Dynamic scheduling in manufacturing systems using brownian approximations

Recently, Brownian networks have emerged as an effective stochastic model to approximate multiclass queueing networks with dynamic scheduling capability, under conditions of balanced heavy loading. This paper is a tutorial introduction to dynamic scheduling in manufacturing systems using Brownian networks. The article starts with motivational examples. It then provides a review of relevant weak convergence concepts, followed by a description of the limiting behaviour of queueing systems under heavy traffic. The Brownian approximation procedure is discussed in detail and generic case studies are provided to illustrate the procedure and demonstrate its effectiveness. This paper places emphasis only on the results and aspires to provide the reader with an up-to-date understanding of dynamic scheduling based on Brownian approximations.

On the performance of strain smoothing for quadratic and enriched finite element approximations (XFEM/GFEM/PUFEM)

By using the strain smoothing technique proposed by Chen et al. (Comput. Mech. 2000; 25: 137-156) for meshless methods in the context of the finite element method (FEM), Liu et al. (Comput. Mech. 2007; 39(6): 859-877) developed the Smoothed FEM (SFEM). Although the SFEM is not yet well understood mathematically, numerical experiments point to potentially useful features of this particularly simple modification of the FEM. To date, the SFEM has only been investigated for bilinear and Wachspress approximations and is limited to linear reproducing conditions. The goal of this paper is to extend the strain smoothing to higher order elements and to investigate numerically in which condition strain smoothing is beneficial to accuracy and convergence of enriched finite element approximations. We focus on three widely used enrichment schemes, namely: (a) weak discontinuities; (b) strong discontinuities; (c) near-tip linear elastic fracture mechanics functions. The main conclusion is that strain smoothing in enriched approximation is only beneficial when the enrichment functions are polynomial (cases (a) and (b)), but that non-polynomial enrichment of type (c) lead to inferior methods compared to the standard enriched FEM (e.g. XFEM). Copyright (C) 2011 John Wiley & Sons, Ltd.

The Borkar-Meyn theorem for asynchronous stochastic approximations

In this paper, we give a generalization of a result by Borkar and Meyn (2000) 1], on the stability and convergence of synchronous-update stochastic approximation algorithms, to the case of asynchronous stochastic approximations with delays. We then describe an interesting application of the result to asynchronous distributed temporal difference (TD) learning with function approximation and delays. (C) 2011 Elsevier B.V. All rights reserved.

Notes on approximations for turbulent flows with large temperature differences

The diffusion terms in the mean velocity and temperature equations of turbulent flow are analysed to decide when variations of fluid properties can produce appreciable errors. # A theoretical demonstration is given that in the mean-flow continuity equation for a gas the error in assuming constant density is small if the flow is turbulent, even when the temperature variations are large. # Separate discussion is given of the case of local heat sources in turbulence, as large errors can occur there.

Two-dimensional approximations of 3-dimensional eigenvalue problems in plate-theory

The eigenvalues and eigenfunctions corresponding to the three-dimensional equations for the linear elastic equilibrium of a clamped plate of thickness 2ϵ, are shown to converge (in a specific sense) to the eigenvalues and eigenfunctions of the well-known two-dimensional biharmonic operator of plate theory, as ϵ approaches zero. In the process, it is found in particular that the displacements and stresses are indeed of the specific forms usually assumed a priori in the literature. It is also shown that the limit eigenvalues and eigenfunctions can be equivalently characterized as the leading terms in an asymptotic expansion of the three-dimensional solutions, in terms of powers of ϵ. The method presented here applies equally well to the stationary problem of linear plate theory, as shown elsewhere by P. Destuynder.

Stiff string approximations in Rayleigh-Ritz method for rotating beams

The governing differential equation of the rotating beam reduces to that of a stiff string when the centrifugal force is assumed as constant. The solution of the static homogeneous part of this equation is enhanced with a polynomial term and used in the Rayleighs method. Numerical experiments show better agreement with converged finite element solutions compared to polynomials. Using this as an estimate for the first mode shape, higher mode shape approximations are obtained using Gram-Schmidt orthogonalization. Estimates for the first five natural frequencies of uniform and tapered beams are obtained accurately using a very low order Rayleigh-Ritz approximation.

The effects of disorder in dimerized quantum magnets in mean field approximations

15 p.