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Abstract: Quenching process is a thermo-elastic-plasticity problem with a high material non-linearity. The numerical oscillation is likely caused in the simulation of quenching process. In order to avoid the numerical oscillation and improve the calculation accuracy of temperature and phase-transformation fields in the quenching process, a new self-adaptive time-step size method is presented. The method can adjust the time-step size according to the maximum and minimum differences of temperature fields between the previous simulation step and the current simulation step. FEM software for evaluating the temperature, stress/strain and phase-transformation is also developed. A cooling example with numerical analytical results and a quenching example with experiment results are used to verify the calculation accuracy of this software. Five methods including the method in this paper, two constant time-step sizes and two geometric proportion time-step sizes are applied to simulate the quenching process of a 40Cr steel cylinder, respectively. A comparison of the simulation results shows that, the method presented in this paper can effectively avoid the numerical oscillation, ensure the calculation accuracy and cost less calculation time. [Copyright &y& Elsevier]

Abstract: The paper discusses a straightforward approach for evaluating the distance covered by a spreading liquid pool, when the axisymmetric hypothesis is no longer valid. This distance is evaluated by a three-steps methodology: the pre-processing of input data (bund radius, if present, and radial velocity); the simulation of pool spreading by a model based on the axisymmetric hypothesis; and the post-processing of results. The paper reports some geometrical correlations to pre- and post-process the data, with regard to four case-studies. Some numerical examples are also presented to prove that the pre-processed input data and post-processed results differ from those based on the axisymmetric hypothesis. Finally, we validate our modeling approach with the experimental data of Cronin and Evans [P.S. Cronin, J.A. Evans, A series of experiments to study the spreading of liquid pools with different bund arrangements, HSE Contract Research Report 405/2002, Advantica Technologies Limited, 2002]. [Copyright &y& Elsevier]

Abstract: Using slope enclosures may provide sharper bounds for the range of a function than using enclosures of the derivative. Hence, slope enclosures may be useful in verifying the assumptions for existence tests or in algorithms for global optimization. Previous papers by Kolev and Ratz show how to compute slope enclosures for convex and concave functions. In this paper, we generalize these formulas and show how to obtain slope enclosures for a function that has exactly one point of inflection or whose derivative has exactly one point of inflection. [Copyright &y& Elsevier]

Abstract: In this paper, we point out that the generalized iteration method presented in a recent paper by Ling and Hu [X.-F. Ling, X.-Z. Hu, On the iterative algorithm for large sparse saddle point problems, Appl. Math. Comput. 178 (2006) 372–379] belongs to the inexact Uzawa algorithm, and an improper statement in a theorem in that paper is corrected. [Copyright &y& Elsevier]

Abstract: This paper introduces an algorithm for coupling the boundary element method and the scaled boundary finite element method. Although the particular application concerns the determination of stress intensity factors at crack tips, the approach is general in nature. The motivation for the work is the combination of the semi-analytical solution accuracy of the SBFEM with the geometric flexibility of the BEM for general engineering usage. The paper presents the development of the algorithm along similar lines to FEM/BEM coupling approaches. Example problems verify the accuracy of the approach, even for coarse discretisations, and demonstrate excellent convergence properties of the algorithm. [Copyright &y& Elsevier]

The paper presents finite-dimensional dynamical control systems described by linear fractional-order state equations with multiple delays in control. The constrained controls are considered. The set of admissible control values is assumed to be a compact set containing 0, a convex and compact set containing 0 in its interior, a cone with vertex at zero and a nonempty interior, or a convex and close cone with nonempty interior and vertex at zero. The definitions of various types of constrained controllability of the linear fractional systems with delays in control are formulated. New necessary and sufficient conditions for constrained relative controllability of fractional-order control systems with delayed controls are established and proved. Numerical examples are provided to illustrate the obtained theoretical results. [ABSTRACT FROM AUTHOR]

