Parabolic Method Research Articles

On a discrete-time GI$^X$/Geo/1/N-G queue with randomized working vacations and at most $J$ vacations

This paper considers a discrete-time GI$^X$/Geo/1/N-G queue with randomized working vacations, where upon arrival, a negative customer removes one positive (ordinary) customer in service if any is present and disappears immediately; otherwise, it has no effect on the system if the system is empty. As soon as the system becomes empty, the server immediately takes a working vacation. If there are no customers in the system at the end of the working vacation, the server takes another working vacation with probability $p$ or remains dormant in the system with probability $1-p$. Otherwise, the server starts to serve the customers with the normal service rate immediately if there are some customers at the end of a working vacation. This pattern does not terminate until the server has taken $J$ successive working vacations. Steady-state system length distributions at various epochs such as, pre-arrival, arbitrary and outside observer's observation epochs have been obtained. Based on the various system length distributions, we also give some important performance measures including blocking probabilities, mean queue length, probability mass function of waiting time and other performance measures along with some numerical examples. Then, we use the parabolic method to search the optimum value of the normal service rate under a established cost function.

A two-dimensional analytical model for channel potential and threshold voltage of short channel dual material gate lightly doped drain MOSFET

An analytical model for the channel potential and the threshold voltage of the short channel dual-material-gate lightly doped drain (DMG-LDD) metal—oxide—semiconductor field-effect transistor (MOSFET) is presented using the parabolic approximation method. The proposed model takes into account the effects of the LDD region length, the LDD region doping, the lengths of the gate materials and their respective work functions, along with all the major geometrical parameters of the MOSFET. The impact of the LDD region length, the LDD region doping, and the channel length on the channel potential is studied in detail. Furthermore, the threshold voltage of the device is calculated using the minimum middle channel potential, and the result obtained is compared with the DMG MOSFET threshold voltage to show the improvement in the threshold voltage roll-off. It is shown that the DMG-LDD MOSFET structure alleviates the problem of short channel effects (SCEs) and the drain induced barrier lowering (DIBL) more efficiently. The proposed model is verified by comparing the theoretical results with the simulated data obtained by using the commercially available ATLAS™ 2D device simulator.

Comparison of parabolic filtration methods for 3D filtered back projection in pulsed EPR imaging

Pulse electron paramagnetic resonance imaging (Pulse EPRI) is a robust method for noninvasively measuring local oxygen concentrations in vivo. For 3D tomographic EPRI, the most commonly used reconstruction algorithm is filtered back projection (FBP), in which the parabolic filtration process strongly influences image quality. In this work, we designed and compared 7 parabolic filtration methods to reconstruct both simulated and real phantoms. To evaluate these methods, we designed 3 error criteria and 1 spatial resolution criterion. It was determined that the 2 point derivative filtration method and the two-ramp-filter method have unavoidable negative effects resulting in diminished spatial resolution and increased artifacts respectively. For the noiseless phantom the rectangular-window parabolic filtration method and sinc-window parabolic filtration method were found to be optimal, providing high spatial resolution and small errors. In the presence of noise, the 3 point derivative method and Hamming-window parabolic filtration method resulted in the best compromise between low image noise and high spatial resolution. The 3 point derivative method is faster than Hamming-window parabolic filtration method, so we conclude that the 3 point derivative method is optimal for 3D FBP.

A WRF–CMAQ study on spring time vertical ozone structure in Southeast Texas

A WRF–SMOKE–CMAQ modeling system was used to simulate vertical profiles of ozone, temperature and wind as well as surface ozone and meteorology during the Study of Houston Atmospheric Radical Precursors (SHARP) in May 2009. WRF and CMAQ sensitivity studies were conducted to define a proper combination of model configurations.With objective analysis WRF showed considerable skills in simulating temperature and wind profiles. CMAQ did well in replicating daily regional average ozone, with only minor overprediction for most of the days. According to the surface ozone statistics and the ozone biases along the vertical profiles, the model displayed little sensitivity to the two CMAQ model options: (i) fixed night time PBL height vs. WRF calculated night time PBL heights, and (ii) the combination of the Euler-backward iterative chemistry schemes and Yamartino advection (EBI/YAMO) vs. the Sparse-Matrix Vectorized Gear chemistry and Parabolic Method advection (SMV-GEAR/PPM) schemes. CMAQ shows substantial underprediction of ozone in the upper troposphere, but demonstrated fair skills in reproducing the ozone profile in the lower to middle troposphere, with typically a few ppb negative biases which tend to increase with height. However, the model usually cannot reproduce high variability in the ozone profiles due to the fixed default profiles and lack of data assimilation capability. While the default CMAQ static profile setup for boundary condition (BC) does not properly reflect the actual dynamic atmosphere, it remains a reasonable choice, since using downscaled real-time global chemistry model BCs demands considerable efforts and would still depend on the performance of the global model.

