Algorithmic approximations for the busy period distribution of the M/M/c retrial queue

In this paper we deal with the main multiserver retrial queue of M/M/c type with exponential repeated attempts. This model is known to be analytically intractable due to the spatial heterogeneity of the underlying Markov chain, caused by the retrial feature. For this reason several models have been proposed for approximating its stationary distribution, that lead to satisfactory numerical implementations. This paper extends these studies by developing efficient algorithmic procedures for calculating the busy period distribution of the main approximation models of Wilkinson [Wilkinson, R.I., 1956. Theories for toll traffic engineering in the USA, The Bell System Technical Journal 35, 421–514], Falin [Falin, G.I., 1983. Calculations of probability characteristics of a multiline system with repeated calls, Moscow University Computational Mathematics and Cybernetics 1, 43–49] and Neuts and Rao [Neuts, M.F., Rao, B.M., 1990. Numerical investigation of a multiserver retrial model, Queueing Systems 7, 169–190]. Moreover, we develop stable recursive schemes for the computation of the busy period moments. The corresponding distributions for the total number of customers served during a busy period are also studied. Several numerical results illustrate the efficiency of the methods and reveal interesting facts concerning the behavior of the M/M/c retrial queue.     

Amorphous and crystalline states of ultrasoft colloids: a molecular dynamics study

In this work, we study the temperature-induced development of “dynamically arrested” states in dense suspensions of “soft colloids” (multi-arm star polymers and/or block-copolymers micelles) by means of molecular dynamics (MD) simulations. Temperature increase in marginal solvents results in “soft sphere” swelling, dynamical arrest, and eventually crystallization. However, two distinct “dynamically arrested” states were found, one almost amorphous (“glassy”) and one with a considerable degree of crystallinity, yet lower than that of the fully equilibrated crystal. It is remarkable that even that latter state permitted self-diffusion in the timescale of the simulations, an effect that underlies the importance of the “ultra-soft” nature of inter-particle potential. The “number of connections” criterion for crystallinity proved to be very successful in identifying the ultimate thermodynamic trend from the very early stages of the α-relaxation. This paper was presented at the Third Annual Rheology Conference, AERC 2006, April 27–29, 2006, Crete, Greece.     

Screen‐Printed Disposable Sensors Modified with Bismuth Precursors for Rapid Voltammetric Determination of 3 Ecotoxic Nitrophenols

This work reports the application of screen‐printed electrodes bulk‐modified with bismuth precursors to the voltammetric determination of 2‐nitrophenol (2‐NP), 4‐nitrophenol (4‐NP) and 2,4‐dinitrophenol (2,4‐DNP) in water samples. A bismuth film was formed at the electrode surface via in situ reduction of the precursor compound contained in the electrode matrix by cathodic polarization at ?1.20 V. The formation of bismuth layer at the precursor‐modified electrodes was assessed by cyclic voltammetric (CV) at different pH values and by optical techniques. The target nitrophenols were voltammetrically determined by recording their reduction peaks in the differential pulse (DP) mode. The composition and content of the precursor compounds in the printed ink and the effect of the pH of the supporting electrolyte on the DP reduction currents of the 3 target nitrophenols were studied. The limits of quantification (LOQs) in three water matrices (distilled water, tap water and surface water) were in the range 1.1–2.2 µmol L^?1_. Using a simple solid‐phase extraction (SPE) procedure with Lichrolut EN cartridges and elution with methanol, a preconcentration factor of 100 was achieved; the LOQs were 0.021, 0.027 and 0.025 µmol L^?1 for 2‐NP, 4‐NP and 2,4‐DNP, respectively. The recoveries of samples spiked with the 3 target nitrophenols at two concentration levels (0.04 and 0.1 µmol L^?1) were always >87 %.     

