Stability and performance of greedy server systems

Consider a queueing system in which arriving customers are placed on a circle and wait for service. A traveling server moves at constant speed on the circle, stopping at the location of the customers until service completion. The server is greedy: always moving in the direction of the nearest customer. Coffman and Gilbert conjectured that this system is stable if the traffic intensity is smaller than 1; however, a proof or counterexample remains unknown. In this review, we present a picture of the current state of this conjecture and suggest new related open problems.     

Distribution and Composition of Organic Matter in Oil- and Bitumen-cotaining Rocks in Deposits of Different Ages

The core samples of oil- and bitumen-containing rocks from Tatarstan's deposits of different ages were studied by thermal analysis methods (DTA, TG, DTG). Based on the obtained data, a procedure was elaborated for determining the enclosed organic matter content and the index of its fraction composition. A significant increase of the organic matter content in the core and its enrichment in high-molecular aromatic structures were shown to occur for the oil-containing rock samples when passing from the Devonian to Carboniferous and Permian deposits. The core samples of the Devonian oil-containing rocks may be divided into three groups: the samples taken from the zones where waste water flooding has been started relatively recently (1), or fresh water flooding has been carried on for a long time (2) and the samples of rock containing clay minerals as impurities. Thus, thermal analysis can be used in geochemical studies to identify the organic matter enclosed by oil- and bitumen-containing rocks. This revised version was published online in August 2006 with corrections to the Cover Date.     

Dopamine-assisted rapid fabrication of nanoscale protein arrays by colloidal lithography

The development of cost-effective methodologies for the precise nanometer-scale positioning of biomolecules permits the low-cost production of various biofunctional devices for a range of biomedical and nanotechnological applications. By combining colloidal lithography and the mussel-inspired multifunctional polydopamine coating, we present a novel parallel benchtop method that allows rapid nanoscale patterning of proteins without the need for electrically powered equipment in the fabrication process. The PDA-immobilized binary nanopattern consisting of BSA surrounded by PLL-g-PEG is fabricated over a large area, and the integrity of the pattern is confirmed using AFM and FM.     

On Transience Conditions for Markov Chains and Random Walks

We prove a new transience criterion for Markov chains on an arbitrary state space and give a corollary for real-valued chains. We show by example that in the case of a homogeneous random walk with infinite mean the proposed sufficient conditions are close to those necessary. We give a new proof of the well-known criterion for finiteness of the supremum of a random walk.     

The Lavrentiev Phenomenon in Nonlinear Elasticity

In 1985 J.M. Ball and V.J. Mizel raised the question of whether there exist nonlinearly elastic materials possessing a physically natural stored energy density, i.e., one which is independent of an observer's coordinate frame (objective) and is invariant under the group of orthogonal linear transformations of space (isotropic), as well as physically reasonable boundary value problems for such materials such that the infimum of the total stored energy for those continuous deformations of the material meeting the boundary condition (admissible deformations) which belong to a Sobolev space W ^{1 p} 2 for some p ₂>1 is strictly greater than its infimum for those admissible continuous deformations belonging to some Sobolev space W ¹ p ₁, p ₁<p ₂, despite the density of W ^{1 p} 2 in W ¹ p ₁. The question was motivated by M. Lavrentiev's demonstration in 1926 of the presence of such a gap for a 1-dimensional variational boundary value problem on a bounded interval whose smooth integrand satisfied the conditions of Tonelli's existence theorem (as well as the development of improved versions in the 1980's). The present article describes a positive response to the question raised in 1985. Namely, we provide examples of nonlinearly elastic materials in 2-dimensions and physically reasonable boundary value problems for these materials in which a positive gap exists between the infimum of the total stored energy over admissible continuous deformations belonging to a Sobolev space W ^{1 p} 2 and its infimum over admissible continuous deformations belonging to a Sobolev space W ^{1 p} 1, with p ₁<p ₂. The physical and computational significance of such results is also discussed.     

Measurements of Zeta Potential on Corroding,High-Purity Iron Particles: Influence of Corrosion Inhibitors

Adsorption of cetyl trimethyl ammonium bromide (CTAB), and two commercial inhibitor base chemicals; an oleic imidazoline salt (OI) and a phosphate ester (PE), onto high purity, corroding iron particles was studied by zeta potential measurements in a 0.1 Wt% sodium chloride (NaCl) solution under 1 bar CO₂ at 22°C. The particles were exposed to the inhibitor compounds for 24 hours before measurements were done. The results show that the measured zeta potential in the absence of inhibitor is zero at both pH 4.0 ± 0.2 and pH 5.8 ± 0.2. It is concluded that this might be caused by the electrochemical reactions occurring at the steel surface when placed in an electrical field. When adding inhibitor, which slows the electrochemical reactions at the steel surface, the zeta potential moves away from zero and an adsorption isotherm is obtained for all three inhibitors. The measured potential is probably a mixed potential where the apparent potential measured is a combination of the potential at the shear plane and a contribution form the electrochemical reactions occurring on the surface.     

Waiting Time Asymptotics in the Single Server Queue with Service in Random Order

We consider the single server queue with service in random order. For a large class of heavy-tailed service time distributions, we determine the asymptotic behavior of the waiting time distribution. For the special case of Poisson arrivals and regularly varying service time distribution with index ?ν, it is shown that the waiting time distribution is also regularly varying, with index 1?ν, and the pre-factor is determined explicitly. Another contribution of the paper is the heavy-traffic analysis of the waiting time distribution in the M/G/1 case. We consider not only the case of finite service time variance, but also the case of regularly varying service time distribution with infinite variance.