Assessment of the Maintenance of the Effectiveness of Safety Schemes by Inspection and Age-replacement of Protective Devices

Expressions are derived for quantities measuring deficienciesoccurring in the protective capabilities of safety schemes comprisedof devices which are subject to random failure. The devicesare assumed to be prone to two modes of failure, one which isreadily detectable in service, and one which is undetectablein service. The expressions take into account the effects ofpreventive maintenance procedures in which devices are inspectedat regularly spaced times to discover and renew devices whichhave failed "detectably", and also devices are replaced aftera specified age in service to mitigate the effects of "undetectable"failures. These expressions are evaluated for devices havingconstant failure rate (i.e. exponential failure distributions)for both modes of failure; and also for a constant "detectable"-failurerate and an increasing "undetectable"-failure rate (i.e. representedby a second order gamma function failure distribution).     

Predictor-corrector pseudospectral methods for stochastic partial differential equations with additive white noise

Commonly used finite-difference numerical schemes show some deficiencies in the integration of certain types of stochastic partial differential equations with additive white noise. In this paper efficient predictor-corrector spectral schemes to integrate these equations are discussed. They are all based on the discretization of the system in Fourier space. The nonlinear terms are treated using a pseudospectral approach so as to speed up the computations without a significant loss of accuracy. The proposed schemes are applied to solve, both in one and two spatial dimensions, two paradigmatic continuum models arising in the context of nonequilibrium dynamics of growing interfaces: the Kardar-Parisi-Zhang and Lai-Das Sarma-Villain equations. Numerical results about the Lai-Das Sarma-Villain equation in two spatial dimensions have not been previously reported in the literature.     

Establishing the broadcast efficiency of the Subset Difference Revocation Scheme

When an organisation chooses a system to make regular broadcasts to a changing user base, there is an inevitable trade off between the number of keys a user must store and the number of keys used in the broadcast. The Complete Subtree and Subset Difference Revocation Schemes were proposed as efficient solutions to this problem. However, all measurements of the broadcast size have been in terms of upper bounds on the worst-case. Also, the bound on the latter scheme is only relevant for small numbers of revoked users, despite the fact that both schemes allow any number of such users. Since the broadcast size can be critical for limited memory devices, we aid comparative analysis of these important techniques by establishing the worst-case broadcast size for both revocation schemes.      

On some difference schemes for singular singularly-perturbed boundary value problems

Summary Singularly perturbed boundary value ordinary differential problems are considered, where the problem defining the reduced solution is singular. For numerical approximation, families of symmetric difference schemes, which are equivalent to certain collocation schemes based on Gauss and Lobatto points, are used. Convergence results, previously obtained for the regular singularly perturbed case, are extended. While Gauss schemes are extended with no change, Lobatto schemes require a small modification in the mesh selection procedure. With meshes as prescribed in the text, highly accurate solutions can be obtained with these schemes for singular singularly perturbed problems at a very reasonable cost. This is demonstrated by examples.This research was completed while the author was visiting the Department of Applied Mathematics, Weizmann Inst., Rehovot, Israel. The author was supported in part under NSERC grant A4306     

Conservative finite-difference scheme for the problem of propagation of a femtosecond pulse in a photonic crystal with combined nonlinearity

A conservative finite-difference scheme is constructed for the problem of propagation of a light pulse in a one-dimensional nonlinear photonic crystal with combined nonlinearity. The invariants of the corresponding differential problem and their difference analogues are given. The scheme is compared with those based on the widespread splitting method. For combined cubic and quadratic nonlinearity in photonic crystal layers, it is shown that the classical splitting method is ineffective, since it requires time steps that are smaller by one or more orders of magnitude. The finite-difference scheme proposed conserves the propagation invariants, which cannot be achieved for splitting schemes even on considerably finer grids. Nonreflecting conditions substantially improve the efficiency of conservative finite-difference schemes as applied to the simulation of complex nonlinear effects in photonic crystals, which require much smaller steps in space and time than those used in the case of linear propagation. The simulation is based on the approach proposed by the authors for the given class of problems.     

Essentially Symplectic Boundary Value Methods for Linear Hamiltonian Systems

1.IlltroductiollInmanyareasofphysics,mechanics,etc.,HamiltoniansystemsofODEsplayaveryimportantrole.Suchsystemshavethefollowinggeneralform:where,bydenotingwithOfandimthenullmatrixandtheidentitymatrixofordermarespectively,SimplepropertiesofthematrixJZmarethefollowingones:Inequation(1)AH(~,t)isthegradientofascalarfunctionH(y,t),usuallycalledHamiltonian.InthecasewhereH(y,t)=H(y),thenthevalueofthisfunctionremainsconstantalongt.hesollltion7/(t),t,hatis'*ReceivedFebruaryI3,1995.l)Worksupporte…     

离散纵标方法诸格式的误差分析

In this paper some common used numerical schemes for solving discrete ordinate equations are considered and the error estimates are studied for the combined spatial and angular approximations.The conclusions show that the error order of scalar flux in all of these schemes can not be second order even if the source term f is smooth enouth.In addition,when we introduce a kind of graded grids,the simple step character scheme has same accuracy as “high order“ ones.     

