Method of asymptotic semiinvariants for studying a mathematical model of a random access network

To study a mathematical model of a random access network with a finite number of sources, retrials, and a conflict warning stage, we propose a method of asymptotic semiinvariants under a growing number of sources, which allows us to find the asymptotic probability distribution of the number of requests in a retrial pool. We present results of numerical implementation of a prelimit distribution of the number of requests in the retrial pool. We compare the prelimit and asymptotic semiinvariants.     

Geomechanics rock mechanics aspects in deep well drilling

Based on the proposed modeling approach to deep well drilling with the use of equations of state of an elastoplastic medium with dilatancy, the authors have found nonlinear relationship between dimension of probable failure zones in the wellbore vicinity and the value of lateral thrust coefficient, as well as they explain the causes of rise in speed of drilling at the depth of 3–4 kilometers.     

Impedance Measurements as a Simple Tool to Control the Quality of Conjugated Polymers Designed for Photovoltaic Applications

The problem of batch‐to‐batch variation of electronic properties and purity of conjugated polymers used as electron donor and photon harvesting materials in organic solar cells is addressed. A simple method is developed for rapid analysis of electronic quality of polymer‐based materials. It is shown that appearance of impurities capable of charge trapping changes electrophysical properties of conjugated polymers. In particular, a clear correlation between the effective relaxation time τeff and relative photovoltaic performance (η/η_max) is revealed for samples of poly(3‐hexylthiophene) intentionally polluted with a palladium catalyst. This dependence is also valid for all other investigated samples of conjugated polymers. Therefore, fast impedance measurements at three different frequencies allow one to draw conclusions about the purity of the analyzed polymer sample and even estimate its photovoltaic performance. The developed method might find extensive applications as a simple tool for product quality control in the laboratory and industrial‐scale production of conjugated polymers for electronic applications.     

Synthesis, X-ray structure and luminescent properties of Sm^3＋ ternary complex with novel heterocyclic β-diketone and 1,10-phenanthroline （Phen）

A new neutral ternary samarium complex Sm(Phen)HL3 in which Phen is 1,10-phenanthroline and HL is (1,3-bis(1,3-dimethyl-1H-pyrazol-4-yl)-1,3-propanedione) was synthesized. Molecular structure of this complex was determined by X-ray diffraction. Under UV-light this complex is demonstrated bright red luminescence (λmax=647 nm), which was corresponding to the electric dipole 4G5/2→6H9/2 transition in Sm3+ ion. UV-absorption, excitation and emission spectra of the title compound were investigated.     

IMPLEMENTATION OF MATHEMATICA FOR DEVELOPMENT AND APPLICATION OF EOS MODELS. I: DERIVATION OF THE EXPRESSIONS FOR HARD-CHAIN AND HARD-SPHERE COMPRESSIBILITY FACTORS

This work discusses an implementation of the computer program Mathematica for developing an algorithm for derivation of the analytical expressions for hard-sphere and hard-chain compressibility factors. This systematic analysis allows a selection of the appropriate parameter values.     

Asymptotic analysis of lubricated heavily loaded point contacts

The paper is devoted to the development of an asymptotic approach to solution of the steady isothermal problem of elastohydrodynamic lubrication (EHL) for heavily loaded point contacts. It is shown that the whole contact region can be subdivided into three subregions: the central one that is adjacent to the other two regions occupied by the ends of the horseshoe‐shaped pressure/gap distribution zone. The central region, in turn, can be subdivided into the Hertzian region and its adjacent inlet and exit zones that, in turn, are adjacent to the inlet and exit boundaries of the contact, respectively. Moreover, in the central region, in the inlet and exit zones of heavily loaded point EHL contact, the EHL problem can be reduced to asymptotically valid equations identical to the ones obtained in the inlet and exit zones of heavily loaded line EHL contacts. The latter means that many of the well‐known properties of heavily loaded line EHL contacts are also valid for heavily loaded point EHL contacts. These asymptotically valid equations can be analysed and numerically solved based on the stable methods using a specific regularisation approach that were developed for lubricated line contacts. Cases of pre‐critical and over‐critical lubrication regimes are considered. The by‐product of this asymptotic analysis is an easy analytical derivation of formulas for the lubrication film thickness for pre‐critical and over‐critical lubrication regimes. The method is validated by the results of some experimental and numerical studies published by a number of researches. Copyright © 2013 John Wiley & Sons, Ltd.     

rhAPC reduces the endothelial cell permeability via a decrease of contractile tensions induced by endothelial cells

All cells generate contractile tension. This strain is crucial for mechanically controlling the cell shape, function and survival. In this study, the CellDrum technology quantifying cell's (the cellular) mechanical tension on a pico-scale was used to investigate the effect of lipopolysaccharide (LPS) on human aortic endothelial cell (HAoEC) tension. The LPS effect during gram-negative sepsis on endothelial cells is cell contraction causing endothelium permeability increase. The aim was to finding out whether recombinant activated protein C (rhAPC) would reverse the endothelial cell response in an in-vitro sepsis model. In this study, the established in-vitro sepsis model was confirmed by interleukin 6 (IL-6) levels at the proteomic and genomic levels by ELISA, real time-PCR and reactive oxygen species (ROS) activation by florescence staining. The thrombin cellular contraction effect on endothelial cells was used as a positive control when the CellDrum technology was applied. Additionally, the Ras homolog gene family, member A (RhoA) mRNA expression level was checked by real time-PCR to support contractile tension results. According to contractile tension results, the mechanical predominance of actin stress fibers was a reason of the increased endothelial contractile tension leading to enhanced endothelium contractility and thus permeability enhancement. The originality of this data supports firstly the basic measurement principles of the CellDrum technology and secondly that rhAPC has a beneficial effect on sepsis influenced cellular tension. The technology presented here is promising for future high-throughput cellular tension analysis that will help identify pathological contractile tension responses of cells and prove further cell in-vitro models.     

Ignition waves in a stirred PEM fuel cell

A mathematical model of slow transient behavior in an autohumidified stirred tank reactor (STR) polymer electrolyte membrane (PEM) fuel cell is developed. The key feature of the model is the positive feedback between current, water production, and membrane resistance which leads to two stable “ignited” states, corresponding to either a uniform current distribution or a partially ignited cell with localized current production. The switching between the two regimes is accompanied by hysteresis and transient behavior on the order of 2-4 h in a small cell. We compare the numerical results to experimental data gathered by [Benziger et al. 2005. Chemical Engineering Science 60 (6), 1743-1759] and show that the lateral diffusion of water within the ionomer membrane is a possible mechanism behind the hysteresis and slow transient behavior they observed.