Scheduling a no-wait flow shop containing unbounded batching machines

We study the problem of scheduling n jobs in a no-wait flow shop consisting of m batching machines. Each job has to be processed by all the machines. All jobs visit the machines in the same order. A job completed on an upstream machine should be immediately transferred to the downstream machine. Batching machines can process several jobs simultaneously in a batch so that all jobs of the same batch start and complete together. The processing time of a batch is equal to the maximum processing time of the jobs in this batch. We assume that the capacity of any batch is unbounded. The problem is to find an optimal batch schedule such that the maximum job completion time, that is the makespan, is minimized. For m = 2, we prove that there exists an optimal schedule with at most two batches and construct such a schedule in O(n log n) time. For m = 3, we prove that the number of batches can be limited to nine and give an example where all optimal schedules have seven batches. Furthermore, we prove that the best schedules with at most one, two and three batches are 3-, 2- and 3/2-approximate solutions, respectively. The first two bounds are tight for corresponding schedules. Finally, we suggest an assignment method that solves the problem with m machines and at most r batches in O(n^{m(r-2)+1+[m/r]}) time, if m and r are fixed. The method can be generalized to minimize an arbitrary maximum cost or total cost objective function.     

TATP模拟物的设计及安全性评估

三过氧化三丙酮（TATP）直接用于安检培训具有危险性高、安全隐患多的问题。设计出可代替TATP在X光机、CT机等高通量安检仪中成像的模拟物。物质组成为m(葡萄糖)∶m(十六醇)∶m(蔗糖)=25.77∶9.68∶14.55，与TATP具有相似的外观及有效原子序数，元素质量分数相差小于0.020%，堆积密度相差0.012 g/cm³。为确保模拟物在红外、拉曼等高灵敏性安检仪中亦存在特征信号，在混合物中加入适量TATP。结果表明，当TATP的加入量为20%（质量分数）时，可有效地表征出混合物中TATP的红外、拉曼特征峰；同时，体系相容性较好，机械感度低，且不具有爆炸性。优化后的配方为:m(葡萄糖)∶m(十六醇)∶m(蔗糖)∶m(TATP）=20.62∶7.74∶11.64∶10.00。该模拟物与TATP的相似度高、安全性好，可直接用于安检人员培训。     

Single operation earliness–tardiness scheduling with machine activation costs

We consider a static, single operation, non-pre-emptive, deterministic scheduling problem in which a set of n jobs is to be processed on k identical machines. Jobs assigned to each machine have a common due date. The number of machines (k) is unknown. Activating a machine will require additional costs to be incurred. The objective is to find an optimal sequence, the optimal number of machines (k), and the respective due dates to minimize the weighted sum of earliness, tardiness, and machine activation costs. We propose a polynomial time algorithm to solve the problem.     

Lot Sizing with Several Groups of Single-Cycling Retailers and One Warehouse

In this paper I describe a consecutiveness rule for grouping N retailers into m groups with independent single-cycle policies for each group which enables the creation of groups using a shortest-path approach. I also suggest a very efficient algorithm to compute the lot sizes for any single-cycle policy which can easily be incorporated into the shortest-path model for the creation of m single-cycle groups.     

Classification of 2 × 2 non-strictly hyperbolic systems for plane waves in isotropic elastic solids

The governing equations for plane waves in generally nonlinear isotropic elastic solids are a system of 6 × 6 hyperbolic conversation laws. For the half-space Riemann problem in which the initial conditions at t = 0, x > 0 and the boundary conditions at x = 0, t > 0 are constant, the system is equivalent to 3 × 3 system in the full-space Riemann problem. It is further reduced to a 2 × 2 system due to the fact that one of the characteristic wave speeds is linearly degenerate. For hyperelastic materials for which there exists a potential W whose gradients provide the strains, the wave curves near an isolated umbilic point are represented by the potential of the form

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which contains two parameters k and m. The classification of the geometry of wave curves depends on the values of k and m and can be classified into five cases. The potential function considered here is equivalent to considered by Schaeffer and Shearer where a and b are parameters. The classification presented here seems to provide simpler algebraic expressions. It also renders more refined classification as shown in the paper.     