Hamiltonian differencing of fluid dynamics

By analyzing the Hamiltonian structures of several representations of continuous Lagrangian fluid dynamics, a universal Hamiltonian form is developed which unifies those structures and applies both to the continuous and spatially discrete cases. Then the universal Hamiltonian form is used as a “template” for generating numerical differencing schemes which retain the underlying Hamiltonian structure of the continuous theory. Examples are discussed of these spatial differencing schemes for the Euler equations in one, two, and three dimensions. In one dimension, the nondissipative part of the von Neumann-Richtmeyer scheme is recovered as a special case.     

Smoothness Analysis of Subdivision Schemes by Proximity

Linear curve subdivision schemes may be perturbed in various ways, for example, by modifying them such as to work in a manifold, surface, or group. The analysis of such perturbed and often nonlinear schemes "T" is based on their proximity to the linear schemes "S" which they are derived from. This paper considers two aspects of this problem: One is to find proximity inequalities which together with C^k smoothness of S imply C^k smoothness of T. The other is to verify these proximity inequalities for several ways to construct the nonlinear scheme T analogous to the linear scheme S. The first question is treated for general k, whereas the second one is treated only in the case k = 2. The main result of the paper is that convergent geodesic/projection/Lie group analogues of a certain class of factorizable linear schemes have C² limit curves.     

Models of Network Access Using Feedback Fluid Queues

At the access to networks, in contrast to the core, distances and feedback delays, as well as link capacities are small, which has network engineering implications that are investigated in this paper. We consider a single point in the access network which multiplexes several bursty users. The users adapt their sending rates based on feedback from the access multiplexer. Important parameters are the user's peak transmission rate p, which is the access line speed, the user's guaranteed minimum rate r, and the bound on the fraction of lost data. Two feedback schemes are proposed. In both schemes the users are allowed to send at rate p if the system is relatively lightly loaded, at rate r during periods of congestion, and at a rate between r and p, in an intermediate region. For both feedback schemes we present an exact analysis, under the assumption that the users' file sizes and think times have exponential distributions. We use our techniques to design the schemes jointly with admission control, i.e., the selection of the number of admissible users, to maximize throughput for given p, r and . Next we consider the case in which the number of users is large. Under a specific scaling, we derive explicit large deviations asymptotics for both models. We discuss the extension to general distributions of user data and think times.     

Asymptotic Preserving Schemes for Semiconductor Boltzmann Equation in the Diffusive Regime

As is known, the numerical stiffness arising from the small mean free path is one of the main difficulties in the kinetic equations. In this paper, we derive both the split and the unsplit schemes for the linear semiconductor Boltzmann equation with a diffusive scaling. In the two schemes, the anisotropic collision operator is realized by the "BGK"-penalty method, which is proposed by Filbet and Jin [F. Filbet and S. Jin, J. Comp. Phys. 229(20), 7625-7648, 2010] for the kinetic equations and the related problems having stiff sources. According to the numerical results, both of the schemes are shown to be uniformly convergent and asymptotic-preserving. Besides, numerical evidences suggest that the unsplit scheme has a better numerical stability than the split scheme.     

三元区间数型多属性决策正交投影模型及其在边坡支护方案评价中的应用

针对用TOPSIS法进行三元区间数型多属性决策的不足,用各方案到"理想方案"的"垂面"距离代替TOPSIS法中的欧氏距离,提出一种三元区间数型多属性决策正交投影模型.模型将"理想方案"平移至坐标原点后,转换为0向量,只用平移后的"负理想方案"计算各方案到"理想方案"的"垂面"距离,根据距离最小原则排序得到最终决策结果.通过一个边坡支护方案评价的例子进行了计算分析,并与用其他方法得到的结果进行了对比,说明了模型的有效性.     

Two Novel Classes of Arbitrary High-Order Structure-Preserving Algorithms for Canonical Hamiltonian Systems

In this paper, we systematically construct two classes of structure-preserving schemes with arbitrary order of accuracy for canonical Hamiltonian systems. The one class is the symplectic scheme, which contains two new families of parameterized symplectic schemes that are derived by basing on the generating function method and the symmetric composition method, respectively. Each member in these schemes is symplectic for any fixed parameter. A more general form of generating functions is introduced, which generalizes the three classical generating functions that are widely used to construct symplectic algorithms. The other class is a novel family of energy and quadratic invariants preserving schemes, which is devised by adjusting the parameter in parameterized symplectic schemes to guarantee energy conservation at each time step. The existence of the solutions of these schemes is verified. Numerical experiments demonstrate the theoretical analysis and conservation of the proposed schemes.     

