The stochastic Gross-Pitaevskii equation: II

We provide a derivation of a more accurate version of the stochastic Gross-Pitaevskii equation, as introduced by Gardiner et al (2002 J. Phys. B: At. Mol. Opt. Phys. 35 1555). This derivation does not rely on the concept of local energy and momentum conservation and is based on a quasiclassical Wigner function representation of a 'high temperature' master equation for a Bose gas, which includes only modes below an energy cut-off ER that are sufficiently highly occupied (the condensate band). The modes above this cutoff (the non-condensate band) are treated as being essentially thermalized. The interaction between these two bands, known as growth and scattering processes, provides noise and damping terms in the equation of motion for the condensate band, which we call the stochastic Gross-Pitaevskii equation. This approach is distinguished by the control of the approximations made in its derivation and by the feasibility of its numerical implementation.

Nitrogen removal from sludge digester liquids by nitrification/denitrification or partial nitritation/anammox: environmental and economical considerations

In wastewater treatment plants with anaerobic sludge digestion, 15-20% of the nitrogen load is recirculated to the main stream with the return liquors from dewatering. Separate treatment of this ammonium-rich digester supernatant significantly reduces the nitrogen load of the activated sludge system. Two biological applications are considered for nitrogen elimination: (i) classical autotrophic nitrification/heterotrophic denitrification and (ii) partial nitritation/autotrophic anaerobic ammonium oxidation (anammox). With both applications 85-90% nitrogen removal can be achieved, but there are considerable differences in terms of sustainability and costs. The final gaseous products for heterotrophic denitrification are generally not measured and are assumed to be nitrogen gas (N-2). However, significant nitrous oxide (N2O) production can occur at elevated nitrite concentrations in the reactor. Denitrification via nitrite instead of nitrate has been promoted in recent years in order to reduce the oxygen and the organic carbon requirements. Obviously this achievement turns out to be rather disadvantageous from an overall environmental point of view. On the other hand no unfavorable intermediates are emitted during anaerobic ammonium oxidation. A cost estimate for both applications demonstrates that partial nitritation/anammox is also more economical than classical nitrification/denitrification. Therefore autotrophic nitrogen elimination should be used in future to treat ammonium-rich sludge liquors.

A novel wastewater treatment process: Simultaneous nitrification, denitrification and phosphorus removal

Simultaneous nitrification and denitrification (SND) via the nitrite pathway and anaerobic-anoxic enhanced biological phosphorus removal (EBPR) are two processes that can significantly reduce the COD demand for nitrogen and phosphorus removal. The combination of these two processes has the potential of achieving simultaneous nitrogen and phosphorus removal with a minimal requirement for COD. A lab-scale sequencing batch reactor (SBR) was operated in alternating anaerobic-aerobic mode with a low dissolved oxygen concentration (DO, 0.5 mg/L) during the aerobic period, and was demonstrated to accomplish nitrification, denitrification and phosphorus removal. Under anaerobic conditions, COD was taken up and converted to polyhydroxyalkanoates (PHA), accompanied with phosphorus release. In the subsequent aerobic stage, PHA was oxidized and phosphorus was taken up to less than 0.5 mg/L at the end of the cycle. Ammonia was also oxidised during the aerobic period, but without accumulation of nitrite or nitrate in the system, indicating the occurrence of simultaneous nitrification and denitrification. However, off-gas analysis found that the final denitrification product was mainly nitrous oxide (N2O) not N-2. Further experimental results demonstrated that nitrogen removal was via nitrite, not nitrate. These experiments also showed that denitrifying glycogen.-accumulating organisms rather than denitrifying polyphosphate-accumulating organisms were responsible for the denitrification activity.