Ghost calibration and the pricing of barrier options and CDS in spectrally one-sided Lévy models: the parabolic Laplace inversion method

Recently, the advantages of conformal deformations of the contours of integration in pricing formulas were demonstrated in the context of wide classes of Lévy models and the Heston model. In the present paper, we construct efficient conformal deformations of the contours of integration in the pricing formulas for barrier options and CDS in the setting of spectrally one-sided Lévy models, taking advantage of Rogers’s trick [J. Appl. Prob., 2000, 37, 1173–1180] that greatly simplifies calculation of the Wiener-Hopf factors. We extend the trick to wide classes of Lévy processes of infinite variation with zero diffusion component. In the resulting formulas (both in the finite variation and the infinite variation cases), we make quasi-parabolic deformations as in Boyarchenko and Levendorskiĭ [Int. J. Theor. Appl. Finance, 2013, 16 (3), 1350011], which greatly increase the rate of convergence of the integrals. We demonstrate that in many cases the proposed method is more accurate than the standard realization of Laplace inversion. We also exhibit examples in which the standard realization is so unstable that it cannot be used for any choice of the error control parameters. This may lead to a ghost calibration: a situation where a parameter set of a model is declared to be a ‘good fit’ to the data only because the errors of calibration and of the numerical method used for pricing (almost) cancel each other out.

Operator splitting kernel based numerical method for a generalized Leland’s model

We construct a first order in time and second order in space, positivity preserving numerical method for a generalized Hoggard–Whalley–Wilmott, Leland’s model. We develop the hyperbolic–parabolic operator splitting method, using a kernel based algorithm for the parabolic part and van Leer flux limiter approach for the hyperbolic sub-problem. Properties of the proposed algorithms are discussed. Various numerical examples confirm the efficiency of the proposed method and verify the theoretical statements.

Analytical modeling of subthreshold current and subthreshold swing of Gaussian-doped strained-Si-on-insulator MOSFETs

This paper presents the analytical modeling of subthreshold current and subthreshold swing of short-channel fully-depleted (FD) strained-Si-on-insulator (SSOI) MOSFETs having vertical Gaussian-like doping profile in the channel. The subthreshold current and subthreshold swing have been derived using the parabolic approximation method. In addition to the effect of strain on silicon layer, various other device parameters such as channel length (L), gate-oxide thickness (tox), strained-Si channel thickness (ts-Si), peak doping concentration (NP), project range (Rp) and straggle (σp) of the Gaussian profile have been considered while predicting the device characteristics. The present work may help to overcome the degradation in subthreshold characteristics with strain engineering. These subthreshold current and swing models provide valuable information for strained-Si MOSFET design. Accuracy of the proposed models is verified using the commercially available ATLAS™, a two-dimensional (2D) device simulator from SILVACO.

Analytical study of Dual Material Surrounding Gate MOSFET to suppress short-channel effects (SCEs)

In this paper, a 2D analytical model for the Dual Material Surrounding Gate MOSFET (DMSG) by solving the Poisson equation has been proposed and verified using ATLAS TCAD device simulator. Analytical modeling of parameters like threshold voltage, surface potential and Electric field distribution is developed using parabolic approximation method. A comparative study of the SCEs for DMSG and SMSG device structures of same dimensions has been carried out. Result reveals that DMSG MOSFET provides higher efficacy to prevent short-channel effects (SCEs) as compared to a conventional SMSG MOSFET due to the presence of the perceivable step in the surface potential profile which effectively screen the drain potential variation in the source side of the channel. A nice agreement between the results obtained from the model and the results obtained from numerical TCAD device simulator provides the validity and correctness of the developed model.