Non-Newtonian Fluids in Spout-Fluid Beds: Mass Transfer Coefficient at Low Reynolds Numbers

Following on from the work of Anabtawi et al. (2003), this study examined how the volumetric liquid-phase mass transfer coefficient, k_La, of oxygen in air in three-phase spout-fluid beds was affected by varying the system parameters of bed height, bed diameter, gas velocity, and liquid velocity. The liquid used was 0.1% CMC solution, displaying a pseudo-plastic rheology, with 1.75 mm glass spheres as packing. The values of the Sherwood number were lower than in previous studies (Anabtawi et al., 2003), in the range 9,000-186,000. Gas velocity had a similar effect on k_La as in a bubble column, with results also giving good agreement with previous work on two-phase and three-phase spouted bed systems. The correlation obtained for the effect of liquid velocity on k_La compared well with that of Schumpe et al. (1989). An increase in the height of packing increased k_La to the power of 0.319, with an increase in column diameter also causing an increase in k_La, which is in agreement with the results of Akita and Yoshida (1973).     

D.c. properties of ZnO thin films prepared by r.f. magnetron sputtering

In the development of ZnO-based varistors the electrical properties of ZnO/Bi₂O₃ junctions and of the two individual oxides are being investigated. Following our recent work on a.c. conductivity in Al---ZnO---Al sandwich structures we currently report d.c. measurements. The structures were prepared by r.f. magnetron sputtering in an argon/oxygen mixture in the ratio 4:1. Capacitance-voltage data confirm that the Al/ZnO interface does not form a Schottky barrier and measurements of the dependence of capacitance on film thickness indicate that the relative permittivity of the films is approximately 9.7. With increasing voltage the current density changed from an ohmic to a power-law dependence with exponent n≈3. Furthermore measurements of current density as a function of reciprocal temperature showed a linear dependence above about 240 K, with a very low activation energy below this temperature consistent with a hopping process. The higher temperature results may be explained assuming a room-temperature electron concentration n₀ and space-charge-limited conductivity, dominated by traps exponentially distributed with energy E below the conduction band edge according to N = N₀exp(−E/kT_t), where k is Boltzmann's constant. Typical derived values of these parameters are: n₀ = 7.2 × 10¹⁶ m⁻³, N₀ = 1.31 × 10⁴⁵ J⁻¹ m⁻³ and T_t = 623 K. The total trap concentration and the electron mobility were estimated to be 1.13 × 10²⁵ m⁻³ and (5.7−13.1) ×10⁻³m²V⁻¹s⁻¹ respectively.     

Flowshops with processing flexibility across production stages

This paper addresses a scheduling problem for a two stage hybrid flowshop (HFS) environment with significant processing flexibility across stages. A job can be either completely processed at one of the stages or its processing is split in a prespecified fashion between stages. For the latter case, the routing is only in one direction, from the 'upstream' stage to the 'downstream' stage. A stage may consist of one or more parallel identical machines. We first study the special case of a single machine per stage and present a pseudopolynomial dynamic programming algorithm to minimize makespan. Then, we provide a heuristic for the HFS_m1,m2 problem with m_k machines at stage k = 1,2, and prove its worst case and average performance. Also, we extend our algorithms to the case of stage dependent processing times. Finally, we report computational results on the average performance of HFS_m1,m2 with comparable flowshop and parallel machine environments, and provide managerial guidelines for process choice decisions.     

Driver age, car mass and accident exposure— A synthesis of available data

The tendency of younger drivers to be more likely than older drivers to drive smaller cars has been an important consideration in a number of prior investigations of the relation between car size and traffic safety. The purpose of the present study is to quantify this effect on a firmer basis than hitherto by fitting data from seven independent sources to a unified general model. More specifically, when the exposure measures “per unit distance of travel” or “per registered car” are used in studies of car mass effects on traffic safety, the exposure information often does not contain the variable driver age. This work develops a general procedure for disaggregating such exposure data into three driver (or owner) age categories; A₁: 16–24; A₂: 25–34; and A₃: 35 years. Data from the seven sources are fined to the equation

f(i,m) = H_i[1 + G _i(m/900 − 1)]

where m is the ear mass in kg, and f(i,m) is the fraction of cars of mass m which are driven (owned) by persons in the A_i, (i = 1, 2, 3) age category. The form of this equation permits easy comparison of 900 and 1800 kg cars. Those particular masses that have been chosen for illustrative comparisons in earlier work. The seven sets of data are used to derive overall average values of the parameters H₁ and G₁. The data from all seven sources show consistent effects which are summarized in one analytical expression which is well suited for use in future studies of car size effects because it reflects a synthesis of much prior data and it permits sensitivity analyses to be performed conveniently.     

