Modeling sequence scrambling and related phenomena in mixed-model production lines

In this paper we examine the various effects that workstations and rework loops with identical parallel processors and stochastic processing times have on the performance of a mixed-model production line. Of particular interest are issues related to sequence scrambling. In many production systems (especially those operating on just-in-time or in-line vehicle sequencing principles), the sequence of orders is selected carefully to optimize line efficiency while taking into account various line balancing and product spacing constraints. However, this sequence is often altered due to stochastic factors during production. This leads to significant economic consequences, due to either the degraded performance of the production line, or the added cost of restoring the sequence (via the use of systems such as mix banks or automated storage and retrieval systems). We develop analytical formulas to quantify both the extent of sequence scrambling caused by a station of the production line, and the effects of this scrambling on downstream performance. We also develop a detailed Markov chain model to analyze related issues regarding line stoppages and throughput. We demonstrate the usefulness of our methods on a range of illustrative numerical examples, and discuss the implications from a managerial point of view.     

用高中数学求解异面直线公垂线方程

用高中向量基础知识和待定法可非常方便地得出n（n≥3）维线性空间中异面直线的公垂线方程.若在大学数学教学中挖掘与中学数学的衔接和联系,则可在很大程度上降低大学数学的教学难度.     

ELASTIC CALCULATION OF STRESSES IN RINGS USING AIRY STRESS FUNCTION

Stress calculation formulae for a ring have been obtained by using Airy stress function of the plane strain field with the decomposition of the solutions for normal stresses of Airy biharmonic equation into two parts when it is loaded under two opposite inside forces along a diameter. One part should fulfill a constraint condition about normal stress distribution along the circumference at an energy valley to do the minimum work. Other part is a stress residue constant. In order to verify these formulae and the computed results, the computed contour lines of equi-maximal shear stresses were plotted and quite compared with that of photo-elasticity test results. This constraint condition about normal stress distribution along circumference is confirmed by using Greens’ theorem. An additional compression exists along the circumference of the loaded ring, explaining the divorcement and displacement of singularity points at inner and outer boundaries.     

输电线路等效电阻的计算

本文通过对趋肤效应的分析 ,讨论了输电线路中的焦耳热 ,并给出其等效电阻的计算结果     

Effect of numerical integration in the DGFEM for nonlinear convection‐diffusion problems

This paper is concerned with the effect of numerical integration applied to the discontinuous Galerkin finite element discretization of nonlinear convection‐diffusion problems in 2D. In the space semidiscretization the volume and line integrals are evaluated by numerical quadratures. Our goal is to estimate the error caused by the numerical integration and to show what numerical quadratures guarantee that the accuracy of the method with exact integration is preserved. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

The microscopic investigation of structures of moving flux lines by neutron and muon techniques

We have used a variety of microscopic techniques to reveal the structure and motion of flux line arrangements, when the flux lines in low T _c type II superconductors are caused to move by a transport current. Using small-angle neutron scattering by the flux line lattice (FLL), we are able to demonstrate directly the alignment by motion of the nearest-neighbor FLL direction. This tends to be parallel to the direction of flux line motion, as had been suspected from two-dimensional simulations. We also see the destruction of the ordered FLL by plastic flow and the bending of flux lines. Another technique that our collaboration has employed is the direct measurement of flux line motion, using the ultra-high-resolution spectroscopy of the neutron spin-echo technique to observe the energy change of neutrons diffracted by moving flux lines. The muon spin rotation (μSR) technique gives the distribution of values of magnetic field within the FLL. We have recently succeeded in performing μSR measurements while the FLL is moving. Such measurements give complementary information about the local speed and orientation of the FLL motion. We conclude by discussing the possible application of this technique to thin film superconductors.     

Saddle-point method and resurgent analysis

The topological part of the theory of the parameter-dependent Laplace integral is known to consist of two stages. At the first stage, the integration contour is reduced to a sum of paths of steepest descent for some value of the parameter. At the second stage, this decomposition (and hence the asymptotic expansion of the integral) is continued to all other parameter values. In the present paper, the second stage is studied with the help of resurgent analysis techniques. Translated fromMatematicheskie Zametki, Vol. 61, No. 2, pp. 278–296, February, 1997. Translated by B. Yu. Sternin and V. E. Shatalov     

The representability number of a chain

For each pair of linear orderings (L,M), the representability number repr_M(L) of L in M is the least ordinal α such that L can be order-embedded into the lexicographic power . The case is relevant to utility theory. The main results in this paper are as follows. (i) If κ is a regular cardinal that is not order-embeddable in M, then repr_M(κ)=κ; as a consequence, for each κω₁. (ii) If M is an uncountable linear ordering with the property that A×_lex2 is not order-embeddable in M for each uncountable AM, then for any ordinal α; in particular, . (iii) If L is either an Aronszajn line or a Souslin line, then .     

Transient gas flow simulation using an Adaptive Method of LinesSimulation d'écoulements dans un gazoduc par la méthode adaptative de lignes

Designing natural gas pipelines to safely and efficiently handle unsteady flows, requires knowledge of pressure drop, flowrate and temperature distribution throughout the system. The accurate prediction of these parameters is essential in order to achieve optimum cumulative deliverability, and safe and reliable operation. An Adaptive Method of Lines algorithm is formulated for the solution of Euler system of equations, which fully simulates slow and fast transients. Two test cases present the improvement of the numerical solution from grid adaptation. Good results are obtained both for slow and fast transients simulations proving that the suggested numerical procedure is appropriate for such predictions. To cite this article: E. Tentis et al., C. R. Mecanique 331 (2003).