A note on the value function for constrained control problems

We consider the Mayer optimal control problem with dynamics given by a nonconvex differential inclusion, whose trajectories are constrained to a given set and we obtain a relation between the costate function that appears in the maximum principle and the value function. This relation extends the known conditions existing in the literature for unconstrained problems to those for problems under state constraints.     

浅析医药包装

随着市场经济的深入，医药包装正成为我国经济发展的朝阳产业，文中意在介绍先进的医药包装材料。分析其应用情况及发展趋势和动态。     

Protecting local access telecommunications networks: Toward a minimum-cost solution

The problem of designing fibre-optic networks for local-access telecommunications generates (at least) three non-trivial subproblems. In the first of these subproblems one must determine how many fibre-optic cables (fibres) are required at either end of a street. In the next subproblem a minimum-cost network must be designed to support the fibres. The network must also provide distinct paths from either end of the street to the central exchange(s). Finally, the fibre-optic cables must be placed in protective covers. These covers are available in a number of different sizes, allowing some flexibility when covering each section of the network. In this paper we describe a dynamic programming (DP) formulation for finding a minimum-cost (protective) covering for the network (the third of the subproblems). This problem is a generalised set covering problem with side constraints and is further complicated by the introduction of fixed and variable welding costs. The DP formulation selects covers along each arc (in the network), but cannot exactly model the fixed costs and so does not guarantee optimality. We also describe an integer programming (IP) formulation for assessing the quality of the DP solutions. The cost of the networks constructed by the IP model is less than those designed using the DP model, but the saving is not significant for the problems examined (less than 0.1%). This indicates that the DP model will generally give very good solutions. Furthermore, as the problem dimensions grow, DP gives significantly better solution times than IP.     

Determination of molecular weight and molecular sizes of polymers by high temperature gel permeation chromatography with a static and dynamic laser light scattering detector

Flow-mode static and dynamic laser light scattering (SLS/DLS) studies of polymers, including polystyrene, polyethylene, polypropylene and poly(dimethylsiloxane) (PDMS), in 1,2,4-trichlorobenzene (TCB) at 150 °C were performed on a high temperature gel permeation chromatography (GPC) coupled with a SLS/DLS detector. Both absolute molecular weight (M) and molecular sizes (radius of gyration, R_g and hydrodynamic radius, R_h) of polymers eluting from the GPC columns were obtained simultaneously. The conformation of different polymers in TCB at 150 °C were discussed according to the scaling relationships between R_g, R_h and M and the ρ-ratio (ρ=R_g/R_h). Flow-mode DLS results of PDMS were verified by batch-mode DLS study of the same sample. The presented technique was proved to be a convenient and quick method to study the shape and conformation of polymers in solution at high temperature. However, the flow-mode DLS was only applicable for high molecular weight polymers with a higher refractive index increment such as PDMS.     

一类非线性MIMO不确定系统的动态输出反馈镇定

考察其标称系统的相对阶大于{1,1,…,1}同时含匹配和非匹配不确定性的MIMO 非线性系统的动态输出反馈镇定问题.文中直接用Lyaunov方法构造一类输出反馈动态补 偿器,该补偿器可以实现对所论非线性不确定系统的动态输出反馈渐近镇定.     

STRESS INTENSITY FACTORS AND WEIGHT FUNCTIONS FOR SEMI-ELLIPTICAL SURFACE CRACKS IN FINITE-THICKNESS PLATES UNDER TWO-DIMENSIONAL STRESS DISTRIBUTION

Abstract— A Fourier series approach is proposed to calculate stress intensity factors using weight functions for semi-elliptical surface cracks in flat plates subjected to two-dimensional stress distributions. The weight functions were derived from reference stress intensity factors obtained by three-dimensional finite element analyses. The close form weight functions derived are suitable for the calculation of stress intensity factors for semi-elliptical surface cracks in flat plates under two-dimensional stress distributions with the crack aspect ratio in the range of 0.1 ≤ a/c ≤ 1 and relative depth in the range of 0 ≤ a/t ≤ 0.8. Solutions were verified using several two-dimensional non-linear stress distributions; the maximum difference being 6%.     