Optimisation of binary integrators for decentralised detection

Binary integrators are an important part of the receiver in many operating radar systems. The optimisation of a binary integrator is not a simple task, because it requires the solution of a (k x n)-dimensional nonlinear optimisation problem, where n is the number of integrated bits (or the number of sensors in a distributed radar or sensor network) and k is the number of the design parameters of the single-pulse detector. An algorithm that converts the multi-dimensional optimisation problem into a one-dimensional problem, so reducing considerably the computational complexity, is developed. This reduction in computational complexity makes the real-time optimisation possible and practical, so it is very helpful for mobile sites in which the optimisation should be performed continually. The proposed algorithm can be applied when either the 'AND' or the 'OR' integration rule is adopted. The results are illustrated by means of two study cases. In the first case, the binary integrator of a constant false alarm rate radar detector is optimised; in the second one a decentralised detection system composed by n similar sensors is considered and the decision rules are jointly optimised according to the Neyman-Pearson criterion.     

Element Availability Importance in Generalized k-out-of-r-from-n Systems

An algorithm for evaluating the overall system availability and the availability importance of elements in a generalized consecutive k-out-of-r-from-n:F system is presented. This system consists of n linearly ordered nonidentical elements with different reliability characteristics and performance rates. Each element can have two states: (i) complete failure with a performance rate of zero; and (ii) perfect functioning with a nominal performance rate. The system fails if the sum of the performance rates of any r consecutive elements is lower than a demand W. The suggested algorithm, based on an extended universal moment generating function, is convenient for numerical implementation. Analytical and numerical examples of evaluating availability importance indices are presented.     

Structural relaxation in poly(ethylene oxide)-salt solutions

We present the results of molecular dynamics simulations of PEO_xNaI polymer electrolytes, performed to study the influence of NaI on the dynamics of PEO. By calculating the mean square displacement of the CH₂ groups we observe that the Rouse-like motion, typical for short polymer chains, is slowed down under the influence of NaI. This slowing down is also observed in the self part of the intermediate scattering function F^s(k,t), as an increase in the relaxation time. By using the Gaussian approximation it is shown that the stretched exponential relaxation in the small k-limit of F^s(k,t) is a result of the Rouse-like motion of the polymers. We find that our results are in good agreement with neutron spin-echo experiments.     

Temperature dependence of stage II fatigue crack growth rate

A critical assessment has been performed by compiling experimental data concerning the temperature dependence of stage II fatigue crack growth. For aluminium alloys, high strength steels, austenitic stainless steels and superalloys, the power coefficient, m, for the Paris relationship is temperature dependent and all ln(da/dN) vs ln(ΔK) curves cross at one point, designated as the pivot point (PP), which is a material-dependent parameter. The assumption is made that PP corresponds to a transition point for the fatigue crack growth mechanism.     

Thermal optical properties of TiO2 films

A fibre optic experimental arrangement was used to determine the thermo-optic coefficient (dn/dT) of electron beam deposited titanium dioxide coatings on the cleaved end faces of multimode optical fibres for a wavelength range between 600 and 1050 nm. The temperature-induced change in the index of refraction (n) and extinction coefficient (k) were successfully determined from reflection spectra. Measurements of n and k at various wavelengths for different temperatures enabled the determination of dn/dT and dk/dT. It was found that dn/dT takes different values at different temperature ranges. For example, at 800 nm, dn/dT was (−1.77±0.7)×10⁻⁴ K⁻¹, between 18°C and 120°C, and took a value of (−3.04±0.7)×10⁻⁴ K⁻¹ between 220°C and 325°C.     

Resistance curves for crack growth under plane-stress conditions in an elastic perfectly-plastic material

A recently developed solution for the plastic strain, ε^P_y(x, t), on the crack line is used in conjunction with a critical strain criterion to construct curves for k_R(a) versus a, where a is the increase in crack length. Resistance curves have been computed for various values of the critical plastic strain. They show a monotonic increase of K_R(a) with increase in crack length, to a constant steady-state value.     

