An Incompressible Fluid in a Weakly Deformable Shell. Part I: Analysis of the Model

We consider the flow of a viscous incompressible fluid in a pipe when the boundary is a deformable shell of Naghdi type. We prove that the corresponding system of partial differential equations has a solution when the deformation of the shell is smooth and small enough. We propose an algorithm that uncouples the unknowns and prove its convergence.     

Nonlinear analysis of laser droplet generation by means of 0–1 test for chaos

We apply the recently improved version of the 0–1 test for chaos to real experimental time series of laser droplet generation process. In particular two marginal regimes of dripping are considered: spontaneous and forced dripping. The outcomes of the test reveal that both spontaneous and forced dripping time series can be characterized as chaotic, which coincides with the previous analysis based on nonlinear time series analysis.     

Critical behavior of electric field gradient in MnSi studied by muon level-crossing resonance

The electric quadrupole interaction of⁵⁵Mn nuclei was studied in the weakly ferromagnetic system MnSi using muon level-crossing resonance (LCR) technique. The temperature dependence of the electric field gradient (EFG) shows a critical behavior near the ferromagnetic transition temperature, indicating that the EFG due to the conduction electron is strongly correlated with the magnetic susceptibility in the itinerant electron magnetism. The temperature dependence of EFG is in reasonable agreement with the self-consistent renormalization theory developed by Moriya and coworkers.We gratefully acknowledge helpful discussion with Dr. N. Nishida. We also wish to thank Keith Hoyle and Curtis Ballard for technical support.     

Reply to the note on the flow behaviour of combustion gas in the boundary layer of an MHD generator

The temperature profile in Fig. 3 of Ref. 1 is better approximated by a relation for a turbulent boundary layer than a laminar boundary layer. The critical Reynolds number is expected to be lowered in the flow train of MHD combustion gas because of large turbulence in the combustor and by roughness along the duct.     

Ionic conduction of the perovskite-type halides

The ionic conduction in the perovskite-type halides, CsPbCl₃, CsPbCl₃ and KMnCl₃, was studied. Measurements were made of ac conductivity at temperatures from 150°C to the melting point, and of ionic transport number using the Tubandt, EMF and ion-blocking methods. The effects of impurity doping on the ionic conductivity of CsPbCl₃ were also studied using the samples of composition, CsPb_0.99M_0.01Cl_2.99 (M = Li, Na, K, Ag). It was concluded that these materials are halide-ion condcutors. The ionic conductivities of CsPbCl₃ and CsPbBr₃ are close to those of the well known halide-ion conductors, PbCl₂ and PbBr₂. The ionic transport numbers were found to be > 0.9 for CsPbCl₃ and CsPbBr₃, and about 0.99 for KMnCl₃. The conduction was considered to be caused by the migration of halide-ion vacancies V_X (X = Cl, Br). The activation energies for the migration of V_X were 0.29 eV for CsPbCl₃, 0.25 eV for CsPbBr₃ and 0.39 eV for KMnCl₃. The vacancy diffusion coefficients of these materials were found to be verylarge. However, the impurity doping did not increase the ionic conductivity markedly because of small dopant solubility.     

A Lot-sizing Model for Just-in-time Manufacturing

We consider the problem of determining lot sizes of multiple items that are manufactured by a single capacitated facility. The manufacturing facility may represent a bottleneck processing activity on the shop floor or a storeroom that provides components to the shop floor. Items flow from the facility to a downstream facility, where they are assembled according to a specified mix. Just-in-time (JIT) manufacturing requires a balanced flow of items, in the proper mix, between successive facilities. Our model determines lot sizes of the various items based on available capacity and four attributes of each item: demand rate, holding cost, set-up time and processing time. Holding costs for each item accrue until the appropriate mix of items is available for shipment downstream. We develop a lot-sizing heuristic that minimizes total holding cost per time unit over all items, subject to capacity availability and the required mix of items.     

Developing and Maintaining an Equity Index Fund

An index fund is a portfolio of shares designed to replicate the investment performance of a market index. The index represents the behaviour of the market as a whole. This paper describes the selection of an index fund which minimizes expected tracking error. Using a multivariate model of returns on shares, a development of a univariate model by Taylor, the selection problem is formulated as a quadratic programme. The effects of various constraints on tracking error are demonstrated. Several policies for the readjustment of a fund are examined in the context of the differing objectives of fund managers. As a general rule, regular readjustment is shown to be a more expensive policy than irregular updating.     

Scheduling Parts in a Combined Production-transportation Work Cell

This paper is concerned with a combined production-transportation scheduling problem. The problem comprises a simple, two-machine, automated manufacturing cell, which either stands alone or is a subunit of a complete flexible manufacturing system. The cell consists of two machines in series with a dedicated part-handling device such as a crane or robotic arm for transferring parts from the first machine to the second. The loading of a new piece on the first machine and the ejection of a finished piece from the second machine are performed by dedicated automated mechanisms. The introduction of parts into the system is done n at a time, whereby the parts are reshuffled into a sequence that minimizes completion time. All processing and transfer times are considered deterministic—a reasonable assumption for a cell comprising a robotic transfer device and two CNC machining units. What complicates the problem is the assumption of a non-negligible time for the transfer device to return (empty) from the second machine to the first. The operation is a generalization of a two-machine flowshop problem, and is formulated as a specially structured, asymmetric travelling salesman problem. An approximate polynomial time 0(n log n) algorithm is proffered. The procedure incorporates a lower bound using the Gilmore–Gomory algorithm for the no-wait, two-machine flowshop problem.     

A posteriori error estimates for optimal control problems governed by parabolic equations

Summary. In this paper, we derive a posteriori error estimates for the finite element approximation of quadratic optimal control problem governed by linear parabolic equation. We obtain a posteriori error estimates for both the state and the control approximation. Such estimates, which are apparently not available in the literature, are an important step towards developing reliable adaptive finite element approximation schemes for the control problem. Received July 7, 2000 / Revised version received January 22, 2001 / Published online January 30, 2002 RID="*" ID="*" Supported by EPSRC research grant GR/R31980