Suspension force and mechanism of debris flows

The paper discusses the postulated suspension force, by which it is possible to explain some enigmatic phenomena observed in different types of mass movements. This force is generated in thick suspensions as a result of friction between sinking solid particles and static water. The suspension force is related to the seepage force but they have opposite directions. Both forces form flow networks. Having explained the suspension force, the paper describes how this influences the movement of material, particularly in debris flows. Enigmatic features and the mechanism of debris flows and lahars are explained by virtue of the suspension force. Electronic Publication     

A framework of virtual prototyping environment for the design and analysis of mechanical mechanism with clearance

Mechanical mechanisms with clearance abound in technological fields such as robotics, machine and steam turbine industry. The dynamic performance of these mechanisms in working condition can be achieved provided that the effects of the different on the mechanisms (such as mechanism dynamics, technological effects and thermal behaviour) are thoroughly understood. Virtual prototyping provides an integration of multi-domain dynamic simulation for the design and analysis process. In the current paper, a framework of virtual prototyping environment for the design and analysis of mechanical mechanism with clearance is presented. A case study with such a simulation strategy is studied for the optimum design and analysis of the technological parameter.     

Model Validation for Bridge-Road-Vehicle Dynamic Interaction System

The dynamic response of highway bridges subjected to moving truckloads has been observed to be dependent on (1) dynamic characteristics of the bridge; (2) truck configuration, speed, and lane position on the bridge; and (3) road surface roughness profile of the bridge and its approach. Historically, truckloads were measured to determine the load spectra for girder bridges. However, truckload measurements are either made for a short period of time [for example, weigh-in-motion (WIM) data] or are statistically biased (for example, weigh stations) and cost prohibitive. The objective of this paper is to present results of a 3D computer-based model for the simulation of multiple trucks on girder bridges. The model is based on the grillage approach and is applied to four steel girder bridges tested under normal truck traffic. Actual truckload data collected using a discrete bridge WIM system are used in the model. The data include axle loads, truck gross weight, axle configuration, and statistical data on multiple presence (side by side or following). The results are presented as a function of the static and dynamic stresses in each girder and compared with code provisions for dynamic load factor. The study provides an alternate method for the development of live-load models for bridge design and evaluation.     

Dynamic vulcanisation of EPDM/PE-based thermoplastic vulcanisates studied along the extruder axis

Simple blending and dynamic vulcanisation of EPDM/PE blends using the resol/SnCl₂ system was studied in an extruder using a series of sampling devices. The melting of the PE pellets occurs just in front of and in the first kneading zone. Upon complete melting of the PE phase, the EPDM/PE blends reach very quickly their final morphology. Crosslinking of the EPDM phase to high levels occurs already when the PE phase is not yet fully molten. The higher the EPDM content, the higher the viscous dissipation, the higher the melt temperature and, consequently, the higher the crosslinking rate. For the EPDM/PE (50/50; w/w) TPV a transition from continuous via co-continuous to fully dispersed EPDM is observed, which is driven by crosslinking. Although the degree of crosslinking of the EPDM rubber is very high, this does not prevent phase inversion of the blend. The EPDM/PE interface is rather blurred, because PE crystalline lamellae are growing into the EPDM domains, probably because of the high compatibility between PE and EPDM (60 wt% of ethene). This study shows that dynamic vulcanisation in extruders proceeds quite differently from that in batch kneaders, where melting, mixing and crosslinking are separated in time. In extruders mass and heat transport, melting of the thermoplastic, morphology development (including dispersion and phase inversion), distribution and dissolution of (crosslinking) chemicals and crosslinking of the rubber do not occur as independent phenomena, but mutually and/or continuously interact.