Positive numerical splitting method for the Hull and White 2D Black–Scholes equation

We consider the locally one‐dimensional backward Euler splitting method to solve numerically the Hull and White problem for pricing European options with stochastic volatility in the presence of a mixed derivative term. We prove the first‐order convergence of the time‐splitting. The parabolic equation degenerates on the boundary x = 0 and we apply a fitted finite volume scheme to the equation to resolve the degeneracy and derive the fully discrete problem as we also investigate the discrete maximum principle. Numerical experiments illustrate the efficiency of our difference scheme. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 822–846, 2015     

Interpolating minimal energy C1‐Surfaces on Powell–Sabin Triangulations: Application to the resolution of elliptic problems

In this article, we present a method to obtain a C¹‐surface, defined on a bounded polygonal domain Ω, which interpolates a specific dataset and minimizes a certain “energy functional.” The minimization space chosen is the one associated to the Powell–Sabin finite element, whose elements are C¹‐quadratic splines. We develop a general theoretical framework for that, and we consider two main applications of the theory. For both of them, we give convergence results, and we present some numerical and graphical examples. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 798–821, 2015     

A local parallel superconvergence method for the incompressible flow by coarsening projection

In this article, we investigate a local parallel superconvergence method by coarsening projection for the incompressible Stokes flow. The method is a combination of the local superconvergence technique and the given framework of local parallel method. For the smooth subdomains, the local superconvergence method is applied in a higher order finite dimensional space corresponding to an appropriate coarse mesh on interior domain. Moreover, a useful and flexible local parallel method is designed to obtain the local parallel superconvergence results of presented method, which offset theoretical limitation of the model without the smoothness of the exact solution and a priori regularity of the underlying problem over the whole domain. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1209–1223, 2015     

Free vibration of non-uniform nanobeams using Rayleigh–Ritz method

In this article, boundary characteristic orthogonal polynomials have been implemented in the Rayleigh–Ritz method to investigate free vibration of non-uniform Euler–Bernoulli nanobeams based on nonlocal elasticity theory. Non-uniform cross section of nanobeams has been considered by taking linear as well as quadratic variations of Young's modulus and density along the space coordinate. Detailed analysis has been reported for all the possible cases of such variations. The objective of the present study is to analyze the effects of nonlocal parameter, boundary condition, length-to-diameter ratio and non-uniform parameter on the frequency parameters. It is found that clamped nanobeams are having highest frequency parameters than other types of boundary conditions for a particular set of parameters. It is also observed that frequency parameters decrease with increase in scaling effect parameter. First four deflection shapes of non-uniform nanobeams have also been incorporated. In this analysis, some of the new results in terms of boundary conditions have also been included.     

Effect of oblique incidence angle of sunlight on the optimized folding angle of V-shaped organic solar cells

We numerically investigate the effect of the incidence angle of sunlight on the optimized folding angle of V-shaped organic solar cells (VOSCs) to obtain the best power conversion efficiency in a realistically operating environment. The light absorbance at the active layer is calculated based on the finite element method with respect to the incidence angle of sunlight and the folding angle of the VOSC. We calculate the generation energy density per day at each folding angle by integrating the angular response of the short-circuit current and the open-circuit voltage with the consideration of the variation of the incidence angle during daytime. We show that the optimized folding angle of the VOSC based on the variation of the generation energy density per day is close to that determined from the variation of the electric power density in normal incidence, which has been widely used to optimize the folding angle of VOSCs.     

Residual symmetry reductions and interaction solutions of the (2+1)-dimensional Burgers equation

In nonlinear physics,it is very difficult to study interactions among different types of nonlinear waves.In this paper,the nonlocal symmetry related to the truncated Painleve′expansion of the(2+1)-dimensional Burgers equation is localized after introducing multiple new variables to extend the original equation into a new system.Then the corresponding group invariant solutions are found,from which interaction solutions among different types of nonlinear waves can be found.Furthermore,the Burgers equation is also studied by using the generalized tanh expansion method and a new Ba¨cklund transformation(BT)is obtained.From this BT,novel interactive solutions among different nonlinear excitations are found.     

Hot carrier degradation mechanism interpretation by lateral distribution of interface and bulk trap density

We investigated the drain avalanche hot carrier effect (DAHC) of p-type metal-oxide-semiconductor field effect transistor of 0.14 μm channel length (PMOSFET) with SiON gate dielectric. Using three different stress conditions of substrate maximum current, the changes to threshold voltage, maximum transconductance, saturation current and channel leakage current was monitored. Concurrently, the lateral distribution of interface trap density (N_it) and bulk trapped charge density (N_ot) with stress time has been extracted along the 70 nm half channels from gate edge to drain junction, which is the first endeavor in describing charge traps along sub 100 nm short channels. The degradation of the PMOSFET was described by combining electrical property with N_it and N_ot profiles. Hot electron punch through (HEIP) effect was evidenced by negative Not distribution near the drain junction while more severe hot carrier degradation was successfully demonstrated by the empirical power law dependence of the electrical parameters N_it and N_ot. We have studied the evolution of degradation behavior along highly scaled tens of nanometer channel, and N_it and N_ot profile offers systematic study and interpretation of degradation mechanism of hot carrier effect in MOSFET devices.     

Fabrication of Cu2ZnSn(SxSe1−x)4 thin film solar cell by single step sulfo-selenization of stacked metallic precursors

We have synthesized an efficient Cu₂ZnSn(S_xSe_1−x)₄ (CZTSSe) absorbers by using single-step rapid thermal sulfo-selenization process of sputtered stack metallic precursor (Zn/Sn/Cu) films. The structural and morphological studies confirm that the suitability of the rapid thermal sulfo-selenization process for the synthesis of a CZTSSe absorber without any secondary phases with large grains. The annealing atmosphere with a mixed-chalcogen source enhances the grain growth of the CZTSSe absorber as compared with pure Cu₂ZnSnS₄ (CZTS) and Cu₂ZnSnSe₄ (CZTSe) absorbers. The CZTSSe thin film solar cell shows the best conversion efficiency of ∼7%.     

Analytical and empirical studies on the characteristic resistances of no-insulation GdBCO racetrack pancake coil under various operating currents

This paper presents the effects of the Lorentz force on the electrical behaviors of the no-insulation (NI) GdBCO racetrack pancake (RP) coil without turn-to-turn insulation by performing charging/discharging and sudden-discharging tests. The simulation results of the 2-dimensional finite element method showed that the Lorentz forces were generated towards the center of the winding pack consisting of 60-turn GdBCO CCs, which could enhanced the turn-to-turn contact within the RP coil. The charging/discharging test results indicated that the characteristic resistance (R_c) of the NI RP coil decreased with increasing operating current, which was caused by an increase of the Lorentz force. Further, the results of the sudden-discharging tests exhibited that the Lorentz force was dissipated instantly during the sudden-discharge of the coil, since the operating current immediately decreased to zero. Overall, this study clearly demonstrated that the Lorentz force induced by the operating current exerts the electrical behaviors of an NI RP coil.