Response of steel fibre reinforced cementitious composite (SFRCC) panels subjected to high velocity impact of short projectiles have great significance in designing protective structures. Numerical investigation carried out to determine the high velocity impact responses of SFRCC (300 mm square) panels is presented. In order to model the high velocity impact behaviour of SFRCC in the post peak region, the constitutive model of Riedel, Hiermaier and Thoma (RHT) is used with suitable modification in damage parameters. The numerical studies presented in this paper are validated using the experimental investigations carried out by the authors. The influences of steel fibrevolumes (0, 2, 4, 6, 8, and 10%) and thickness of panels (50, 60, 75, 100 mm), on depth of penetration (DOP) and crater dimensions is also investigated. Based on the numerical simulations, the important phenomenon like scabbing and perforation in the SFRCC panels are predicted for the chosen in-service ammunition (7.62 mm calibre) and munitions (AK - 47 rifle). [ABSTRACT FROM AUTHOR]

In general, many numerical techniques are in place for the study of buckling and post-buckling responses of the composite structures, but these are computationally expensive. Relatively few equivalent analytical techniques are available, especially for evaluation of post-buckling responses. In this paper an analytical approach is presented for the determination of post-buckling responses of rectangular panels made of symmetric orthotropic laminates and supported by stiffeners (especially used in the monocoque and semi-monocoque aircraft structures), and subjected to combined compressive and shear loads, majorly based on the effective width concept. They are used to calculate the loss in the stiffness of the panels and the compressive stresses induced in the stiffening members, under a combined effect of shear and compressive stresses. For illustration, a series of parametric curves that are characteristic of the post-buckling behavior of the orthotropic panels (of aspect ratio 2.5) with transverse stiffeners have been reported. [ABSTRACT FROM AUTHOR]

This paper presents experimental and numerical study of dynamic response of laminated glass fiber reinforced polymer (GFRP) composite plate due to blunt projectile impact considering incidence velocity lower than the ballistic limit. The experimentation of impact tests were performed with pneumatic gun which was used to propel a 52 g cylindrical steel projectile of diameter 19 mm on the laminated composite plate (0°/90°) 5 of size 140 mm × 140 mm × 3.12 mm. A three dimensional Finite Element model has also been presented in ANSYS/AUTODYN, a commercial hydro code, considering shock effect of impact in material modeling. The numerical results were validated with actual results. The timehistories of velocity and acceleration of projectile along with the deflection, resistance force, energy absorption and damage pattern in the target plate have been studied. The numerical predictions of damage in the target and velocity history of the projectile show good correlation with the actual results. [ABSTRACT FROM AUTHOR]

Shaped plates assume importance in the design of armoured personal vehicles (APV). These plates are used as blast mitigation structures against land mine blasts. These shaped plates deflect and absorb a certain part of the energy imparted to them. The blast mitigating capacity at a particular impulse level mainly depends on material and the geometric parameters of the plate under consideration. The objective of this paper is to conduct a finite element (FE) based failure analysis and parametric study on the blast mitigating capability of steel plates. The important parameters of interest are the mass of the explosive and the included angle of the V shaped plate. A numerical study on V-shaped plates is carried out with ABAQUS to predict the midpoint deflection and impulse transmitted. The verified simulation procedure is repeated for conducting the parametric study. The study may be used in setting up guide lines for the design of V shaped plates for protecting vehicles. [ABSTRACT FROM AUTHOR]

Most low-cost consumer grade digital camera systems are currently designed to sense only one color component per image pixel and interpolate the other missing color components (at each pixel)duringreconstruction. The sensing process, which employs aColor Filter Array (CFA), maps each pixel to a single color based on a color pattern. The CFA color pattern and the interpolation process (widely known as demosaicing) have a significant impact on the quality of the reconstructed image. In this paper, A directional CFA interpolation method that is based on multiscale color gradients. The method is easy to implement since it does not make any hard decision, noniterative and threshold free. This method, the horizontal and vertical color difference estimates are blended based on the ratio of the total absolute values of vertical and horizontal color difference gradients over a local window. Method is applied to Bayer and Lukac pattern with great results which shows that the relationship between gradients at different scales can be a very effective feature to optimally combine directional estimates. Result can be used to compare efficiency of both pattern in this method. [ABSTRACT FROM AUTHOR]

