Bayesian feedback versus Markovian feedback in a two-level atom

We compare two different approaches to the control of the dynamics of a continuously monitored open quantum system. The first is Markovian feedback, as introduced in quantum optics by Wiseman and Milburn [Phys. Rev. Lett. 70, 548 (1993)]. The second is feedback based on an estimate of the system state, developed recently by Doherty and Jacobs [Phys. Rev. A 60, 2700 (1999)]. Here we choose to call it, for brevity, Bayesian feedback. For systems with nonlinear dynamics, we expect these two methods of feedback control to give markedly different results. The simplest possible nonlinear system is a driven and damped two-level atom, so we choose this as our model system. The monitoring is taken to be homodyne detection of the atomic fluorescence, and the control is by modulating the driving. The aim of the feedback in both cases is to stabilize the internal state of the atom as close as possible to an arbitrarily chosen pure state, in the presence of inefficient detection and other forms of decoherence. Our results (obtained without recourse to stochastic simulations) prove that Bayesian feedback is never inferior, and is usually superior, to Markovian feedback. However, it would be far more difficult to implement than Markovian feedback and it loses its superiority when obvious simplifying approximations are made. It is thus not clear which form of feedback would be better in the face of inevitable experimental imperfections.

Interference rejection capabilities of different types of array antennas in cellular systems

The suitable use of array antennas in cellular systems results in improvement in the signal-to-interference ratio (StR), This property is the basis for introducing smart or adaptive antenna systems. in general, the SIR depends on the array configuration and is a function of the direction of the desired user and interferers. Here, the SIR performance for linear and circular arrays is analysed and compared.

The damped and coherently-driven Jaynes-Cummings model

We investigate the influence of a single-mode cavity on the Autler-Townes doublet that arises when a three-level atom is strongly driven by a laser field tuned to one of the atomic transitions and probed by a tunable, weak field coupled to the other transition. We assume that the cavity mode is coupled to the driven transition and the cavity and laser frequencies are equal to the atomic transition frequency. We find that the Autler-Townes spectrum can have one, two or three peaks depending on the relative magnitudes of the Rabi frequencies of the cavity and driving fields. We show that, in order to understand the three-peaked spectrum, it is necessary to go beyond the secular approximation, leading to interesting quantum interference effects. We find that the positions and relative intensities of the three spectral components are affected strongly by the atom-cavity coupling strength g and the cavity damping K. For an increasing g and/or decreasing K the triplet evolves into a single peak. This results in 'undressing' of the system such that the atom collapses into its ground state. We interpret the spectral features in terms of the semiclassical dressed-atom model, and also provide complementary views of the cavity effects in terms of quantum Langevin equations and the fully quantized, 'double -dressing' model.

The metamorphosis of lambda-fold K-3,K-3-designs into lambda-fold 6-cycle systems

In this paper necessary and sufficient conditions are given for the metamorphosis of a lambda-fold K-3,K-3-design of order n into a lambda-fold 6-cycle system of order n, by retaining one 6-cycle subgraph from each copy of K-3,K-3, and then rearranging the set of all the remaining edges, three from each K-3,K-3, into further 6-cycles so that the result is a lambda-fold 6-cycle system.

Development of a novel titration and off-gas analysis (TOGA) sensor for study of biological processes in wastewater treatment systems

The development of the new TOGA (titration and off-gas analysis) sensor for the detailed study of biological processes in wastewater treatment systems is outlined. The main innovation of the sensor is the amalgamation of titrimetric and off-gas measurement techniques. The resulting measured signals are: hydrogen ion production rate (HPR), oxygen transfer rate (OTR), nitrogen transfer rate (NTR), and carbon dioxide transfer rate (CTR). While OTR and NTR are applicable to aerobic and anoxic conditions, respectively, HPR and CTR are useful signals under all of the conditions found in biological wastewater treatment systems, namely, aerobic, anoxic and anaerobic. The sensor is therefore a powerful tool for studying the key biological processes under all these conditions. A major benefit from the integration of the titrimetric and off-gas analysis methods is that the acid/base buffering systems, in particular the bicarbonate system, are properly accounted for. Experimental data resulting from the TOGA sensor in aerobic, anoxic, and anaerobic conditions demonstrates the strength of the new sensor. In the aerobic environment, carbon oxidation (using acetate as an example carbon source) and nitrification are studied. Both the carbon and ammonia removal rates measured by the sensor compare very well with those obtained from off-line chemical analysis. Further, the aerobic acetate removal process is examined at a fundamental level using the metabolic pathway and stoichiometry established in the literature, whereby the rate of formation of storage products is identified. Under anoxic conditions, the denitrification process is monitored and, again, the measured rate of nitrogen gas transfer (NTR) matches well with the removal of the oxidised nitrogen compounds (measured chemically). In the anaerobic environment, the enhanced biological phosphorus process was investigated. In this case, the measured sensor signals (HPR and CTR) resulting from acetate uptake were used to determine the ratio of the rates of carbon dioxide production by competing groups of microorganisms, which consequently is a measure of the activity of these organisms. The sensor involves the use of expensive equipment such as a mass spectrometer and requires special gases to operate, thus incurring significant capital and operational costs. This makes the sensor more an advanced laboratory tool than an on-line sensor. (C) 2003 Wiley Periodicals, Inc.

