Interpolation for nonlinear BVP in circular membrane with known upper and lower solutions

AbstractA successive nonextrapolatory linear interpolation is described to solve a singular two-point boundary value problem arising in circular membrane theory. The problem is associated with a second-order nonlinear ordinary differential equation for which the upper and lower bounds of the solution is analytically established/known. The importance and the scope of these bounds in solving the problem is stressed. Also depicted graphically are the lower and upper solutions as well as the true and iterated solutions. In addition, discussed are the reasons why linear interpolation, and not nonlinear interpolation or bisection which are possible procedures, has been employed

Computing queue length and waiting timedistributions in finite-buffer discrete-time multiserver queues with late and early arrivals

AbstractThis paper presents modelling and analysis of discrete-time multiserver finite-buffer queue with general interarrival and geometric service time. Using the supplementary variable technique, and considering the remaining interarrival time as a supplementary variable, two variants of this model, namely the late arrival system with delayed access (LAS-DA) and early arrival system (EAS), have been examined. For both the cases, steady-state system length distributions at arbitrary, prearrival, and outside observer's observation epochs have been obtained. Further, the waiting time distribution in the queue is also discussed. Various performance measures such as probability of loss, average number of busy servers and average waiting time in the queue etc. have been presented. It is hoped that the results obtained in this paper may provide useful information to designers of telecommunication systems, practitioners, and others

A batch-service queueing model with a discrete batch Markovian arrival process

Queueing systems with batch service have been investigated extensively during the past decades. However, nearly all the studied models share the common feature that an uncorrelated arrival process is considered, which is unrealistic in several real-life situations. In this paper, we study a discrete-time queueing model, with a server that only initiates service when the amount of customers in system (system content) reaches or exceeds a threshold. Correlation is taken into account by assuming a discrete batch Markovian arrival process (D-BMAP), i.e. the distribution of the number of customer arrivals per slot depends on a background state which is determined by a first-order Markov chain. We deduce the probability generating function of the system content at random slot marks and we examine the influence of correlation in the arrival process on the behavior of the system. We show that correlation merely has a small impact on the threshold that minimizes the mean system content. In addition, we demonstrate that correlation might have a significant influence on the system content and therefore has to be included in the model

Modeling of WEDM Parameters while Machining Mg-SiC Metal Matrix Composite

In this paper an attempt has been made to study the effects of the process parameters of wire cut electrical discharge machining (WEDM) on Magnesium-Silicon Carbide MMC with 5% SiC in particulate form. For the analysis, six factors, namely pulse on time, pulse off time, spark gap voltage, peak current, dielectric flushing pressure and servo feed have been taken and a Taguchi L16 orthogonal array for two levels was used. Response surface methodology was also used to develop second-order models for material removal rate (MRR) and surface roughness (SR). From the analysis of variances, it has been observed that pulse on time and pulse off time were the most significant parameters among all those observed in predicting the MRR and SR, respectively

TEM Study on the Evolution of Ge Nanocrystals in Si Oxide Matrix as a Function of Ge Concentration and the Si Reduction Process

Growth and evolution of germanium (Ge) nanocrystals embedded into a silicon oxide (SiO₂) system have been studied based on the Ge content of co-sputtered Ge-SiO₂ films using transmission electron microscopy (TEM) and X-ray photoelectron spectroscopy. It was found that when the proportion of Ge relative to Ge oxide is 20%, TEM showed that annealing the samples at 800°C for 60 min resulted in the formation of a denuded region between the silicon/silicon oxide (Si/SiO₂) interface and a band of Ge nanocrystals towards the surface of the film. By introducing a 20nm thick thermal oxide barrier on top of the silicon (Si) substrate on which the film is deposited, no denuded region in the bulk of this sample is observed. It is proposed that this barrier is effective in reducing both Ge diffusion into the Si substrate and Si diffusion from the substrate into the film. Si diffusing from the Si substrate reduces the Ge oxide into Ge which can subsequently diffuse into the Si substrate. However, the oxide barrier is able to confine the Ge within the oxide matrix so that the denuded region in the bulk of the film cannot form. However the reduction in diffusion should be more significant for Ge as its diffusion coefficient is lower than Si due to its larger size. It is suggested that the denuded region consists of amorphous Ge diffusing towards the Si/SiO₂ interface. When the Ge content is increased to slightly more than 70%, TEM showed that Ge nanocrysyals formed after annealing at 800°C for only 30 min for samples with and without the oxide barrier. There is no denuded region between the Ge nanocrystals band and the Si/SiO₂ interface for both samples but it was observed that coarsening effects were more prominent in the film deposited on top of the oxide barrier. The reduction effect of Si on Ge oxide should not play a significant role in these samples as the Ge content is high.Singapore-MIT Alliance (SMA