Determination of Copper(II) Through Anodic Stripping Voltammetry in Tartrate Buffer Using an Antimony Film Screen-printed Carbon Electrode

The voltammetric performance of an in situ plated antimony film screen-printed carbon electrode in hydrochloric acid, acetate buffer, and tartrate buffer was evaluated for the detection of copper(II) with differential pulse anodic stripping voltammetry. The tartrate buffer was superior, providing high sensitivity and good separation of copper and antimony stripping peaks. The analytical conditions for the determination of copper(II) were optimized. The detection limit was estimated to be 0.14?µg?L^?1 copper(II) and the relative standard deviation for 2.5?µg?L^?1 copper(II) was 3%. The applicability of the method was illustrated by the analysis of soil conditioner samples.     

Electronic localization in disordered systems

A brief review is given of the current understanding of the electronic structure, transport properties and the nature of the electronic states in disordered systems. A simple explanation for the observed exponential behaviour in the density of states (Urbach tails) based on short-range Gaussian fluctuations is presented. The theory of Anderson localization in a disordered system is reviewed. Basic concepts, and the physics underlying the effects of weak localization, are discussed. The scaling as well as the self-consistent theory of localization are briefly reviewed. It is then argued that the problem of localization in a random potential within the so-called ladder approximation is formally equivalent to the problem of finding a bound state in a shallow potential well. Therefore all states are exponentially localized in d=1 and d=2. The fractal nature of the states is also discussed. Scaling properties in highly anisotropic systems are also discussed. A brief presentation of the recently observed metal-to-insulator transition in dequals;2 is given and, finally, a few remarks about interaction effects in disordered systems are presented.     

Costas Soukoulis: An outline of his research work

I present a summary of Costas Soukoulis' research work and I point out the most significant of his contributions. His recent work on the Casimir interaction, in which I was involved, is summarized.     

Localization and off-diagonal disorder

The question of localization is examined in the framework of a tight-binding Hamiltonian with randomness in the off-diagonal matrix elements. It is shown that the mobility edges, although they may move initially inwards into the band with increasing off-diagonal randomness, eventually move outwards leaving always a region of extended states around the middle of the band.     

Surface plasmons in layered structures and their role in superconductivity

The contribution of surface plasmons to electron-electron interaction is examined by calculating the effective Coulomb repulsion μ in the case of periodically spaced conducting planes separated by an insulator of dielectric constant ?_i. Substantial reduction in μ is obtained when $\text{?}{}_{\mathrm{i}}\text{》 1}$.     

Exponential absorption edges in GeS

The absorption coefficient of GeS at the absorption edge behaves according to Urbach's rule. The electron-phonon interaction involves all LO phonon modes expected in the directions studied. The phonon involved in the b-axis direction has a frequency value equal to 0.034 eV while for the three LO phonons in the a-axis direction the values 0.015, 0.040 and 0.444eV were found respectively. A comparison with results for isomorphic GeSe indicates that the ionic trend obtained using the electron-phonon coupling constant σ₀ agrees with the trend which is established using ionicity values from Philip's scale.     

Disposable screen-printed sensors modified with bismuth precursor compounds for the rapid voltammetric screening of trace Pb(II) and Cd(II)

In this article, a study of novel screen-printed electrodes bulk-modified with five potential bismuth precursor compounds (bismuth citrate, bismuth titanate, bismuth oxide, bismuth aluminate and bismuth zirconate) is presented for the determination of Cd(II) and Pb(II) by anodic stripping voltammetry. During the electrolytic deposition step, the precursor was reduced and served as the source of bismuth. Different key parameters were investigated in detail such as the nature of the bismuth precursor compound, the precursor content in the carbon ink, the polarisation range of the sensors, the supporting electrolyte, the stripping waveform, the deposition time, the deposition potential and the long-term stability of the sensors under continuous use. Using bismuth citrate as the precursor, the limit of detection was 0.9 μg L⁻¹ for Pb(II) and 1.1 μg L⁻¹ for Cd(II). The reproducibility on the same sensor (expressed as % relative standard deviation, (n = 8)) was 5.4% for Pb(II) and 7.2% for Cd(II) at the 20 μg L⁻¹ level. Finally, the sensors were applied to the determination of Cd(II) and Pb(II) in water samples.