. All rights reserved.

Embracing ligands. Synthesis, characterisation and the correlation between 59Co NMR and ligand field parameters of Co(III) complexes with a new class of nitrogen-thioether multidentate ligand

The syntheses of the hexadentate ligands 2,2,10,10-tetra(methyleneamine)-4,8-dithiaundecane (PrN(4)S(2)amp), 2,2,11,11-tetra(methyleneamine)-4,9-dithiadodecane (BuN(4)S(2)amp), and 1,2-bis(4,4-methyleneamine)-2-thiapentyl)benzene (XyN(4)S(2)amp) are reported and the complexes [Co(RN(4)S(2)amp)](3+) (R = Pr, Bu, Xy) characterised by single crystal X-ray study. The low-temperature (11 K) absorption spectra have been measured in Nafion films. From the observed positions of both spin-allowed (1)A(1g) --> T-1(1g) and (1)A(1g) --> T-1(2g) and spin forbidden (1)A(1g) --> T-3(1g) and (1)A(1g) --> T-3(2g) bands, octahedral ligand-field parameters (10D(q), B and C) have been determined. DFT calculations suggest that significant interaction between the d-d and CT excitations occurs for the complexes. The calculations offer an explanation for the observed deviations from linearity of the relationship between Co-59 magnetogyric ratio and beta(DeltaE)(-1) (beta = the nephelauxetic ratio; DeltaE the energy of the (1)A(1g) --> T-1(1g) transition) for a series of amine and mixed amine/thioether donor complexes.

Numerical modelling of thermal effects in rats due to high-field magnetic resonance imaging (0.5-1 GHz)

A finite-difference time-domain (FDTD) thermal model has been developed to compute the temperature elevation in the Sprague Dawley rat due to electromagnetic energy deposition in high-field magnetic resonance imaging (MRI). The field strengths examined ranged from 11.75-23.5 T (corresponding to H-1 resonances of 0.5-1 GHz) and an N-stub birdcage resonator was used to both transmit radio-frequency energy and receive the MRI signals. With an in-plane resolution of 1.95 mm, the inhomogeneous rat phantom forms a segmented model of 12 different tissue types, each having its electrical and thermal parameters assigned. The steady-state temperature distribution was calculated using a Pennes 'bioheat' approach. The numerical algorithm used to calculate the induced temperature distribution has been successfully validated against analytical solutions in the form of simplified spherical models with electrical and thermal properties of rat muscle. As well as assisting with the design of MRI experiments and apparatus, the numerical procedures developed in this study could help in future research and design of tumour-treating hyperthermia applicators to be used on rats in vivo.

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.

Effects of Al2O3 on phase equilibria in the olivine primary phase field of the MgO-"FeO"-SiO2-Al2O3 system in equilibrium with metallic iron

Liquidus temperatures and phase equilibria have been determined in the olivine primary phase field of the MgO-FeO-SiO2-Al2O3 system. Liquidus isotherms have been determined in the temperature range from 1748 to 1873K. The results are presented in the form of pseudo-ternary sections of the MgO-FeO-SiO2 with 2 and 3wt% Al2O3 in the liquid. The study enables the liquidus to be described for a range of SiO2/MgO ratios. It was found that liquidus temperatures in the olivine primary phase field decrease with the addition of Al2O3.

Critical Temperature of a Trapped Bose Gas: Comparison of Theory and Experiment

We apply the projected Gross-Pitaevskii equation (PGPE) formalism to the experimental problem of the shift in critical temperature T-c of a harmonically confined Bose gas as reported in Gerbier , Phys. Rev. Lett. 92, 030405 (2004). The PGPE method includes critical fluctuations and we find the results differ from various mean-field theories, and are in best agreement with experimental data. To unequivocally observe beyond mean-field effects, however, the experimental precision must either improve by an order of magnitude, or consider more strongly interacting systems. This is the first application of a classical field method to make quantitative comparison with experiment.

Minimising cold damage during reproductive development among temperate rice genotypes. I. Avoiding low temperature with the use of appropriate sowing time and photoperiod-sensitive varieties

Multiple-sown field trials in 4 consecutive years in the Riverina region of south-eastern Australia provided 24 different combinations of temperature and day length, which enabled the development of crop phenology models. A crop model was developed for 7 cultivars from diverse origins to identify if photoperiod sensitivity is involved in determining phenological development, and if that is advantageous in avoiding low-temperature damage. Cultivars that were mildly photoperiod-sensitive were identified from sowing to flowering and from panicle initiation to flowering. The crop models were run for 47 years of temperature data to quantify the risk of encountering low temperature during the critical young microspore stage for 5 different sowing dates. Cultivars that were mildly photoperiod-sensitive, such as Amaroo, had a reduced likelihood of encountering low temperature for a wider range of sowing dates compared with photoperiod-insensitive cultivars. The benefits of increased photoperiod sensitivity include greater sowing flexibility and reduced water use as growth duration is shortened when sowing is delayed. Determining the optimal sowing date also requires other considerations, e. g. the risk of cold damage at other sensitive stages such as flowering and the response of yield to a delay in flowering under non-limiting conditions. It was concluded that appropriate sowing time and the use of photoperiod-sensitive cultivars can be advantageous in the Riverina region in avoiding low temperature damage during reproductive development.

Temperature and the respiratory properties of whole blood in two reptiles, Pogona barbata and Emydura signata

We investigated the capacity of two reptiles, an agamid lizard Pogona barbata and a chelid turtle Emydura signata, to compensate for the effects of temperature by making changes in their whole blood respiratory properties. This was accomplished by measuring the P-50 (at 10, 20 and 30 degrees C), hematocrit (Hct), haemoglobin concentration ([Hb]) and mean cell haemoglobin concentration (MCHC) in field acclimatised and laboratory acclimated individuals. The acute effect of temperature on P50 in P barbata, expressed as heat of oxygenation (Delta H), ranged from -16.8 +/- 1.84 to -28.5 +/- 2.73 kJ/mole. P-50 of field acclimatised P barbata increased significantly from early spring to summer at the test temperatures of 20 degrees C (43.1 +/- 1.2 to 48.8 +/- 2.1 mmHg) and 30 degrees C (54.7 +/- 1.2 to 65.2 +/- 2.3 mmHg), but showed no acclimation under laboratory conditions. For E. signata, Delta H ranged from -31.1 +/- 6.32 to -48.2 +/- 3.59 kJ/mole. Field acclimatisation and laboratory acclimation of P-50 did not occur. However, in E. signata, there was a significant increase in [Hb] and MCHC from early spring to summer in turtles collected from the wild (1.0 +/- 0.1 to 1.7 +/- 0.2 mmol/L and 4.0 +/- 0.3 to 6.7 +/- 0.7 mmol/L, respectively). (C) 2005 Published by Elsevier Inc.