Some limit theorems for regenerative queues

We consider a single server queue with the interarrival times and the service times forming a regenerative sequence. This traffic class includes the standard models: lid, periodic, Markov modulated (e.g., BMAP model of Lucantoni [18]) and their superpositions. This class also includes the recently proposed traffic models in high speed networks, exhibiting long range dependence. Under minimal conditions we obtain the rates of convergence to stationary distributions, finiteness of stationary moments, various functional limit theorems and the continuity of stationary distributions and moments. We use the continuity results to obtain approximations for stationary distributions and moments of an MMPP/GI/1 queue where the modulating chain has a countable state space. We extend all our results to feedforward networks where the external arrivals to each queue can be regenerative. In the end we show that the output process of a leaky bucket is regenerative if the input process is and hence our results extend to a queue with arrivals controlled by a leaky bucket.

Superconductivity in the nonadiabatic limit

Isotope-shift exponent (cu) and the pressure coefficient of superconducting transition temperature (beta) have been studied in the nonadiabatic limit. We have considered the effect of nonadiabaticity in both within and beyond the Migdal-Eliashberg formalism. It reveals from our study that the pressure coefficient of superconducting transition is high for the low-T-c region and low for the high-T-c region and the minimum value of alpha is obtained where the transition temperature is maximum. Lowest value of isotope-shift exponent is obtained for small momentum exchange between the electrons and the bosonic field. Qualitative variation of beta with temperature is consistent with the experimental results of the hole doped superconductors for small momentum exchange.

"Small-particle limit" the second harmonic generation from noble metal nanoparticles

In this paper, we have probed the origin of SHG in copper nanoparticles by polarization-resolved hyper-Rayleigh scattering (HRS). Results obtained with various sizes of copper nanoparticles at four different wavelengths covering the wavelength range 738-1907 nm reveal that the origin of second harmonic generation (SHG) in these particles is purely dipolar in nature as long as the size (d) of the particles remains smaller compared to the wavelength (;.) of light ("small-particle limit"). However, contribution of the higher order multipoles coupled with retardation effect becomes apparent with an increase in the d/lambda ratio. We have identified the "small-particle limit" in the second harmonic generation from noble metal nanoparticles by evaluating the critical d/lambda ratio at which the retardation effect sets in the noble metal nanoparticles. We have found that the second-order nonlinear optical property of copper nanoparticles closely resembles that of gold, but not that of silver. (C) 2009 Elsevier B.V. All rights reserved.

Calciothermic reduction of TiO2: A diagrammatic assessment of the thermodynamic limit of deoxidation

Calciothermic reduction of TiO2 provides a potentially low-cost route to titanium production. Presented in this article is a suitably designed diagram, useful for assessing the degree of reduction of TiO2 and residual oxygen contamination in metal as a function of reduction temperature and other process parameters. The oxygen chemical potential diagram à la Ellingham-Richardson-Jeffes is useful for visualization of the thermodynamics of reduction reactions at high temperatures. Although traditionally the diagram depicts oxygen potentials corresponding to the oxidation of different metals to their corresponding oxides or of lower oxides to higher oxides, oxygen potentials associated with solution phases at constant composition can be readily superimposed. The usefulness of the diagram for an insightful analysis of calciothermic reduction, either direct or through an electrochemical process, is discussed. Identified are possible process variations, modeling and optimization strategies.

Vertical uplift capacity of two interfering horizontal anchors in sand using an upper bound limit analysis

The vertical uplift resistance of two interfering rigid rough strip anchors embedded horizontally in sand at shallow depths has been examined. The analysis is performed by using an upper bound theorem o limit analysis in combination with finite elements and linear programming. It is specified that both the anchors are loaded to failure simultaneously at the same magnitude of the failure load. For different clear spacing (S) between the anchors, the magnitude of the efficiency factor (xi(gamma)) is determined. On account of interference, the magnitude of xi(gamma) is found to reduce continuously with a decrease in the spacing between the anchors. The results from the numerical analysis were found to compare reasonably well with the available theoretical data from the literature.