Investigation of electrical conductivity as a function of dopant-ion radius in the systems Zr0.75Ce0.08M0.17O1.92 (M=Nd, Sm, Gd, Dy, Ho, Y, Er, Yb, Sc)

Electrical conductivity versus dopant ionic radius studies in zirconia- and ceria-based, solid oxide fuel cell (SOFC) electrolyte systems have shown that oxygen-ion conductivity is highest when the host and dopant ions are similar in size [J. Am. Ceram. Soc. 48 (1965) 286; Solid State Ionics 37 (1989) 67; Solid State Ionics 5 (1981) 547]. Under these conditions, it is thought that the conduction paths within the crystal lattice become less distorted [Solid State Ionics 8 (1983) 201]. In this study, binary ZrO2-M2O3 unit cells were expanded, via the partial substitution of Ce+4 for Zr+4 into the lattice, in an attempt to identify new, ternary, zirconia/ceria-based electrolyte systems with enhanced electrical conductivity. The compositions Zr0.75Ce0.08M0.17O1.92 (M = Nd, Sm, Gd, Dy, Ho, Y, Yb, Sc) were prepared using traditional solid state techniques. Bulk phase characterisation and precise lattice parameter measurements were performed with X-ray diffraction techniques. Four-probe DC conductivity measurements between 400 and 900 degreesC showed that the dopant-ion radius influenced electrical conductivity. The conductivity versus dopant-ion radius trends previously observed in zirconia-based, binary systems are clearly apparent in the ternary systems investigated in this study. The addition of ceria was found to have a negative influence on the electrical conductivity over the temperature range 400-900 degreesC. It is suggested that distortion of the oxygen-ion conduction path by the presence of the larger M+3 and Ce+4 species (relative to Zr+4) is the reason for the decreasing electrical conductivity as a function of increasing dopant size and ceria addition, respectively. (C) 2002 Elsevier Science B.V. All rights reserved.

Control of nitrate recirculation flow in predenitrification systems

The control of the nitrate recirculation flow in a predenitrification system is addressed. An elementary mass balance analysis on the utilisation efficiency of the influent biodegradable COD (bCOD) for nitrate removal indicates that the control problem can be broken down into two parts: maintaining the anoxic zone anoxic (i.e. nitrate is present throughout the anoxic zone) and maximising the usage of influent soluble bCOD for denitrification. Simulation studies using the Simulation Benchmark developed in the European COST program show that both objectives can be achieved by maintaining the nitrate concentration at the outlet of the anoxic zone at around 2 mgN/L. This setpoint appears to be robust towards variations in the influent characteristics and sludge kinetics.

Benchmarking nitrogen removal suspended-carrier biofilm systems using dynamic simulation

We are witnessing an enormous growth in biological nitrogen removal from wastewater. It presents specific challenges beyond traditional COD (carbon) removal. A possibility for optimised process design is the use of biomass-supporting media. In this paper, attached growth processes (AGP) are evaluated using dynamic simulations. The advantages of these systems that were qualitatively described elsewhere, are validated quantitatively based on a simulation benchmark for activated sludge treatment systems. This simulation benchmark is extended with a biofilm model that allows for fast and accurate simulation of the conversion of different substrates in a biofilm. The economic feasibility of this system is evaluated using the data generated with the benchmark simulations. Capital savings due to volume reduction and reduced sludge production are weighed out against increased aeration costs. In this evaluation, effluent quality is integrated as well.