A family of non-oscillatory 6-point interpolatory subdivision schemes

In this paper we propose and analyze a new family of nonlinear subdivision schemes which can be considered non-oscillatory versions of the 6-point Deslauries-Dubuc (DD) interpolatory scheme, just as the Power _p schemes are considered nonlinear non-oscillatory versions of the 4-point DD interpolatory scheme. Their design principle may be related to that of the Power _p schemes and it is based on a weighted analog of the Power _p mean. We prove that the new schemes reproduce exactly polynomials of degree three and stay ’close’ to the 6-point DD scheme in smooth regions. In addition, we prove that the first and second difference schemes are well defined for each member of the family, which allows us to give a simple proof of the uniform convergence of these schemes and also to study their stability as in [19, 22]. However our theoretical study of stability is not conclusive and we perform a series of numerical experiments that seem to point out that only a few members of the new family of schemes are stable. On the other hand, extensive numerical testing reveals that, for smooth data, the approximation order and the regularity of the limit function may be similar to that of the 6-point DD scheme and larger than what is obtained with the Power _p schemes.     

Adaptive energy preserving methods for partial differential equations

A framework for constructing integral preserving numerical schemes for time-dependent partial differential equations on non-uniform grids is presented. The approach can be used with both finite difference and partition of unity methods, thereby including finite element methods. The schemes are then extended to accommodate r-, h- and p-adaptivity. To illustrate the ideas, the method is applied to the Korteweg–de Vries equation and the sine-Gordon equation. Results from numerical experiments are presented.     

High‐order compact difference schemes for the modified anomalous subdiffusion equation

In this article, two kinds of high‐order compact finite difference schemes for second‐order derivative are developed. Then a second‐order numerical scheme for a Riemann–Liouvile derivative is established based on a fractional centered difference operator. We apply these methods to a fractional anomalous subdiffusion equation to construct two kinds of novel numerical schemes. The solvability, stability, and convergence analysis of these difference schemes are studied by using Fourier method. The convergence orders of these numerical schemes are and , respectively. Finally, numerical experiments are displayed which are in line with the theoretical analysis. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 213–242, 2016     

The numerical solution of a model problem biharmonic equation by using Extrapolated Alternating Direction Implicit methods

The numerical solution of the 2-dimensional biharmonic equation over the unit square by using Extrapolated Alternating Direction Implicit (E.A.D.I.) methods is studied. To approximate the biharmonic equation both a 13-point and a 25-point difference replacements are considered. In each case E.A.D.I. schemes are used together with the acceleration parameter fixed during the iterations or varying according to the Douglas set of parameters. Finally optimum E.A.D.I. schemes are given for every value of the numberN of mesh subdivisions in each co-ordinate direction.     

Numerical analysis of differential operators on raw point clouds

3D acquisition devices acquire object surfaces with growing accuracy by obtaining 3D point samples of the surface. This sampling depends on the geometry of the device and of the scanned object and is therefore very irregular. Many numerical schemes have been proposed for applying PDEs to regularly meshed 3D data. Nevertheless, for high precision applications it remains necessary to compute differential operators on raw point clouds prior to any meshing. Indeed differential operators such as the mean curvature or the principal curvatures provide crucial information for the orientation and meshing process itself. This paper reviews a half dozen local schemes which have been proposed to compute discrete curvature-like shape indicators on raw point clouds. All of them will be analyzed mathematically in a unified framework by computing their asymptotic form when the size of the neighborhood tends to zero. They are given in terms of the principal curvatures or of higher order intrinsic differential operators which, in return, characterize the discrete operators. All considered local schemes are of two kinds: either they perform a polynomial local regression, or they compute directly local moments. But the polynomial regression of order 1 is demonstrated to play a special role, because its iterations yield a scale space. This analysis is completed with numerical experiments comparing the accuracies of these schemes. We demonstrate that this accuracy is enhanced for all operators by applying previously the scale space.     

Two-stage complex Rosenbrock schemes for stiff systems

New two-stage Rosenbrock schemes with complex coefficients are proposed for stiff systems of differential equations. The schemes are fourth-order accurate and satisfy enhanced stability requirements. A one-parameter family of L1-stable schemes with coefficients explicitly calculated by formulas involving only fractions and radicals is constructed. A single L2-stable scheme is found in this family. The coefficients of the fourth-order accurate L4-stable scheme previously obtained by P.D Shirkov are refined. Several fourth-order schemes are constructed that are high-order accurate for linear problems and possess the limiting order of L-decay. The schemes proposed are proved to converge. A symbolic computation algorithm is developed that constructs order conditions for multistage Rosenbrock schemes with complex coefficients. This algorithm is used to design the schemes proposed and to obtain fifth-order accurate conditions.     

Efficient numerical schemes for the solution of generalized time fractional Burgers type equations

The main aim of this paper is to propose two semi-implicit Fourier pseudospectral schemes for the solution of generalized time fractional Burgers type equations, with an analysis of consistency, stability, and convergence. Under some assumptions, the unconditional stability of the schemes is shown. In implementation of these schemes, the fast Fourier transform (FFT) can be used efficiently to improve the computational cost. Various test problems are included to illustrate the results that we have obtained regarding the proposed schemes. The results of numerical experiments are compared with analytical solutions and other existing methods in the literature to show the efficiency of proposed schemes in both accuracy and CPU time. As numerical solution of fractional stochastic nonlinear partial differential equations driven by Brownian motions are among current related research interests, we report the performance of these schemes on stochastic time fractional Burgers equation as well.