Limit Loads of Wires with Twisted Joints

In the design of a windmill using a sail type rotor, there arose a need to protect the structure against damage due to overloading in excessive winds. This need was satisfied by using a novel form of load limiter in the support system of sails of the windmill. This note will analyze the load capacity wires so that one can design wires for any specified limit load.

Continuation of limit cycles near saddle homoclinic points using splines in phase space

We present a new algorithm for continuation of limit cycles of autonomous systems as a system parameter is varied. The algorithm works in phase space with an ordered set of points on the limit cycle, along with spline interpolation. Currently popular algorithms in bifurcation analysis packages compute time-domain approximations of limit cycles using either shooting or collocation. The present approach seems useful for continuation near saddle homoclinic points, where it encounters a corner while time-domain methods essentially encounter a discontinuity (a relatively short period of rapid variation). Other phase space-based algorithms use rescaled arclength in place of time, but subsequently resemble the time-domain methods. Compared to these, we introduce additional freedom through a variable stretching of arclength based on local curvature, through the use of an auxiliary index-based variable. Several numerical examples are presented. Comparisons with results from the popular package, MATCONT, are favorable close to saddle homoclinic points.

A Note on the Determination of Plastic Limit of Fine-Grained Soils

Plastic limit of fine-grained soils is conventionally determined in the laboratory by the soil thread rolling method. Many adverse comments have been recorded in the geotechnical engineering literature on the method about its reproducibility and operator dependency. The presen experimental study, which is based on a well-planned and meticulously executed experimental program, critically evaluates the effect of size of the rolled soil thread on the plastic limit of fine-grained soil and the operator dependency of the results. The results have shown that if the plastic limit tests are performed by a trained operator, then consistent results can be obtained and that the effect of size of the rolled soil thread on plastic limit is negligibly small.

Thermochemistry and lower combustion limit of ammonium perchlorate in presence of methylammonium perchlorates

The heats of combustion of mono-, di-, tri- and tetramethylammonium perchlorates have been determined by bomb calorimetry. The data have been used to explain why the thermal behavior of ammonium perchlorate (AP) is considerably modified in presence of these compounds as shown by differential thermal analysis. Above a particular concentration of methylammonium perchlorate (MAP), AP ignites in a single step around 290°C. The minimum concentration of a MAP (mono-, di-, tri- or tetra-) needed to cause ignition of AP in a single step depends on intramolecular “elemental stoichiometric coefficient” of the mixtures that has the same value regardless of the MAP. Furthermore, the calorimetric values of these mixtures are the same. The heat evolved on ignition of such a composition appears to determine the lower concentration limit of combustion of its mixture with AP.

Limit analysis of annular slabs - reply

Abstract is not available.