In this paper, we present new asymptotic expansions of the gamma function related to the Nemes, Gosper and Burnside formulas. [ABSTRACT FROM AUTHOR]

Topological characteristics of links of complex networks influence the dynamical processes executed on networks triggered by links, such as cascading failures triggered by links in power grids and epidemic spread due to link infection. The line graph transforms links in the original graph into nodes. In this paper, we investigate how graph metrics in the original graph are mapped into those for its line graph. In particular, we study the degree distribution and the assortativity of a graph and its line graph. Specifically, we show, both analytically and numerically, the degree distribution of the line graph of an Erdős–Rényi graph follows the same distribution as its original graph. We derive a formula for the assortativity of line graphs and indicate that the assortativity of a line graph is not linearly related to its original graph. Additionally, line graphs of various graphs, e.g. Erdős–Rényi graphs, scale-free graphs, show positive assortativity. In contrast, we find certain types of trees and non-trees whose line graphs have negative assortativity. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we study the asymptotic behavior of the positive solutions of the systems of the two difference equations where the constants are positive real numbers, and the initial values are also positive real numbers. [Copyright &y& Elsevier]

Abstract: The subject of this paper is a system of two rational type difference equations with constant coefficients in the form: where , , , , . The asymptotic behavior of the solutions and the phase portrait are described. Moreover, an attractor is investigated. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the problem of asymptotic stability of neutral systems. A new delay-dependent stability condition is derived in terms of linear matrix inequality to ensure a large upper bound of the time-delay by non-uniformly dividing the delay interval into multiple segments. A new Lyapunov–Krasovskii functional is constructed with different weighting matrices corresponding to different segments in the Lyapunov–Krasovskii functional, where both constant time delays and time-varying delays have been taken into account. Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods. [Copyright &y& Elsevier]

Abstract: In this paper, we generalize the main theorem of Liz and Ferreiro [E. Liz, J.B. Ferreiro, A note on the global stability of generalized difference equations, Appl. Math. Lett. 15 (2002) 655–659] and some other global stability results for nonautonomous higher-order difference equations to the case when contraction-type steps are incorporated together with the steps when the difference sequence can increase. The relation to the -method for discretization of delay equations is discussed, and some sufficient stability conditions for the numerical scheme are deduced. Several examples are presented to demonstrate sharpness and applications of the results. [Copyright &y& Elsevier]

Abstract: In this paper, a new method for solving nonlinear equations is presented. Analysis of the convergence shows that the asymptotic convergence order of this method is . Some numerical results are given to demonstrate its efficiency. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the numerical properties of -methods for the solution of alternately advanced and retarded differential equations with piecewise continuous arguments. Using two -methods, namely the one-leg -method and the linear -method, the necessary and sufficient conditions under which the analytic stability region is contained in the numerical stability region are obtained, and the conditions of oscillations for the -methods are also obtained. It is proved that oscillations of the analytic solution are preserved by the -methods. Furthermore, the relationships between stability and oscillations are revealed. Some numerical experiments are presented to illustrate our results. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with the numerical solution of nonlinear functional differential and functional equations. The adaptation of one-leg methods is considered. It is proved that an A-stable one-leg method is globally stable and a strongly A-stable one-leg method is asymptotically stable under suitable conditions. A numerical test is given to confirm the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we present a new secant-like method for solving nonlinear equations. Analysis of the convergence shows that the asymptotic convergence order of this method is . Some numerical results are given to demonstrate its efficiency. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we propose other versions of Gauss, Cholesky and Householder methods based on using a tensor product and matrix addition. These versions are convenient to the iterative methods and should be performed in parallel computations. [Copyright &y& Elsevier]