A 2D Analytical Modeling of Single Halo Triple Material Surrounding Gate (SHTMSG) MOSFET

In the proposed work a 2D analytical modeling of single halo Triple material Surrounding Gate (SH-TMSG) MOSFET is developed. The Surface potential and Electric Field has been derived using parabolic approximation method and the simulation results are analyzed. The essential substantive is provided which elicits the deterioration of short channel effects and the results of the analytical model are delineated and compared with MEDICI simulation results and it is well corroborated.

Deterioration Of Short Channel Effects In Dual Halo Based Triple Material Surrounding Gate (Dh-Tmsg) Mosfet

In the proposed work, the analytical model for Surface potential and Electric field has been carried out in a novel structure named dual halo triple material Surrounding-gate metal-oxide-semiconductor field effect transistor (DHTMSG). The new device has been incorporated with symmetrical dual halo regions near source and drain ends, while the gate terminal consists of three different metals with different work functions. The results prove that the device significantly deteriorates the short channel effects which are studied by analytical model for surface potential and electric field using parabolic approximation method. The analytical results are endorsed by the simulation results.

Performance Analysis of Gate Misaligned Triple Material Double Gate (TMDG) MOSFET

In the literature, the misalignment effects in a nanoscale MOSFETis analyzed for dual material Double gate MOSFET. The analysis is used in the design criterion of the device. In this paper, a two dimensional analytical model of gate misalignment effects in Triple Material Double Gate (TM -DG) MOSFET is presented for the first time. The gate misalignment effect in the drain side is considered. Based on the misaligned gate, the device is split in to six regions. The boundary conditions are obtained considering the electric flux and the potential. The parameters are deriv ed using region based approach. Parameters like surface potential and electric field is studied. In general various methods like superposition method, Fourier series method, Numerical methods are used to analyze the device. In our paper, the parabolic approximation method is used for analytical modeling of TM -DG MOSFET since it is more accurate than the other methods available in the literature. The results are simulated and compared with dual material double gate MOSFET. The device performance is analyzed and it helps in the design scenario.

A 2D sub-threshold current model for single halo triple material surrounding gate (SHTMSG) MOSFETs

In the proposed work analytical modeling of single halo triple material surrounding gate (SH-TMSG) MOSFET is developed. The threshold voltage and subthreshold current has been derived using parabolic approximation method and the simulation results are analyzed. The threshold voltage roll off is reduced and it denotes the deterioration of short channel effects. The results of the analytical model are delineated and compared with MEDICI simulation results and it is well corroborated.

High-order conservative reconstruction schemes for finite volume methods in cylindrical and spherical coordinates

High-order reconstruction schemes for the solution of hyperbolic conservation laws in orthogonal curvilinear coordinates are revised in the finite volume approach. The formulation employs a piecewise polynomial approximation to the zone-average values to reconstruct left and right interface states from within a computational zone to arbitrary order of accuracy by inverting a Vandermonde-like linear system of equations with spatially varying coefficients. The approach is general and can be used on uniform and non-uniform meshes although explicit expressions are derived for polynomials from second to fifth degree in cylindrical and spherical geometries with uniform grid spacing. It is shown that, in regions of large curvature, the resulting expressions differ considerably from their Cartesian counterparts and that the lack of such corrections can severely degrade the accuracy of the solution close to the coordinate origin. Limiting techniques and monotonicity constraints are revised for conventional reconstruction schemes, namely, the piecewise linear method (PLM), third-order weighted essentially non-oscillatory (WENO) scheme and the piecewise parabolic method (PPM).The performance of the improved reconstruction schemes is investigated in a number of selected numerical benchmarks involving the solution of both scalar and systems of nonlinear equations (such as the equations of gas dynamics and magnetohydrodynamics) in cylindrical and spherical geometries in one and two dimensions. Results confirm that the proposed approach yields considerably smaller errors, higher convergence rates and it avoid spurious numerical effects at a symmetry axis.