Re-examination of one-point methods of liquid limit determination

This Paper deals with the analysis of liquid limit of soils, an inferential parameter of universal acceptance. It has been undertaken primarily to re-examine one-point methods of determination of liquid limit water contents. It has been shown by basic characteristics of soils and associated physico-chemical factors that critical shear strengths at liquid limit water contents arise out of force field equilibrium and are independent of soil type. This leads to the formation of a scientific base for liquid limit determination by one-point methods, which hitherto was formulated purely on statistical analysis of data. Available methods (Norman, 1959; Karlsson, 1961; Clayton & Jukes, 1978) of one-point liquid limit determination have been critically re-examined. A simple one-point cone penetrometer method of computing liquid limit has been suggested and compared with other methods. Experimental data of Sherwood & Ryley (1970) have been employed for comparison of different cone penetration methods. Results indicate that, apart from mere statistical considerations, one-point methods have a strong scientific base on the uniqueness of modified flow line irrespective of soil type. Normalized flow line is obtained by normalization of water contents by liquid limit values thereby nullifying the effects of surface areas and associated physico-chemical factors that are otherwise reflected in different responses at macrolevel.Cet article traite de l'analyse de la limite de liquidité des sols, paramètre déductif universellement accepté. Cette analyse a été entreprise en premier lieu pour ré-examiner les méthodes à un point destinées à la détermination de la teneur en eau à la limite de liquidité. Il a été démontré par les caractéristiques fondamentales de sols et par des facteurs physico-chimiques associés que les résistances critiques à la rupture au cisaillement pour des teneurs en eau à la limite de liquidité résultent de l'équilibre des champs de forces et sont indépendantes du type de sol concerné. On peut donc constituer une base scientifique pour la détermination de la limite de liquidité par des méthodes à un point lesquelles, jusqu'alors, n'avaient été formulées que sur la base d'une analyse statistique des données. Les méthodes dont on dispose (Norman, 1959; Karlsson, 1961; Clayton & Jukes, 1978) pour la détermination de la limite de liquidité à un point font l'objet d'un ré-examen critique. Une simple méthode d'analyse à un point à l'aide d'un pénétromètre à cône pour le calcul de la limite de liquidité a été suggérée et comparée à d'autres méthodes. Les données expérimentales de Sherwood & Ryley (1970) ont été utilisées en vue de comparer différentes méthodes de pénétration par cône. En plus de considérations d'ordre purement statistque, les résultats montrent que les méthodes de détermination à un point constituent une base scientifique solide en raison du caractère unique de la ligne de courant modifiée, quel que soit le type de sol La ligne de courant normalisée est obtenue par la normalisation de la teneur en eau en faisant appel à des valeurs de limite de liquidité pour, de cette manière, annuler les effets des surfaces et des facteurs physico-chimiques associés qui sans cela se manifesteraient dans les différentes réponses au niveau macro.

Lower Bound Limit Analysis of Rectangular Slabs

A general method for the development of valid lower bound solutions to uniformly distributed and orthotropically reinforced rectangular concrete slabs obeying normal moment criterion is described. General expressions for moment field have been obtained for nine cases of slabs having all combinations of simply supported and clamped-edge conditions. The lower bound collapse loads have been compared with the upper bound values obtained by the yield line theory. The paper also focuses attention to the need for the development of valid upper bound solutions with the satisfaction of kinematical admissibility and the flow rules associated with the normal moment criterion.

Critical lattice size limit for synchronized chaotic state in one- and two-dimensional diffusively coupled map lattices

We consider diffusively coupled map lattices with P neighbors (where P is arbitrary) and study the stability of the synchronized state. We show that there exists a critical lattice size beyond which the synchronized state is unstable. This generalizes earlier results for nearest neighbor coupling. We confirm the analytical results by performing numerical simulations on coupled map lattices with logistic map at each node. The above analysis is also extended to two-dimensional P-neighbor diffusively coupled map lattices.

Semi-empirical procedures for estimation of residual velocity and ballistic limit for impact on mild steel plates by projectiles

This paper deals with the development of simplified semi-empirical relations for the prediction of residual velocities of small calibre projectiles impacting on mild steel target plates, normally or at an angle, and the ballistic limits for such plates. It has been shown, for several impact cases for which test results on perforation of mild steel plates are available, that most of the existing semi-empirical relations which are applicable only to normal projectile impact do not yield satisfactory estimations of residual velocity. Furthermore, it is difficult to quantify some of the empirical parameters present in these relations for a given problem. With an eye towards simplicity and ease of use, two new regression-based relations employing standard material parameters have been discussed here for predicting residual velocity and ballistic limit for both normal and oblique impact. The latter expressions differ in terms of usage of quasi-static or strain rate-dependent average plate material strength. Residual velocities yielded by the present semi-empirical models compare well with the experimental results. Additionally, ballistic limits from these relations show close correlation with the corresponding finite element-based predictions.

Predicting price-tag for customized goods

We discuss a dynamic pricing model which will aid automobile manufacturer in choosing the right price for customer segment. Though there is oligopoly market structure, the customers get "locked" into a particular technology/company which virtually makes the situation akin to a monopoly. There are associated network externalities and positive feedback. The key idea in monopoly pricing lies in extracting the customer surplus by exploiting the respective elasticities of demand. We present a Walrasian general equilibrium approach to determine the segment price. We compare the prices obtained from optimization model with that from Walrasian dynamics. The results are encouraging and can serve as a critical factor in Customer Relationship Management (CRM) and thereby effectively manage the lock-in.