Challenges for simultaneous nitrification, denitrification, and phosphorus removal in microbial aggregates: mass transfer limitation and nitrous oxide production

The microbial community composition and activity was investigated in aggregates from a lab-scale bioreactor, in which nitrification, denitrification and phosphorus removal occurred simultaneously. The biomass was highly enriched for polyphosphate accumulating organisms facilitating complete removal of phosphorus from the bulk liquid; however, some inorganic nitrogen still remained at the end of the reactor cycle. This was ascribed to incomplete coupling of nitrification and denitrification causing NO3- accumulation. After 2 h of aeration, denitrification was dependent on the activity of nitrifying bacteria facilitating the formation of anoxic zones in the aggregates; hence, denitrification could not occur without simultaneous nitrification towards the end of the reactor cycle. Nitrous oxide was identified as a product of denitrification, when based on stored PHA as carbon source. This observation is of critical importance to the outlook of applying PHA-driven denitrification in activated sludge processes. (c) 2004 Federation of European Microbiological Societies. Published by Elsevier B.V. All rights reserved.

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.

Effect of temperature and free ammonia on nitrification and nitrite accumulation in landfill leachate and analysis of its nitrifying bacterial community by FISH

The cause of seasonal failure of a nitrifying municipal landfill leachate treatment plant utilizing a fixed biofilm was investigated by wastewater analyses and batch respirometric tests at every treatment stage. Nitrification of the leachate treatment plant was severely affected by the seasonal temperature variation. High free ammonia (NH3-N) inhibited not only nitrite oxidizing bacteria (NOB) but also ammonia oxidizing bacteria (AOB). In addition, high pH also increased free ammonia concentration to inhibit nitrifying activity especially when the NH4-N level was high. The effects of temperature and free ammonia of landfill leachate on nitrification and nitrite accumulation were investigated with a semi-pilot scale biofilm airlift reactor. Nitrification rate of landfill leachate increased with temperature when free ammonia in the reactor was below the inhibition level for nitrifiers. Leachate was completely nitrified up to a load of 1.5 kg NH4-N m(-3) d(-1) at 28 degrees C. The activity of NOB was inhibited by NH3-N resulting in accumulation of nitrite. NOB activity decreased more than 50% at 0.7 mg NH3-N L-1. Fluorescence in situ hybridization (FISH) was carried out to analyze the population of AOB and NOB in the nitrite accumulating nitrifying biofilm. NOB were located close to AOB by forming small clusters. A significant fraction of AOB identified by probe Nso1225 specifically also hybridized with the Nitrosonlonas specific probe Nsm156. The main NOB were Nitrobacter and Nitrospira which were present in almost equal amounts in the biofilm as identified by simultaneous hybridization with Nitrobacter specific probe Nit3 and Nitrospira specific probe Ntspa662. (c) 2005 Elsevier Ltd. All rights reserved.

Identifying causes for N2O accumulation in a lab-scale sequencing batch reactor performing simultaneous nitrification, denitrification and phosphorus removal

The recently described process of simultaneous nitrification, denitrification and phosphorus removal (SNDPR) has a great potential to save capital and operating costs for wastewater treatment plants. However, the presence of glycogen-accumulating organisms (GAOs) and the accumulation of nitrous oxide (N2O) can severely compromise the advantages of this process. In this study, these two issues were investigated using a lab-scale sequencing batch reactor performing SNDPR over a 5-month period. The reactor was highly enriched in polyphosphate-accumulating organisms (PAOs) and GAOs representing around 70% of the total microbial community. PAOs were the dominant population at all times and their abundance increased, while GAOs population decreased over the study period. Anoxic batch tests demonstrated that GAOs rather than denitrifying PAOs were responsible for denitrification. NO accumulated from denitrification and more than half of the nitrogen supplied in a reactor cycle was released into the atmosphere as NO. After mixing SNDPR sludge with other denitrifying sludge, N2O present in the bulk liquid was reduced immediately if external carbon was added. We therefore suggest that the N2O accumulation observed in the SNDPR reactor is an artefact of the low microbial diversity facilitated by the use of synthetic wastewater with only a single carbon source. (C) 2005 Elsevier B.V. All rights reserved.

