Renormalization of the electron-phonon interaction: a reformulation of the BCS-gap equation

A recently developed renormalization approach is used to study the electron-phonon coupling in many-electron systems. By starting from an Hamiltonian which includes a small gauge symmetry breaking field, we directly derive a BCS-like equation for the energy gap from the renormalization approach. The effective electron-electron interaction for Cooper pairs does not contain any singularities. Furthermore, it is found that phonon-induced particle-hole excitations only contribute to the attractive electron-electron interaction if their energy difference is smaller than the phonon energy.Comment: 8 pages, version to appear in Eur. Phys. J.

Preparation of high density heavy metal fluoride glasses with extended ultraviolet and infra red ranges, and such high density heavy metal fluoride glasses

A heavy metal fluoride glass composition range (in mol percent) consisting essentially of: (16-30)BaF.sub.2.(8-26)HfF.sub.4.(6-24)InF.sub.3 or GaF.sub.3.(4-16)CdF.sub.2.(6-24)YbF.sub.3.(4-22)ZnF.sub.2. In an alternative embodiment, a heavy metal fluoride glass composition range (in mol percent) comprises (16-30)BaF.sub.2.(8-26)HfF.sub.4.(6-24) of (0-24)InF.sub.3, (0-24)GaF.sub.3 and (0-19)AlF.sub.3.(1-16)CdF.sub.2.(6-24)YbF.sub.3.(4-26)ZnF.sub.2. A preferred heavy metal fluoride glass produced in accordance with the present invention comprises a composition (in mol %) and comprises about 26BaF.sub.2.18HfF.sub.4.7InF.sub.3.5GaF.sub.3.10CdF.sub.2.18YbF.sub.3. 16ZnF.sub.2. A preferred heavy metal fluoride glass has maximum thickness of most preferably about 3 mm. Another preferred heavy metal fluoride glass comprises a composition (in mol %) and comprises about 26BaF.sub.2.18HfF.sub.4.12AlF.sub.3.10CdF.sub.2.18YbF.sub.3.16ZnF.sub.2

Technical Note: Field experiences using UV/VIS sensors for high-resolution monitoring of nitrate in groundwater

peer-reviewedTwo different in situ spectrophotometers are compared that were used in the field to determine nitrate-nitrogen (NO3-N) concentrations at two distinct spring discharge sites. One sensor was a double wavelength spectrophotometer (DWS) and the other a multiple wavelength spectrophotometer (MWS). The objective of the study was to review the hardware options, determine ease of calibration, accuracy, influence of additional substances and to assess positive and negative aspects of the two sensors as well as troubleshooting and trade-offs. Both sensors are sufficient to monitor highly time-resolved NO3-N concentrations in emergent groundwater. However, the chosen path length of the sensors had a significant influence on the sensitivity and the range of detectable NO3-N. The accuracy of the calculated NO3-N concentrations of the sensors can be affected if the content of additional substances such as turbidity, organic matter, nitrite or hydrogen carbonate significantly varies after the sensors have been calibrated to a particular water matrix. The MWS offers more possibilities for calibration and error detection but requires more expertise compared with the DWS.The authors would like to acknowledge the Teagasc Walsh Fellowship scheme for funding the study in Ireland, and the German federal Ministry of Education and Research (BMBF) for sponsoring the SMART-project (grant no. 02WM1079-1086, 02WM1211-1212) for the study in Jordan.Teagasc Walsh Fellowship Programm

Mobilisation or dilution? Nitrate response of karst springs to high rainfall events

peer-reviewedNitrate (NO3−) contamination of groundwater associated with agronomic activity is of major concern in many countries. Where agriculture, thin free draining soils and karst aquifers coincide, groundwater is highly vulnerable to nitrate contamination. As residence times and denitrification potential in such systems are typically low, nitrate can discharge to surface waters unabated. However, such systems also react quickest to agricultural management changes that aim to improve water quality. In response to storm events, nitrate concentrations can alter significantly, i.e. rapidly decreasing or increasing concentrations. The current study examines the response of a specific karst spring situated on a grassland farm in South Ireland to rainfall events utilising high-resolution nitrate and discharge data together with on-farm borehole groundwater fluctuation data. Specifically, the objectives of the study are to formulate a scientific hypothesis of possible scenarios relating to nitrate responses during storm events, and to verify this hypothesis using additional case studies from the literature. This elucidates the controlling key factors that lead to mobilisation and/or dilution of nitrate concentrations during storm events. These were land use, hydrological condition and karstification, which in combination can lead to differential responses of mobilised and/or diluted nitrate concentrations. Furthermore, the results indicate that nitrate response in karst is strongly dependent on nutrient source, whether mobilisation and/or dilution occur and on the pathway taken. This will have consequences for the delivery of nitrate to a surface water receptor. The current study improves our understanding of nitrate responses in karst systems and therefore can guide environmental modellers, policy makers and drinking water managers with respect to the regulations of the European Union (EU) Water Framework Directive (WFD). In future, more research should focus on the high-resolution monitoring of karst aquifers to capture the high variability of hydrochemical processes, which occur at time intervals of hours to days.Teagasc Walsh Fellowship Programm

Optimal Online Tuning of an Adaptive Controller

A novel adaptive controller, suitable for linear and non-linear systems was developed. The controller is a discrete algorithm suitable for computer implementation and is based on gradient descent adaptation rules. Traditional recursive least squares based algorithms suffer from performance deterioration due to the continuous reduction of a covariance matrix used for adaptation. When this covariance matrix becomes too small, recursive least squares algorithms respond slow to changes in model parameters. Gradient descent adaptation was used to avoid the performance deterioration with time associated with regression based adaptation such as Recursive Least Squares methods. Stability was proven with Lyapunov stability theory, using an error filter designed to fulfill stability requirements. Similarities between the proposed controller with PI control have been found. A framework for on-line tuning was developed using the concept of estimation tracks. Estimation tracks allow the estimation gains to be selected from a finite set of possible values, while meeting Lyapunov stability requirements. The trade-off between sufficient excitation for learning and controller performance, typical for dual adaptive control techniques, are met by properly tuning the adaptation and filter gains to drive the rate of adaptation in response to a fixed excitation signal. Two methods for selecting the estimation track were developed. The first method uses simulations to predict the value of the bicriteria cost function that is a combination of prediction and feedback errors, to generate a performance score for each estimation track. The second method uses a linear matrix inequality formulation to find an upper bound on feedback error within the range of uncertainty of the plant parameters and acceptable reference signals. The linear matrix inequality approach was derived from a robust control approach. Numerical simulations were performed to systematically evaluate the performance and computational burden of configuration parameters, such as the number of estimation tracks used for tuning. Comparisons were performed for both tuning methods with an arbitrarily tuned adaptive controller, with arbitrarily selected tuning parameters as well as a common adaptive control algorithm