Electron acoustic soliton energy of the Kadomtsev-Petviashvili equation in the Earth’s magnetotail region at critical ion density

The nonlinear properties of small amplitude electron-acoustic solitary waves (EAWs) in a homogeneous system of unmagnetized collisionless plasma consisted of a cold electron fluid and isothermal ions with two different temperatures obeying Boltzmann type distributions have been investigated. A reductive perturbation method was employed to obtain the Kadomstev-Petviashvili (KP) equation. At the critical ion density, the KP equation is not appropriate for describing the system. Hence, a new set of stretched coordinates
is considered to derive the modified KP equation. Moreover, the solitary solution, soliton energy and the associated electric field at the critical ion density were computed. The present investigation can be of relevance to the electrostatic solitary structures observed in various space plasma environments, such as Earth’s magnetotail region.

Electronic properties of interfaces and defects from many-body perturbation theory: Recent developments and applications

We review some recent developments in many body perturbation theory (MBPT) calculations that have enabled the study of interfaces and defects. Starting from the theoretical basis of MBPT, Hedin's equations are presented, leading to the CW and CWI' approximations. We introduce the perturbative approach, that is the one most commonly used for obtaining quasiparticle (QP) energies. The practical strategy presented for dealing with the frequency dependence of the self energy operator is based on either plasmon-pole models (PPM) or the contour deformation technique, with the latter being more accurate. We also discuss the extrapolar method for reducing the number of unoccupied states which need to be included explicity in the calculations. The use of the PAW method in the framework of MBPT is also described. Finally, results which have been obtained using, MBPT for band offsets a interfaces and for defects presented, with companies on the main difficulties and cancels.

Schematic representation of the QP corrections (marked with ) to the band edges (E and E-v) and a defect level (F) for a Si/SiO2 interface (Si and O atoms are represented in blue and red, respectively, in the ball and stick model) with an oxygen vacancy leading to a Si-Si bond (the Si atoms involved in this bond are colored light blue).

Zel'dovich's method of perturbation theory in quantum mechanics

Many years ago Zel'dovich showed how the Lagrange condition in the theory of differential equations can be utilized in the perturbation theory of quantum mechanics. Zel'dovich's method enables us to circumvent the summation over intermediate states. As compared with other similar methods, in particular the logarithmic perturbation expansion method, we emphasize that this relatively unknown method of Zel'dovich has a remarkable advantage in dealing with excited stares. That is, the ground and excited states can all be treated in the same way. The nodes of the unperturbed wavefunction do not give rise to any complication.

A Petrov-Galerkin method for a singularly perturbed ordinary differential equation with non-smooth data

In this paper, a singularly perturbed ordinary differential equation with non-smooth data is considered. The numerical method is generated by means of a Petrov-Galerkin finite element method with the piecewise-exponential test function and the piecewise-linear trial function. At the discontinuous point of the coefficient, a special technique is used. The method is shown to be first-order accurate and singular perturbation parameter uniform convergence. Finally, numerical results are presented, which are in agreement with theoretical results.

A survey in mathematics for industry: Two-timing and matched asymptotic expansions for singular perturbation problems

Following the derivation of amplitude equations through a new two-time-scale method [O'Malley, R. E., Jr. & Kirkinis, E (2010) A combined renormalization group-multiple scale method for singularly perturbed problems. Stud. Appl. Math. 124, 383-410], we show that a multi-scale method may often be preferable for solving singularly perturbed problems than the method of matched asymptotic expansions. We illustrate this approach with 10 singularly perturbed ordinary and partial differential equations. © 2011 Cambridge University Press.

Efficient probabilistic contingency analysis through a stability measure considering wind perturbation

The integration of stochastic wind power has accentuated a challenge for power system stability assessment. Since the power system is a time-variant system under wind generation fluctuations, pure time-domain simulations are difficult to provide real-time stability assessment. As a result, the worst-case scenario is simulated to give a very conservative assessment of system transient stability. In this study, a probabilistic contingency analysis through a stability measure method is proposed to provide a less conservative contingency analysis which covers 5-min wind fluctuations and a successive fault. This probabilistic approach would estimate the transfer limit of a critical line for a given fault with stochastic wind generation and active control devices in a multi-machine system. This approach achieves a lower computation cost and improved accuracy using a new stability measure and polynomial interpolation, and is feasible for online contingency analysis.