Abstract: The paper describes the development of an algorithm that uses spline interpolation methods in order to calculate the ground relief contours, the area and the volume reservoir associated with a large dam. This algorithm is a great help to the engineer who designs dams in calculating the area and the volume of the reservoir for dams with specific positions and geometric characteristics, for different water levels and over a ground relief with elevation contours which one evaluates, smoothes and draws using cubic splines. The advantages of the algorithm are significant not only for specific computer programs that refer to reservoirs, but also for computer programs relevant to hydraulic calculations of reservoirs and associated structures. [Copyright &y& Elsevier]

Abstract: In this paper, the extended finite element method (X-FEM) is considered for the analysis of fretting fatigue problems. A two-dimensional implementation of the X-FEM is carried out within the finite element software ABAQUS™ by means of user subroutines, and crack propagation in fretting fatigue problems is investigated. On utilizing the non-linear contact capabilities of this code, the numerical technique is applied to a specimen-indenter model. The use of the X-FEM facilitates very accurate stress intensity factor computations on relatively coarse meshes, and furthermore, no remeshing is required for crack growth simulations. The implementation is applied to complete and incomplete contact fretting problems. A study of crack growth is conducted for several bulk loads applied to the specimen, and the influence of the initial crack angle is ascertained. The numerical simulations reveal the merits of applying the X-FEM to fretting fatigue problems. [Copyright &y& Elsevier]

Abstract: The asymptotic solution of the singular stress field near a singular point is generally comprised of one or more singular terms in the form of . Based on the asymptotic solution of the singular stress field and the common numerical solution (stresses or displacements) obtained by an ordinary tool such as the finite element method or boundary element method, a simple and effective numerical method is developed to calculate stress intensity factors for one and two singularities. Three examples show that the stress intensity factors evaluated using the method proposed in this paper are very accurate. [Copyright &y& Elsevier]

Abstract: In this paper, a multi-scale element-free Galerkin method is presented for the Stokes problem. The new method is based on the Hughes’ variational multi-scale formulation, and arises from a decomposition of the velocity field into coarse/resolved scales and fine/unresolved scales. In this method, an unresolved model is obtained in which unresolved scales are incorporated analytically through the bubble functions. Modeling of the unresolved scales corrects the lack of the stability of the standard element-free Galerkin formulation and the resulting stabilized formulation possesses superior properties like that of the streamline upwind/Petrov–Galerkin (SUPG) method and the Galerkin/least-squares (GLS) method. The method allows equal order basis for pressure and velocity because it violates the celebrated Babuska–Brezzi condition. A significant feature of the present method is that the structure of the stabilization tensor τ appears naturally via the solution of the fine-scale problem. Numerical results for example problems confirm that this method has some excellent properties, such as better stability and accuracy. [Copyright &y& Elsevier]

Abstract: In this paper we first generalize the Ostrowski inequality on time scales for k points and then unify corresponding continuous and discrete versions. We also point out some particular Ostrowski type inequalities on time scales as special cases. [Copyright &y& Elsevier]

Abstract: In this paper it is shown that, if a time-varying uncertain system is robustly completely detectable, then there exists an estimator for this system, i.e. the state vector of the system can be estimated asymptotically. If the time-varying uncertain system is robustly completely observable, it is shown that there exists an estimator for this system with assignable rate of convergence of the error. Moreover, specialized constructions are developed for the special class of triangular systems. [Copyright &y& Elsevier]

Abstract: In this paper, the asymptotic behavior of the Morris–Lecar model is studied. Firstly, the phase plane characteristic of the model is investigated, secondly, in terms of the concepts of slow manifold and fast foliation, the asymptotic structure of the Morris–Lecar model is discussed based on Tikhonov''s theorem. Finally, computation and analysis results show that the spiking of action potential of Morris–Lecar neuron actually has the jump onset–jump return structure. [Copyright &y& Elsevier]

Abstract: In this paper, the asymptotical stability of the numerical methods with the constant stepsize for impulsive differential equation where ,, are investigated. The asymptotical stability conditions of the analytic solution of this equation and the numerical solutions are obtained. Finally, some experiments are given. [Copyright &y& Elsevier]

