Statistical mechanics of distribution networks

This thesis presents an analysis of the stability of complex distribution networks. We present a stability analysis against cascading failures. We propose a spin [binary] model, based on concepts of statistical mechanics. We test macroscopic properties of distribution networks with respect to various topological structures and distributions of microparameters. The equilibrium properties of the systems are obtained in a statistical mechanics framework by application of the replica method. We demonstrate the validity of our approach by comparing it with Monte Carlo simulations. We analyse the network properties in terms of phase diagrams and found both qualitative and quantitative dependence of the network properties on the network structure and macroparameters. The structure of the phase diagrams points at the existence of phase transition and the presence of stable and metastable states in the system. We also present an analysis of robustness against overloading in the distribution networks. We propose a model that describes a distribution process in a network. The model incorporates the currents between any connected hubs in the network, local constraints in the form of Kirchoff's law and a global optimizational criterion. The flow of currents in the system is driven by the consumption. We study two principal types of model: infinite and finite link capacity. The key properties are the distributions of currents in the system. We again use a statistical mechanics framework to describe the currents in the system in terms of macroscopic parameters. In order to obtain observable properties we apply the replica method. We are able to assess the criticality of the level of demand with respect to the available resources and the architecture of the network. Furthermore, the parts of the system, where critical currents may emerge, can be identified. This, in turn, provides us with the characteristic description of the spread of the overloading in the systems.

Setting parameters in MRP for the effective management of bought-out inventory in a JIT assembly environment

In recent years, UK industry has seen an explosive growth in the number of `Computer Aided Production Management' (CAPM) system installations. Of the many CAPM systems, materials requirement planning/manufacturing resource planning (MRP/MRPII) is the most widely implemented. Despite the huge investments in MRP systems, over 80 percent are said to have failed within 3 to 5 years of installation. Many people now assume that Just-In-Time (JIT) is the best manufacturing technique. However, those who have implemented JIT have found that it also has many problems. The author argues that the success of a manufacturing company will not be due to a system which complies with a single technique; but due to the integration of many techniques and the ability to make them complement each other in a specific manufacturing environment. This dissertation examines the potential for integrating MRP with JIT and Two-Bin systems to reduce operational costs involved in managing bought-out inventory. Within this framework it shows that controlling MRP is essential to facilitate the integrating process. The behaviour of MRP systems is dependent on the complex interactions between the numerous control parameters used. Methodologies/models are developed to set these parameters. The models are based on the Pareto principle. The idea is to use business targets to set a coherent set of parameters, which not only enables those business targets to be realised, but also facilitates JIT implementation. It illustrates this approach in the context of an actual manufacturing plant - IBM Havant. (IBM Havant is a high volume electronics assembly plant with the majority of the materials bought-out). The parameter setting models are applicable to control bought-out items in a wide range of industries and are not dependent on specific MRP software. The models have produced successful results in several companies and are now being developed as commercial products.

Accurate modelling of pulse transformation by adjustable-in-time medium parameters

A possibility of a strong change of an electromagnetic signal by a short sequence of time cycles of pulses that modulate the medium parameters is shown. The backward wave is demonstrated to be an inevitable result of the medium time change. Dependence of the relation between backward and forward waves on the parameters of the medium modulation is investigated. The finite statistical complexity of the electromagnetic signal transformed by a finite sequence of modulating cycles is calculated. Increase of the complexity with the number of cycles is shown.

Flat-top supercontinuum and tunable femtosecond fiber laser sources at 1.9-2.5 μm

We report the high-energy flat-top supercontinuum covering the mid-infrared wavelength range of 1.9-2.5 μm as well as electronically tunable femtosecond pulses between 1.98-2.22 μm directly from the thulium-doped fiber laser amplifier. Comparison of experimental results with numerical simulations confirms that both sources employ the same nonlinear optical mechanism - Raman soliton frequency shift occurring inside the Tm-fiber amplifier. To illustrate that, we investigate two versions of the compact diode-pumped SESAM mode-locked femtosecond thulium-doped all-silica-fiber-based laser system providing either broadband supercontinuum or tunable Raman soliton output, depending on the parameters of the system. The first system operates in the Raman soliton regime providing femtosecond pulses tunable between 1.98-2.22 μm. Wide and continuous spectral tunability over 240 nm was realized by changing only the amplifier pump diode current. The second system generates high-energy supercontinuum with the superior spectral flatness of better than 1 dB covering the wavelength range of 1.9-2.5 μm, with the total output energy as high as 0.284 μJ, the average power of 2.1 W at 7.5 MHz repetition rate. We simulate the amplifier operation in the Raman soliton self-frequency shift regime and discuss the role of induced Raman scattering in supercontinuum formation inside the fiber amplifier. We compare this system with a more traditional 1.85-2.53 μm supercontinuum source in the external highly-nonlinear commercial chalcogenide fiber using the Raman soliton MOPA as an excitation source. The reported systems1 can be readily applied to a number of industrial applications in the mid-IR, including sensing, stand-off detection, medical surgery and fine material processing.