Modelling of solute transport in a mild heterogeneous porous medium using stochastic finite element method: Effects of random source conditions

Randomness in the source condition other than the heterogeneity in the system parameters can also be a major source of uncertainty in the concentration field. Hence, a more general form of the problem formulation is necessary to consider randomness in both source condition and system parameters. When the source varies with time, the unsteady problem, can be solved using the unit response function. In the case of random system parameters, the response function becomes a random function and depends on the randomness in the system parameters. In the present study, the source is modelled as a random discrete process with either a fixed interval or a random interval (the Poisson process). In this study, an attempt is made to assess the relative effects of various types of source uncertainties on the probabilistic behaviour of the concentration in a porous medium while the system parameters are also modelled as random fields. Analytical expressions of mean and covariance of concentration due to random discrete source are derived in terms of mean and covariance of unit response function. The probabilistic behaviour of the random response function is obtained by using a perturbation-based stochastic finite element method (SFEM), which performs well for mild heterogeneity. The proposed method is applied for analysing both the 1-D as well as the 3-D solute transport problems. The results obtained with SFEM are compared with the Monte Carlo simulation for 1-D problems.

Measurement of the top quark mass at CDF using the “neutrino ϕ weighting” template method on a lepton plus isolated track sample

We present a measurement of the top quark mass with t-tbar dilepton events produced in p-pbar collisions at the Fermilab Tevatron $\sqrt{s}$=1.96 TeV and collected by the CDF II detector. A sample of 328 events with a charged electron or muon and an isolated track, corresponding to an integrated luminosity of 2.9 fb$^{-1}$, are selected as t-tbar candidates. To account for the unconstrained event kinematics, we scan over the phase space of the azimuthal angles ($\phi_{\nu_1},\phi_{\nu_2}$) of neutrinos and reconstruct the top quark mass for each $\phi_{\nu_1},\phi_{\nu_2}$ pair by minimizing a $\chi^2$ function in the t-tbar dilepton hypothesis. We assign $\chi^2$-dependent weights to the solutions in order to build a preferred mass for each event. Preferred mass distributions (templates) are built from simulated t-tbar and background events, and parameterized in order to provide continuous probability density functions. A likelihood fit to the mass distribution in data as a weighted sum of signal and background probability density functions gives a top quark mass of $165.5^{+{3.4}}_{-{3.3}}$(stat.)$\pm 3.1$(syst.) GeV/$c^2$.

Performance analysis of subspace based method for source localization in shallow water

The present paper aims at studying the performance characteristics of a subspace based algorithm for source localization in shallow water such as coastal water. Specifically, we study the performance of Multi Image Subspace Algorithm (MISA). Through first-order perturbation analysis and computer simulation it is shown that MISA is unbiased and statistically efficient. Further, we bring out the role of multipaths (or images) in reducing the error in the localization. It is shown that the presence of multipaths is found to improve the range and depth estimates. This may be attributed to the increased curvature of the wavefront caused by interference from many coherent multipaths.

Learning the global maximum with parameterized learning automata

A feedforward network composed of units of teams of parameterized learning automata is considered as a model of a reinforcement teaming system. The internal state vector of each learning automaton is updated using an algorithm consisting of a gradient following term and a random perturbation term. It is shown that the algorithm weakly converges to a solution of the Langevin equation implying that the algorithm globally maximizes an appropriate function. The algorithm is decentralized, and the units do not have any information exchange during updating. Simulation results on common payoff games and pattern recognition problems show that reasonable rates of convergence can be obtained.