Abstract: In this paper, we consider the linearly viscoelastic equations for Koiter shells. The existence and uniqueness of the solution are proved by Galerkin method. [Copyright &y& Elsevier]

Abstract: In this paper, by the Galerkin method, we give the existence of solutions for the non-autonomous -Laplacian equation . After that, we explore the asymptotic behavior of the equation. The existence and the structures of the -uniform attractor and the -uniform attractor are proved under the conditions below: the nonlinear term is supposed to satisfy the polynomial condition of arbitrary order and , where is arbitrary; and the external force in , is translation bounded and uniformly bounded in with respect to . [Copyright &y& Elsevier]

Abstract: In this paper, a novel residual based error estimator using radial basis functions (RBFs) is proposed. The error estimator evaluates the residual in the strong-form governing equation in the local domain through direct integration. Due to the higher order continuous feature of the RBFs, the higher derivatives of the field function in the strong-form governing equation can be obtained using RBFs. The numerical examples show that the new residual based error estimator is simple, versatile robust and yet effective in the adaptive analyses. It is not only suitable for adaptive analysis that uses numerical method formulated based on mesh, e.g. finite element method, but also meshfree methods where the conventional residual based and recovery based error estimator cannot be used. Furthermore the present error estimator is also feasible for numerical method that is formulated based on both strong and weak formulation in the adaptive analyses. [Copyright &y& Elsevier]

Abstract: Discontinuous Galerkin methods (DG) have particular appeal in problems involving high-order derivatives since they provide a means of weakly enforcing the continuity of the unknown-field derivatives. This paper proposes a new discontinuous Galerkin method for Kirchhoff–Love shells considering only the membrane and bending response. The proposed one-field method utilizes the weak enforcement in such a way that the displacements are the only unknowns, while the rotation continuity is weakly enforced. This work presents the formulation of the new discontinuous Galerkin method for linear elastic shells, demonstrates the consistency and stability of the proposed framework, and establishes the method’s convergence rate. After a description of the formulation implementation into a finite-element code, these properties are demonstrated on numerical applications. [Copyright &y& Elsevier]

Abstract: The properties of fiber reinforced metal matrix composites (MMCs) are anisotropic. These properties can be more appropriately evaluated in polar coordinate. In this paper, the elastic–plastic mechanics model of MMCs is presented based on the combination of macroscopic and meso-scopic analysis in polar coordinate. The influence of micro-parameters such as matrix materials, the fibers and fiber volume fraction of Al/Mg metal matrix composites (MMCs) on the tensile properties of MMCs is also investigated numerically by the representative volume element (RVE) and the numerical results are compared with the experimental data. The results show that the model built in polar coordinate is suitable to the real constructs of MMCs; the fiber plays a major role of load supporting during MMCs stretched. And there is little distinction of the value of maximum stress of MMCs between tests and the numerical analysis. [Copyright &y& Elsevier]

Abstract: This paper describes a simplified mesh generation technique that is based on the finite element method of calculation of beam-shaping diffractive optical elements (DOEs). The mesh generation technique uses the inherent symmetry of the incident beam to generate a mesh. Using the meshes so generated, DOEs that convert a Gaussian intensity beam to one of a specified shape, are calculated. Simulations of the results of such beam-shaping elements will be presented. Such elements have uses in industrial and medical applications where both the shape as well as the intensity distribution on the material that is to be processed is very important. For example, in industrial applications the beam may be used to uniformly heat up a specific area in which case the intensity has to be uniform across the beam. The Gaussian intensity variation of a laser has to be converted to a flat-top beam in order to achieve this. To reiterate, beam shaping refers to changing both the intensity distribution and the shape of the beam. Experimental results of the fabricated gratings will also be presented. These results will include experimental data on the method of additive lithography which can be used to improve the efficiency of DOEs. [Copyright &y& Elsevier]