Glassy Phase Transition and Stability in Black Holes

Black hole thermodynamics, confined to the semi-classical regime, cannot address the thermodynamic stability of a black hole in flat space. Here we show that inclusion of correction beyond the semi-classical approximation makes a black hole thermodynamically stable. This stability is reached through a phase transition. By using Ehrenfest's scheme we further prove that this is a glassy phase transition with a Prigogine-Defay ratio close to 3. This value is well placed within the desired bound (2 to 5) for a glassy phase transition. Thus our analysis indicates a very close connection between the phase transition phenomena of a black hole and glass forming systems. Finally, we discuss the robustness of our results by considering different normalisations for the correction term.Comment: v3, minor changes over v2, references added, LaTeX-2e, 18 pages, 3 ps figures, to appear in Eour. Phys. Jour.

Quasiclassical description of transport through superconducting contacts

We present a theoretical study of transport properties through superconducting contacts based on a new formulation of boundary conditions that mimics interfaces for the quasiclassical theory of superconductivity. These boundary conditions are based on a description of an interface in terms of a simple Hamiltonian. We show how this Hamiltonian description is incorporated into quasiclassical theory via a T-matrix equation by integrating out irrelevant energy scales right at the onset. The resulting boundary conditions reproduce results obtained by conventional quasiclassical boundary conditions, or by boundary conditions based on the scattering approach. This formalism is well suited for the analysis of magnetically active interfaces as well as for calculating time-dependent properties such as the current-voltage characteristics or as current fluctuations in junctions with arbitrary transmission and bias voltage. This approach is illustrated with the calculation of Josephson currents through a variety of superconducting junctions ranging from conventional to d-wave superconductors, and to the analysis of supercurrent through a ferromagnetic nanoparticle. The calculation of the current-voltage characteristics and of noise is applied to the case of a contact between two d-wave superconductors. In particular, we discuss the use of shot noise for the measurement of charge transferred in a multiple Andreev reflection in d-wave superconductors

Suppression of charged particle production at large transverse momentum in central Pb-Pb collisions at sNN=2.76\sqrt{s_{\rm NN}} = 2.76 TeV

Inclusive transverse momentum spectra of primary charged particles in Pb-Pb collisions at $\sqrt{s_{_{\rm NN}}}$ = 2.76 TeV have been measured by the ALICE Collaboration at the LHC. The data are presented for central and peripheral collisions, corresponding to 0-5% and 70-80% of the hadronic Pb-Pb cross section. The measured charged particle spectra in $|\eta|<0.8$ and $0.3 < p_T < 20$ GeV/$c$ are compared to the expectation in pp collisions at the same $\sqrt{s_{\rm NN}}$, scaled by the number of underlying nucleon-nucleon collisions. The comparison is expressed in terms of the nuclear modification factor $R_{\rm AA}$. The result indicates only weak medium effects ($R_{\rm AA} \approx$ 0.7) in peripheral collisions. In central collisions, $R_{\rm AA}$ reaches a minimum of about 0.14 at $p_{\rm T}=6$-7GeV/$c$ and increases significantly at larger $p_{\rm T}$. The measured suppression of high-$p_{\rm T}$ particles is stronger than that observed at lower collision energies, indicating that a very dense medium is formed in central Pb-Pb collisions at the LHC.Comment: 15 pages, 5 captioned figures, 3 tables, authors from page 10, published version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/98

Two-pion Bose-Einstein correlations in central Pb-Pb collisions at sNN\sqrt{s_{\rm NN}} = 2.76 TeV

The first measurement of two-pion Bose-Einstein correlations in central Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 2.76$ TeV at the Large Hadron Collider is presented. We observe a growing trend with energy now not only for the longitudinal and the outward but also for the sideward pion source radius. The pion homogeneity volume and the decoupling time are significantly larger than those measured at RHIC.Comment: 17 pages, 5 captioned figures, 1 table, authors from page 12, published version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/388