A conjecture on small embeddings of partial Steiner triple systems

A well-known, and unresolved, conjecture states that every partial Steiner triple system of order u can be embedded in a Steiner triple system of order v for all v equivalent to 1 or 3 (mod 6), v greater than or equal to 2u + 1. However, some partial Steiner triple systems of order u can be embedded in Steiner triple systems of order v < 2u + 1. A more general conjecture that considers these small embeddings is presented and verified for some cases. (C) 2002 Wiley Periodicals, Inc.

A systematic study of the microwave and thermal cure kinetics of the DGEBA/DDS and DGEBA/DDM epoxy-amine resin systems

The microwave and thermal cure processes for the epoxy-amine systems (epoxy resin diglycidyl ether of bisphenol A, DGEBA) with 4,4'-diaminodiphenyl sulphone (DDS) and 4,4'-diaminodiphenyl methane (DDM) have been investigated for 1:1 stoichiometries by using fiber-optic FT-NIR spectroscopy. The DGEBA used was in the form of Ciba-Geigy GY260 resin. The DDM system was studied at a single cure temperature of 373 K and a single stoichiometry of 20.94 wt% and the DDS system was studied at a stoichiometry of 24.9 wt% and a range of temperatures between 393 and 443 K. The best values of the kinetic rate parameters for the consumption of amines have been determined by a least squares curve fit to a model for epoxy/amine cure. The activation energies for the polymerization of the DGEBA/DDS system were determined for both cure processes and found to be 66 and 69 kJ mol(-1) for the microwave and thermal cure processes, respectively. No evidence was found for any specific effect of the microwave radiation on the rate parameters, and the systems were both found to be characterized by a negative substitution effect. Copyright (C) 2002 John Wiley Sons, Ltd.

Novel miniaturized systems in high-throughput screening

High-throughput screening (HTS) using high-density microplates is the primary method for the discovery of novel lead candidate molecules. However, new strategies that eschew 2D microplate technology, including technologies that enable mass screening of targets against large combinatorial libraries, have the potential to greatly increase throughput and decrease unit cost. This review presents an overview of state-of-the-art microplate-based HTS technology and includes a discussion of emerging miniaturized systems for HTS. We focus on new methods of encoding combinatorial libraries that promise throughputs of as many as 100 000 compounds per second.

Boundary value problems for systems of difference equations associated with systems of second-order ordinary differential equations

We study difference equations which arise as discrete approximations to two-point boundary value problems for systems of second-order ordinary differential equations. We formulate conditions which guarantee a priori bounds on first differences of solutions to the discretized problem. We establish existence results for solutions to the discretized boundary value problems subject to nonlinear boundary conditions. We apply our results to show that solutions to the discrete problem converge to solutions of the continuous problem in an aggregate sense. (C) 2002 Elsevier Science Ltd. All rights reserved.

Entanglement in the steady state of a collective-angular-momentum (Dicke) model

We model the behavior of an ion trap with all ions driven simultaneously and coupled collectively to a heat bath. The equations for this system are similar to the irreversible dynamics of a collective angular momentum system known as the Dicke model. We show how the steady state of the ion trap as a dissipative many-body system driven far from equilibrium can exhibit quantum entanglement. We calculate the entanglement of this steady state for two ions in the trap and in the case of more than two ions we calculate the entanglement between two ions by tracing over all the other ions. The entanglement in the steady state is a maximum for the parameter values corresponding roughly to a bifurcation of a fixed point in the corresponding semiclassical dynamics. We conjecture that this is a general mechanism for entanglement creation in driven dissipative quantum systems.

Universal simulation of Hamiltonian dynamics for quantum systems with finite-dimensional state spaces

What interactions are sufficient to simulate arbitrary quantum dynamics in a composite quantum system? Dodd [Phys. Rev. A 65, 040301(R) (2002)] provided a partial solution to this problem in the form of an efficient algorithm to simulate any desired two-body Hamiltonian evolution using any fixed two-body entangling N-qubit Hamiltonian, and local unitaries. We extend this result to the case where the component systems are qudits, that is, have D dimensions. As a consequence we explain how universal quantum computation can be performed with any fixed two-body entangling N-qudit Hamiltonian, and local unitaries.