Law of large numbers for the many-server earliest-deadline-first queue

A many-server queue operating under the earliest deadline first discipline, where the distributions of service time and deadline are generic, is studied at the law of large numbers scale. Fluid model equations, formulated in terms of the many-server transport equation and the recently introduced measure-valued Skorohod map, are proposed as a means of characterizing the limit. The main results are the uniqueness of solutions to these equations, and the law of large numbers scale convergence to the solutions.     

Comments on the symmetry-adapted perturbation treatments of molecular interaction

Symmetry-adapted perturbation theories published so far are criticised. Extra conditions imposed in most of these formalisms are found to be not always physically adequate. We conclude that the formalism proposed by Hirschfelder and Silbey is the most appropriate.     

Mechanism of Producing Metallic Nanoparticles,with an Emphasis on Silver and Gold Nanoparticles,Using Bottom-Up Methods

Bottom-up nanoparticle (NP) formation is assumed to begin with the reduction of the precursor metallic ions to form zero-valent atoms. Studies in which this assumption was made are reviewed. The standard reduction potential for the formation of aqueous metallic atoms—E⁰(Mⁿ⁺_aq/M⁰_aq)—is significantly lower than the usual standard reduction potential for reducing metallic ions Mⁿ⁺ in aqueous solution to a metal in solid state. E⁰(Mⁿ⁺_aq/M⁰_solid). E⁰(Mⁿ⁺_aq/M⁰_aq) values are negative for many typical metals, including Ag and Au, for which E⁰(Mⁿ⁺_aq/M⁰_solid) is positive. Therefore, many common moderate reduction agents that do not have significantly high negative reduction standard potentials (e.g., hydrogen, carbon monoxide, citrate, hydroxylamine, formaldehyde, ascorbate, squartic acid, and BH₄⁻), and cannot reduce the metallic cations to zero-valent atoms, indicating that the mechanism of NP production should be reconsidered. Both AgNP and AuNP formations were found to be multi-step processes that begin with the formation of clusters constructed from a skeleton of M⁺-M⁺ (M = Ag or Au) bonds that is followed by the reduction of a cation M⁺ in the cluster to M⁰, to form M_n⁰ via the formation of NPs. The plausibility of M⁺-M⁺ formation is reviewed. Studies that suggest a revised mechanism for the formation of AgNPs and AuNPs are also reviewed.     

The kinetics of the reaction F + H2 → HF + H. A critical review of literature data

Published experimental studies concerning the determination of rate constants for the reaction F + H₂ → HF + H are reviewed critically and conclusions are presented as to the most accurate results available. Based on these results, the recommended Arrhenius expression for the temperature range 190–376 K is k = (1.1 ± 0.1) × 10⁻¹⁰ exp |-(450 ± 50)/T| cm³ molecule⁻¹ s⁻¹, and the recommended value for the rate constant at 298 K is k = (2.43 ± 0.15) × 10⁻¹¹ cm³ molecule⁻¹ s⁻¹. The recommended Arrhenius expression for the reaction F + D₂ → DF + D, for the same temperature range, based on the recommended expression for k and accurate results for the kinetic isotope effect k/k is k = (1.06 ± 0.12) × 10^×10 exp |-(635 ± 55)/T|cm³ molecule⁻¹ s⁻¹, and the recommended value for 298 K is k = (1.25 ± 0.10) × 10⁻¹¹ cm³ molecule⁻¹ s⁻¹. © 1997 John Wiley & Sons, Inc. Int J Chem Kinet 29: 67–71, 1997.     

Effect of Macromolecular Crowding on the Conformation of Confined Chain Polymers

Summary: The conformational behavior of flexible linear chain polymers confined in cylindrical pores and slab pores has been studied, employing a hard‐bead chain model and a modification of a recently proposed recoil‐growth bias Monte Carlo methodology, which improves the sampling efficiency in confined environments. It is found that the scaling law that correlates the unconstrained component of the radius of gyration of the polymer with the pore diameter in cylindrical pores is close but neatly different than the de Gennes mean‐field value. The results also indicate that the addition of spherical particles with sizes within the protein limit may be employed to tune the folding of the confined polymer, since in this case the depletion constraints work against the effective stretching forces induced by confinement. Remarkably, the presence of the depleting particles at sufficiently high concentration leads to appreciable changes in the exponents of the conformational scaling laws with respect to the uncrowded system.

Conformational behavior of flexible hard‐bead chain polymers confined in narrow pores.     

Thermophysical properties of {(±)-linalool + propan-1-ol}: A first stage towards the development of a green process

In this paper, densities, speeds of sound and refractive indexes of binary mixture of {(±)-linalool (1) + propan-1-ol (2)} at four temperatures (283.15, 298.15, 313.15, and 328.15) K and 0.1 MPa are reported over the whole composition range. These data were used to calculate excess molar volume, speed of sound deviation, excess isentropic compressibility, refractive index deviation, molar refraction, and molar refraction deviation at the four work temperatures. All magnitudes were fitted to the Redlich–Kister equation. Subsequently prediction of speed of sound and refractive index was carried out using several theoretical models or equations. On the other hand, the density of the same mixture was determined in the same temperature range at pressures from 20 MPa to 40 MPa. Four equation of state (Peng–Robinson, Patel–Teja, SAFT, PC-SAFT) were tested as predictive models of the PρT behavior. The best results were obtained by PC-SAFT, with an average absolute deviation of 0.83%.     

Dam processes with state dependent batch sizes and intermittent production processes with state dependent rates

We consider a dam process with a general (state dependent) release rule and a pure jump input process, where the jump sizes are state dependent. We give sufficient conditions under which the process has a stationary version in the case where the jump times and sizes are governed by a marked point process which is point (Palm) stationary and ergodic. We give special attention to the Markov and Markov regenerative cases for which the main stability condition is weakened. We then study an intermittent production process with state dependent rates. We provide sufficient conditions for stability for this process and show that if these conditions are satisfied, then an interesting new relationship exists between the stationary distribution of this process and a dam process of the type we explore here.Supported in part by The Israel Science Foundation, grant no. 372/93-1.     

On permanental processes

Permanental processes can be viewed as a generalization of squared centered Gaussian processes. We analyze the connections of these processes with the local time process of general Markov processes. The obtained results are related to the notion of infinite divisibility.     

Centralized decision of internal transfer-prices with congestion externalities for two modes of repair with limited repair capacity

The internal transfer-prices set by an organization are what an organization's bases ‘pay’ its service centre, the depot, for its services. Since each base has a limited budget, these transfer-prices control and motivate the base's usage of two types of repair services: normal and expedited. In this paper, we implement a unique approach—transfer-prices with congestion externalities—to determine the optimal transfer-price for the expedited repair service. Inventory systems with limited repair capacity are affected by congestion externalities, which reflect the negative externalities caused by the use of a shared service. We also describe different models that develop transfer prices schemas, and which differ in the way they consider congestion externalities. Numerical illustrations based on data from an air force display the incompatibility between two optimization models. One model ignores congestion externalities, while another considers congestion externalities. In the case of congestion externalities, the base must pay extra for the expedited repair service. The increased costs are due to expanded usage of the limited repair capacity which a particular base is imposing on the rest of the system in the form of longer queues that degrade service quality.