Supercritical CO2/co-solvent extraction of porogens and surfactant templates to obtain ultralow dielectric constant films

A method of pore generation by supercritical CO₂ (SCCO₂) and co-solvent extraction for the preparation of nanohybrid film and mesoporous organosilicate thin film for ultralow dielectric constant materials is investigated. The films were treated with SCCO₂/methyl ethyl ketone-tetrahydrofuran co-solvent combination and it was found that the treatment produced dielectric constant (k) values of 2.30 for closed-pore and 1.61 for open-pore nanohybrid films; 2.14 for cetyl trimethylammonium bromide-based and 2.50 for polyethylene glycol octadecyl ether-based films. These results suggest that the SCCO₂/co-solvent treatment produces closely comparable results with thermal decomposition in terms of Fourier Transform Infrared spectroscopy data, optical constants obtained from variable angle spectroscopic ellipsometry, and k values.     

Fracture angle and strain-energy-density-factor of a crack at hole at an arbitrary angle

For both the maximum stress criterion and strain-energy-density-factor (S) theory, fracture angle (the initial angle of crack growth) − θ_o is predicted by using opening and sliding mate stress intensity factors, k₁ and k₂. These theoretical predictions are consistent with experimental fracture angles.

For the S theory, the crack spreads in the negative θ_o-direction in a plane for which S is a minimum, S_min. This quantity was obtained analytically. The experimental data of the critical S (S_cr) on plexiglass fracture specimens remains essentially constant.     

抗过载长秒量延期电点火具结构设计与性能研究

为提高电点火具的抗过载能力，并满足长延期的要求，在研究提高电点火具抗过载的方法和影响延期药燃烧速度因素的基础上，设计了一种抗过载长秒量延期电点火具。采用复式结构壳体(内外双壳，内壳为铝、外壳为镍铜)来提高其抗过载能力，壳内涂虫胶漆。选用玻璃 金属封结电极塞来提高密封性。点火药为m（聚四氟乙烯）∶m（铝粉）∶m（镁粉）= 40∶30∶30的高能点火药。延期元件选用1Cr18Ni9Ti不锈钢材料管壳。延期药为钨系延期药，组分质量比为m(W)∶m(KClO₄):m(BaCrO₄)∶m(黏结剂)=33∶10∶55∶2。使用泡沫铝作为延期元件和壳体间的缓冲材料，厚度为1.5 mm。运用ANSYS软件，仿真验证了电点火具的抗过载能力，满足设计要求。采用堵、泄结合的方式进行防静电设计:在点火药和壳体之间设计环氧树脂绝缘环，厚度为1.5 mm；在电极塞中部设计0.2 mm宽的空气隙，提高使用安全性。通过对电点火具结构、药剂、材料等方面的优化，提升了电点火具的抗过载能力，满足了长秒量延期要求。     

Energy-density concept in fracture mechanics

A theory of fracture mechanics is proposed in which attention is focused on the intensity of the energy field in the crack tip region. This energy field possesses a 1/r-type of singularity for both elastic and plastic materials. The strength or amplitude of this field will be referred to as the “energy-density factor”, S. Unlike the stress-intensity factor k in classical fracture mechanics which is only a measure of the local stress amplitude, the energy-density factor is also direction sensitive. The difference between k and S is analogous to the difference between a scalar and vector quantity. In this sense, the critical value S_cr specifies the direction of crack initiation as well as the fracture toughness of the material.     

An enhanced global–local higher-order theory for the free edge effect in laminates

According to the double-superposition hypothesis proposed by Li and Liu [Li XY, Liu D. Generalized laminate theories based on double superposition hypothesis. Int J Numer Methods Eng 1997;40:1197–212], an enhanced global–local higher-order theory (EGLHT-mn) is developed to analyze the edge-effect problems in laminates. The in-plane displacement field consists of mth-order (9  m  3) polynomial in global coordinate z along the thickness direction and order 3 power series in local coordinate ζ within each layer whereas the transverse deflection is represented by a nth-order (9  n  3) polynomial of global coordinate z. By imposing the free surface conditions and the geometric and the stress continuity conditions at interfaces, the number of variables of the higher-order theory is independent of the number of layers of the laminates. As an improvement to the global–local theory proposed by Li and Liu (1997), the present higher-order theory takes into account all the effects of shear and normal stresses. A three-node triangular element satisfying the requirement of C¹ weak-continuity conditions between elements is also presented. Comparing to previous published results, it is found that the present higher-order theory is capable of treating free-edge problems in symmetric and unsymmetric laminates under extension, bending and thermal loading. Other characteristic of the present theory is that transverse shear stresses can be accurately computed directly from the constitutive equations without smoothing. However, to determine transverse normal stresses, the local equilibrium equation approach has to been adopted.