Abstract: In immersed interface methods, solids in a fluid are represented by singular forces in the Navier–Stokes equations, and flow jump conditions induced by the singular forces directly enter into numerical schemes. This paper focuses on the implementation of an immersed interface method for simulating fluid–solid interaction in 3D. The method employs the MAC scheme for the spatial discretization, the RK4 scheme for the time integration, and an FFT-based Poisson solver for the pressure Poisson equation. A fluid–solid interface is tracked by Lagrangian markers. Intersections of the interface with MAC grid lines identify finite difference stencils on which jump contributions to finite difference schemes are needed. To find the intersections and to interpolate jump conditions from the Lagrangian markers to the intersections, parametric triangulation of the interface is used. The velocity of the Lagrangian markers is interpolated directly from surrounding MAC grid nodes with interpolation schemes accounting for jump conditions. Numerical examples demonstrate that (1) the method has near second-order accuracy in the infinity norm for velocity, and the accuracy for pressure is between first and second order; (2) the method conserves the volume enclosed by a no-penetration boundary; and (3) the method can efficiently handle multiple moving solids with ease. [Copyright &y& Elsevier]

Abstract: In this paper, we present numerical analysis for the generalized quadrature rule for , where is an oscillatory function, and derive higher order generalized quadrature rules. The results show that the generalized quadrature rules are efficient for Bessel-trigonometric transformations and the accuracy increases when oscillation becomes faster. [Copyright &y& Elsevier]

Abstract: An evanescent wave is produced when a propagating incident wave impinges on an interface between two media or materials at a sub-critical angle. The sub-scale nature of such a wave makes it difficult to be captured computationally. In this paper, the Discontinuous Enrichment Method (DEM) developed in [C. Farhat, I. Harari, L.P. Franca, The discontinuous enrichment method, Comput. Methods Appl. Mech. Engrg. 190 (2001) 6455–6479; C. Farhat, I. Harari, U. Hetmaniuk, A discontinuous Galerkin method with Lagrange multipliers for the solution of Helmholtz problems in the mid-frequency regime, Comput. Methods Appl. Mech. Engrg. 192 (2003) 1389–1419; C. Farhat, I. Harari, U. Hetmaniuk, The discontinuous enrichment method for multiscale analysis, Comput. Methods Appl. Mech. Engrg. 192 (2003) 3195–3210; C. Farhat, R. Tezaur, P. Weidemann-Goiran, Higher-order extensions of a discontinuous Galerkin method for mid-frequency Helmholtz problems, Int. J. Numer. Methods Engrg. 61 (2004) 1938–1956; C. Farhat, P. Wiedemann-Goiran, R. Tezaur, A discontinuous Galerkin method with plane waves and Lagrange multipliers for the solution of short wave exterior Helmholtz problems on unstructured meshes. New computational methods for wave propagation, Wave Motion 39(4) (2004) 307–317; L. Zhang, R. Tezaur, C. Farhat, The discontinuous enrichment method for elastic wave propagation in the medium-frequency regime, Int. J. Numer. Methods Engrg. 66 (2006) 2086–2114; R. Tezaur, C. Farhat, Three-dimensional discontinuous Galerkin elements with plane waves and Lagrange multipliers for the solution of mid-frequency Helmholtz problems, Int. J. Numer. Methods Engrg. 66 (2006) 796–815] is extended to a class of evanescent wave problems. New DEM elements are constructed by enriching polynomial approximations with free-space evanescent solutions in order to achieve high accuracy for problems with fluid/fluid or fluid/solid interfaces on which evanescent waves may occur. The new DEM elements are applied to the solution of various two-dimensional model problems with evanescent waves. Their performance is observed to be better than that of the basic Helmholtz type DEM elements, and superior to that of the classical higher-order polynomial finite element method. [Copyright &y& Elsevier]

Abstract: This paper shows that for any suitably smooth function and arbitrarily selected interpolation nodes in , the Filon method and the Levin method for with the polynomial interpolation approach are identical when is a linear function. Based on this result, a new efficient Levin quadrature for is presented. [Copyright &y& Elsevier]

Abstract: In this paper, some new discrete inequalities in two independent variables which provide explicit bounds on unknown functions are established. The inequalities given here can be used as tools in the qualitative theory of certain finite difference equations. [Copyright &y& Elsevier]