Optimal Parameterized Policies for Resource Allocation in Communication Networks

The problem of finding optimal parameterized feedback policies for dynamic bandwidth allocation in communication networks is studied. We consider a queueing model with two queues to which traffic from different competing flows arrive. The queue length at the buffers is observed every T instants of time, on the basis of which a decision on the amount of bandwidth to be allocated to each buffer for the next T instants is made. We consider two different classes of multilevel closed-loop feedback policies for the system and use a two-timescale simultaneous perturbation stochastic approximation (SPSA) algorithm to find optimal policies within each prescribed class. We study the performance of the proposed algorithm on a numerical setting and show performance comparisons of the two optimal multilevel closedloop policies with optimal open loop policies. We observe that closed loop policies of Class B that tune parameters for both the queues and do not have the constraint that the entire bandwidth be used at each instant exhibit the best results overall as they offer greater flexibility in parameter tuning. Index Terms — Resource allocation, dynamic bandwidth allocation in communication networks, two-timescale SPSA algorithm, optimal parameterized policies. I.

Porous wide band gap BiNbO4 ceramic nanopowder synthesised by low temperature solution-based method for gas sensing applications

In this study, we report the gas sensing behavior of BiNbO4 nanopowder prepared by a low temperature simple solution-based method. Before the sensing behaviour study, the as-synthesized nanopowder was characterized by X-ray diffraction, scanning electron microscopy, transmission electron microscopy, UV-diffuse reflectance spectroscopy, impedance analysis, and surface area measurement. The NH3 sensing behavior of BiNbO4 was then studied by temperature modulation (50-350 degrees C) as well as concentration modulation (20-140 ppm). At the optimum operating temperature of 325 degrees C, the sensitivity was measured to be 90%. The cross-sensitivity of as-synthesized BiNbO4 sensor was also investigated by assessing the sensing behavior toward other gases such as hydrogen sulphide (H2S), ethanol (C2H5OH), and liquid petroleum gas (LPG). Finally, selectivity of the sensing material toward NH3 was characterized by observing the sensor response with gas concentrations in the range 20-140 ppm. The response and recovery time for NH3 sensing at 120 ppm were about 16 s and about 17 s, respectively.

A robust layer adapted difference method for singularly perturbed two-parameter parabolic problems

A finite difference method for a time-dependent singularly perturbed convection-diffusion-reaction problem involving two small parameters in one space dimension is considered. We use the classical implicit Euler method for time discretization and upwind scheme on the Shishkin-Bakhvalov mesh for spatial discretization. The method is analysed for convergence and is shown to be uniform with respect to both the perturbation parameters. The use of the Shishkin-Bakhvalov mesh gives first-order convergence unlike the Shishkin mesh where convergence is deteriorated due to the presence of a logarithmic factor. Numerical results are presented to validate the theoretical estimates obtained.

Simultaneous perturbation methods for adaptive labor staffing in service systems

We consider the problem of optimizing the workforce of a service system. Adapting the staffing levels in such systems is non-trivial due to large variations in workload and the large number of system parameters do not allow for a brute force search. Further, because these parameters change on a weekly basis, the optimization should not take longer than a few hours. Our aim is to find the optimum staffing levels from a discrete high-dimensional parameter set, that minimizes the long run average of the single-stage cost function, while adhering to the constraints relating to queue stability and service-level agreement (SLA) compliance. The single-stage cost function balances the conflicting objectives of utilizing workers better and attaining the target SLAs. We formulate this problem as a constrained parameterized Markov cost process parameterized by the (discrete) staffing levels. We propose novel simultaneous perturbation stochastic approximation (SPSA)-based algorithms for solving the above problem. The algorithms include both first-order as well as second-order methods and incorporate SPSA-based gradient/Hessian estimates for primal descent, while performing dual ascent for the Lagrange multipliers. Both algorithms are online and update the staffing levels in an incremental fashion. Further, they involve a certain generalized smooth projection operator, which is essential to project the continuous-valued worker parameter tuned by our algorithms onto the discrete set. The smoothness is necessary to ensure that the underlying transition dynamics of the constrained Markov cost process is itself smooth (as a function of the continuous-valued parameter): a critical requirement to prove the convergence of both algorithms. We validate our algorithms via performance simulations based on data from five real-life service systems. For the sake of comparison, we also implement a scatter search based algorithm using state-of-the-art optimization tool-kit OptQuest. From the experiments, we observe that both our algorithms converge empirically and consistently outperform OptQuest in most of the settings considered. This finding coupled with the computational advantage of our algorithms make them amenable for adaptive labor staffing in real-life service systems.