Mathematical modelling of a flow-injection system with a membrane separation module

A mathematical model for a flow-injection system with a membrane separation module based on the axially dispersed plug flow model was developed. It takes into account the geometrical dimensions and dispersion properties of the main sections of the manifold, the mass transfer in the channels of the separation module and the characteristics of the membrane (thickness and diffusion coefficient within it). The model was solved analytically in the Laplace domain. The inverse transformation was found to give satisfactory results for reactor Peclet numbers less than 120. Otherwise a numerical solution based on the implicit alternating-direction finite difference method was preferred. The adequacy of the model was confirmed experimentally on a flow-injection manifold with a parallel-plate dialysis module. The unknown flow and membrane parameters were determined by curve fitting. The membrane parameters were determined also by steady-state measurements. Fairly good agreement between the dynamic and steady-state results and with results given in the literature was observed, which, together with other experimental results, supported the validity of the model and showed that it can be used successfully for the mathematical description and optimization of flow-injection systems with membrane separation modules. In this connection, the influence of the reactor parameters and the sample volume on the performance of such a system were investigated and conclusions for improving its sensitivity and sample throughput were drawn. Other possible applications of the model are in membrane technology for characterizing of various membranes and in process engineering for investigating the mass transfer in different dialysers

Bell inequalities for arbitrarily high dimensional systems

We develop a novel approach to Bell inequalities based on a constraint that the correlations exhibited by local realistic theories must satisfy. This is used to construct a family of Bell inequalities for bipartite quantum systems of arbitrarily high dimensionality which are strongly resistant to noise. In particular our work gives an analytic description of numerical results of D. Kaszlikowski, P. Gnacinski, M. Zukowski, W. Miklaszewski, A. Zeilinger, Phys. Rev. Lett. {\bf 85}, 4418 (2000) and T. Durt, D. Kaszlikowski, M. Zukowski, quant-ph/0101084, and generalises them to arbitrarily high dimensionality.Comment: 6 pages, late

On the role of entanglement in quantum computational speed-up

For any quantum algorithm operating on pure states we prove that the presence of multi-partite entanglement, with a number of parties that increases unboundedly with input size, is necessary if the quantum algorithm is to offer an exponential speed-up over classical computation. Furthermore we prove that the algorithm can be classically efficiently simulated to within a prescribed tolerance \eta even if a suitably small amount of global entanglement (depending on \eta) is present. We explicitly identify the occurrence of increasing multi-partite entanglement in Shor's algorithm. Our results do not apply to quantum algorithms operating on mixed states in general and we discuss the suggestion that an exponential computational speed-up might be possible with mixed states in the total absence of entanglement. Finally, despite the essential role of entanglement for pure state algorithms, we argue that it is nevertheless misleading to view entanglement as a key resource for quantum computational power.Comment: Main proofs simplified. A few further explanatory remarks added. 22 pages, plain late

Exploring intermediate phenotypes with EEG: Working memory dysfunction in schizophrenia

This review brings together two strands of investigation in the neuropsychology and neurophysiology of schizophrenia that have been particularly productive over the last 20 years. We review the literature on working memory deficits, particularly in the visual domain, and changes in oscillatory neural activity as measured with electroencephalography (EEG) and magnetoencephalography (MEG). We argue that recent results suggest a link between these two phenomena, in that altered oscillations underlie some of the working memory deficits. We furthermore argue that early sensory mechanisms contribute more to working memory (and other) deficits than previously thought. The final part of our review suggests links between working memory, oscillations, and their alterations in schizophrenia and the dopamine, GABA, glutamate and acetylcholine system. These links have already resulted in the development of new remediation strategies, which have some translational potential

Application of Laplace transforms for the solution of transient mass- and heat-transfer problems in flow systems

A fast numerical technique for the solution of partial differential equations describing timedependent two- or three-dimensional transport phenomena is developed. It is based on transforming the original time-domain equations into the Laplace domain where numerical integration is performed and by subsequent numerical inverse transformation the final solution can be obtained. The computation time is thus reduced by more than one order of magnitude in comparison with the conventional finite-difference techniques. The effectiveness of the proposed technique is demonstrated by illustrative examples

Reconstruction of the phase of matter-wave fields using a momentum resolved cross-correlation technique

We investigate the potential of the so-called XFROG cross-correlation technique originally developed for ultrashort laser pulses for the recovery of the amplitude and phase of the condensate wave function of a Bose-Einstein condensate. Key features of the XFROG method are its high resolution, versatility and stability against noise and some sources of systematic errors. After showing how an analogue of XFROG can be realized for Bose-Einstein condensates, we illustrate its effectiveness in determining the amplitude and phase of the wave function of a vortex state. The impact of a reduction of the number of measurements and of typical sources of noise on the field reconstruction are also analyzed.Comment: 7 pages; 9 figures; article with higher resolution figures available from author