Hybrid Large-Eddy/Reynolds-Averaged Navier–Stokes Simulations of Flow Through a Model Scramjet

The reactive flow through a model scramjet combustor is simulated using a hybrid large-eddy/Reynolds-averaged Navier–Stokes technique. The scramjet configuration considered is similar to the one investigated at the Institute for Chemical Propulsion of the DLR, German Aerospace Center. The model scramjet consists of 15 fuel-injecting holes, located on the base of a wedge-shaped fuel injector, through which hydrogen is injected at sonic conditions. In the present study, only five of the 15 fuel-injecting holes are considered, and periodicity is assumed in the spanwise direction. Several parametric studies are conducted with a view toward determining the sensitivities of the predictions to modeling and algorithmic variations. Different grids (two different topologies), flux reconstruction methods (total variation diminishing and piecewise parabolic method), reaction mechanisms, and inflow boundary conditions (uniform and nonuniform) are used. To enhance fuel–air mixing, a synthetic eddy method is used to generate turbulence in the injector boundary layers and the hydrogen jets. Finally, a partially stirred reactor-type subgrid combustion model is used as a subgrid closure for the species production rates. The results show that, in all the cases, a lifted flame is predicted with varying standoff distances, heat releases, and shapes.

ASPHERICAL NUCLEOSYNTHESIS IN A CORE-COLLAPSE SUPERNOVA WITH 25M☉STANDARD PROGENITOR

The problem of nucleosynthesis was studied within an aspherical supernova model. The explosive burning was computed in a star of 25 M ☉ initial mass on its final stage of evolution. The chemical composition of a presupernova was taken from realistic evolutionary computations. A piecewise parabolic method on a local stencil was applied to simulate the hydrodynamics of the explosion. The gravity was recomputed by a Poisson solver on a fine grid as the explosion developed. A detailed yield of chemical elements was performed as a post-processing step using the tracer particles method. The produced nuclei formed a layer-like structure enclosing large fragments of nickel and iron-group isotopes that were pushed away from the central region by an explosion along the polar direction. The light nuclei were preferentially moving along the equatorial plane forming a torus-like structure.

A fast Galerkin method for parabolic space-time boundary integral equations

An efficient scheme for solving boundary integral equations of the heat equation based on the Galerkin method is introduced. The parabolic fast multipole method (pFMM) is applied to accelerate the ...

New two-level leapfrog scheme for modeling the stochastic Landau-Lifshitz equations

A two-level modification of the classical nondissipative leapfrog scheme with nonlinear flux correction has been developed for fluctuating hydrodynamics problems. The new algorithm has shown to satisfy the fluctuation-dissipation theorem to high accuracy. The results of various numerical tests, including equilibrium, nonequilibrium, one-, and two-dimensional systems, are compared with theoretical predictions, direct molecular simulations, and results produced by MacCormack’s schemes, the piecewise parabolic method, and a third-order Runge-Kutta scheme. The new algorithm is well suited for parallel computations due to its implementation simplicity and compact stencil.

Performance analysis of fully depleted triple material surrounding gate (TMSG) SOI MOSFET

In this paper, analytical model for threshold voltage is derived for fully depleted Triple material Surrounding gate (TMSG) SOI MOSFET. Three gate material of different work functions are introduced in the SOI MOSFET structure to reduce the short channel effects. The two dimensional Poisson equation is solved and based on parabolic approximation method, the model for threshold voltage is developed. The threshold voltage is analyzed for device parameters such as gate length ratios, oxide thickness, silicon thickness, doping concentration. The results of the analytical model values are validated using MEDICI simulation.

A Wind Farm Capacity Credibility Calculation Method Based on Parabola

The capacity credibility of a wind farm is the basic index to evaluate the value of its power generation capacity. As an important reference for the wind farm planning and site selection, calculation of wind farm capacity credibility is significant. Based on a sequential Monte Carlo simulation approach, this paper proposes a parabola calculation method for the wind farm capacity credibility. The method first uses an autoregressive moving average (ARMA) time series approach to simulate the hourly wind speeds, and then set up the reliability model of the wind energy conversion system (WECS). Finally, the parabolic method is used to calculate the effective load-carrying capacity (ELCC), which is the most important part of the capacity credibility of the wind farm. As a testing scenario, the IEEE-RTS79 test system is used to verify the method, and the difference of capacity credibility under different reliability indices is also analyzed.

M/M/1 Retrial Queue with Working Vacation Interruption and Feedback under N-Policy

We consider an M/M/1 retrial queue with working vacations, vacation interruption, Bernoulli feedback, and N-policy simultaneously. During the working vacation period, customers can be served at a lower rate. Using the matrix-analytic method, we get the necessary and sufficient condition for the system to be stable. Furthermore, the stationary probability distribution and some performance measures are also derived. Moreover, we prove the conditional stochastic decomposition for the queue length in the orbit. Finally, we present some numerical examples and use the parabolic method to search the optimum value of service rate in working vacation period.