Abstract: It is very important to understand and estimate the AC loss characteristic of assembled conductors with ferromagnetic substrate. In this paper, the AC loss of cylindrically assembled HTS coated-conductors with ferromagnetic substrate is examined using FEM taking account of the nonlinear E–J characteristics. It is shown that, the current distribution and AC losses depend on the arrangement of the superconducting (SC) layer and the substrate. Moreover, AC loss characteristics depend on the gap length between conductors. The effect of the arrangement of the SC layer and the substrate on the current distribution of SC layer and AC loss is illustrated. [Copyright &y& Elsevier]

Abstract: AC transport current losses of coated conductors with ferromagnetic substrates are higher than the loss calculated by the Norris equation. In order to reduce the AC transport current loss we propose in this paper a structure of the coated conductor that has wider substrate than the SC (Superconducting) layer. The current distribution and AC loss of the proposed model are analyzed by means of FEM. The AC transport current loss is reduced due to the change of current density distribution near the edge of SC layer, consequent to the high value of magnetic permeability of the ferromagnetic substrate, that is wider than the SC layer. [Copyright &y& Elsevier]

Abstract: Advective processes are of central importance in many applications and their treatment is crucial in the numerical modelling of the transport of trace constituents in atmospheric models. High-order numerical methods offer the promise of accurately capturing these advective processes in atmospheric flows and have been shown to efficiently scale to large numbers of processors. In this paper, a conservative transport scheme based on the nodal high-order spectral finite volume method is developed for the cubed-sphere. A third-order explicit strong stability preserving scheme is employed for the time integration. The reconstruction procedure which we developed avoids the (expensive) calculation of the inverse of the reconstruction matrix. Flux-corrected transport algorithm is implemented to enforce monotonicity in the two-dimensional transport scheme. Two standard advection tests, a solid-body rotation and a deformational flow, were performed to evaluate the spectral finite volume method optionally combined with a flux-corrected transport scheme. Spectral accuracy in space is demonstrated with a linear wave equation. [Copyright &y& Elsevier]

Abstract: A magnetohydrodynamic (MHD) accelerator is proposed as a next generation propulsion system. The fundamental acceleration performance has been, so far, evaluated using one-dimensional (1-D) numerical analysis. However, the actual phenomena in the accelerator channel are highly coupled with boundary layers and with electrode phenomena and are three-dimensional. In this paper, research for investigating the three-dimensional (3-D) phenomena of an MHD accelerator is described. The validity of the 3-D numerical analysis is assessed through comparisons with the results of 1-D analysis. An existence of a local Hall current not predicted through 1-D analysis enhances the Joule dissipation and induces a secondary flow. It was found that a significant local Hall current influences the growth of the velocity overshoot, and this phenomenon is promoted particularly in a high Hall parameter environment. This study of 3-D analysis offers a more realistic prediction of the accelerator performance of the MHD accelerator than that of the 1-D predictions. [Copyright &y& Elsevier]

Abstract: Some new iterative formulae having three-order convergence are discussed in this paper. The theoretical analysis and numerical experiments show that new iterative formulae are effective and comparable to well-known method of Newton and Stefensen method. [Copyright &y& Elsevier]

Abstract: Local asymptotic stability of nonlinear systems with real-parametric uncertainty or disturbance is one of the important problems in control systems literature. In this paper, we investigate this problem for nonlinear systems with time-varying disturbance. We assume that the disturbance vector is generated by an exosystem, which is neutrally stable. Thus, the disturbances that we consider include both constant and periodic signals. For this class of nonlinear systems with time-varying disturbance, we derive a necessary condition for local asymptotic stability of equilibria. As corollaries of our general result, we deduce the necessary condition obtained by Byrnes and Sundarapandian [1] for nonlinear systems with constant real parametric uncertainty, and the necessary condition obtained by Brockett [2] for nonlinear autonomous systems. We illustrate our result with several examples. [Copyright &y& Elsevier]