Occurrence and simulation of nitrification in two contrasting sugarcane soils from the Australian wet tropics

The concentration of ammonium-nitrogen (NH4+-N) frequently exceeds that of nitrate-N (NO3--N) in Australian wet tropical sugarcane soils. The amount of mineral N in soil is the net result of complex processes in the field, so the objective of this experiment was to investigate nitrification and ammonification in these soils under laboratory conditions. Aerobic and saturated incubations were performed for 1 week on 2 wet tropical soils. Net NO3--N increased significantly in both soils during both types of incubation. A second series of aerobic incubations of these soils treated with NH4+-N and inoculated with subtropical nitrifying soils was conducted for 48 days. Nitrification in the wet tropical soils was not significantly affected by inoculation, and virtually all added N was nitrified during the incubation period. Mineral N behaviour of the 48-day incubations was captured with the APSIM-SoilN model. As nitrification proceeded under laboratory conditions and was able to be captured by the model, it was concluded that nitrification processes in the wet tropical soils studied were not different from those in the subtropical soils. Processes that remove NO3- from the soil, such as leaching and denitrification, may therefore be important factors affecting the proportions of NH4+-N and NO3--N measured under field conditions.

Integration of sulphate reduction, autotrophic denitrification and nitrification to achieve low-cost excess sludge minimisation for Hong Kong sewage

An integrated anaerobic-aerobic treatment system of sulphate-laden wastewater was proposed here to achieve low sludge production, low energy consumption and effective sulphide control. Before integrating the whole system, the feasibility of autotrophic denitrification utilising dissolved sulphide produced during anaerobic treatment of sulphate rich wastewater was studied here. An upflow anaerobic sludge blanket reactor was operated to treat sulphate-rich synthetic wastewater (TOC = 100 mg/L and sulphate = 500 mg/L) and its effluent with dissolved sulphide and external nitrate solution were fed into an anoxic biofilter. The anaerobic reactor was able to remove 77-85% of TOC at HRT of 3 h and produce 70-90 mg S/L sulphide in dissolved form for the subsequent denitrification. The performance of anoxic reactor was stable, and the anoxic reactor could remove 30 mg N/L nitrate at HRT of 2 h through autotrophic denitrification. Furthermore, sulphur balance for the anoxic filter showed that more than 90% of the removed sulphide was actually oxidised into sulphate, thereby there was no accumulation of sulphur particles in the filter bed. The net sludge productions were approximately 0.15 to 0.18 g VSS/g COD in the anaerobic reactor and 0.22 to 0.31 g VSS/g NO3--N in the anoxic reactor. The findings in this study will be helpful in developing the integrated treatment system to achieve low-cost excess sludge minimisation.

Feasibility of controlling nitrification in predenitrification plants using DO, pH and ORP sensors

Experimental studies were carried out on a bench-scale nitrogen removal system with a predenitrification configuration to gain insights into the spatial and temporal variations of DO, pH and ORP in such systems. It is demonstrated that these signals correlate strongly with the operational states of the system, and could therefore be used as system performance indicators. The DO concentration in the first aerobic zone, when receiving constant aeration, and the net pH change between the last and first aerobic zones display strong correlations with the influent ammonia concentration for the domestic wastewater used in this study. The pH profile along the aerobic zones gives good indication on the extent of nitrification. The experimental results also showed a good correlation between ORP values in the last aerobic zone and effluent ammonia and nitrate concentrations, provided that DO in this zone is controlled at a constant level. These results suggest that the DO, pH and ORP sensors could potentially be used as alternatives to the on-line nutrient sensors for the control of continuous systems. An idea of using a fuzzy inference system to make an integrated use of these signals for on-line aeration control is presented and demonstrated on the bench-scale system with promising results. The use of these sensors has to date only been demonstrated in intermittent systems, such as sequencing batch reactor systems.