Motion by Curvature of Planar Networks

We consider the motion by curvature of a network of smooth curves with multiple junctions in the plane, that is, the geometric gradient flow associated to the length functional. Such a flow represents the evolution of a two--dimensional multiphase system where the energy is simply the sum of the lengths of the interfaces, in particular it is a possible model for the growth of grain boundaries. Moreover, the motion of these networks of curves is the simplest example of curvature flow for sets which are ``essentially'' non regular. As a first step, in this paper we study in detail the case of three curves in the plane concurring at a single triple junction and with the other ends fixed. We show some results about the existence, uniqueness and, in particular, the global regularity of the flow, following the line of analysis carried on in the last years for the evolution by mean curvature of smooth curves and hypersurfaces

Optimal design of solidification processes

An optimal design algorithm is presented for the analysis of general solidification processes, and is demonstrated for the growth of GaAs crystals in a Bridgman furnace. The system is optimal in the sense that the prespecified temperature distribution in the solidifying materials is obtained to maximize product quality. The optimization uses traditional numerical programming techniques which require the evaluation of cost and constraint functions and their sensitivities. The finite element method is incorporated to analyze the crystal solidification problem, evaluate the cost and constraint functions, and compute the sensitivities. These techniques are demonstrated in the crystal growth application by determining an optimal furnace wall temperature distribution to obtain the desired temperature profile in the crystal, and hence to maximize the crystal's quality. Several numerical optimization algorithms are studied to determine the proper convergence criteria, effective 1-D search strategies, appropriate forms of the cost and constraint functions, etc. In particular, we incorporate the conjugate gradient and quasi-Newton methods for unconstrained problems. The efficiency and effectiveness of each algorithm is presented in the example problem

Ottimizzazione del processo di definizione e rilascio in automatico dei cicli di montaggio di compressori centrifughi al Nuovo Pignone Spa

Il presente lavoro è stato svolto presso l'azienda Nuovo Pignone (FI) e tratta dell'attività di definizione dei tempi, delle attrezzature e la creazione dei documenti per ottimizzazione del processo di definizione e rilascio in automatico dei cicli di montaggio di compressori centrifughi

Preparation of atomic oxygen resistant polymeric materials

Polyphenyl quinoxalines (PPQs) are an important family of high performance polymers that offer good chemical and thermal stability coupled with excellent mechanical properties. These aromatic heterocyclic polymers are potentially useful as films, coatings, adhesives, and composite materials that demand stability in harsh environments. Our approach was to prepare PPQs with pendent siloxane groups using the appropriate chemistry and then evaluate these polymers before and after exposure to simulated atomic oxygen. Either monomer, the bis(o-diamine)s or the bis(alpha-diketone)s can be synthesized with a hydroxy group to which the siloxane chain will be attached. Several novel materials were prepared

Hardening and Coherent Precipitates Size Evolution with Aging Fe-12Al-12V Alloy

AbstractFe-Al based alloys have a remarkable potential for high temperature structural applications, provided that the limitation of their low creep resistance is solved. Third element addition (Nb, Ti, Zr or Ta) has proved to perform the task, at the expense of a low ductility. In previous works we have investigated ferritic alloys in the Fe-Al-V system with coherent precipitation of L21 phase (Fe2AlV) and have identified phases in equilibrium at the vertical section Fe1-2xAlxVx. We have found that a wide two-phase field is present in the composition range 0.10≤x≤0.15 (x: atomic fraction) till 720°C. In this work we study the feasibility of a structural application at high temperatures of the Fe-12Al-12V alloy. We look for ageing conditions leading to a stable coherent precipitation that could strengthen the ferritic matrix. In this way, we measured vickers hardness of coherent L21 precipitates at 600, 650 and 700°C. In all cases hardness has a typical behavior with hardness maximum located at longer times and higher intensities as temperature decreases. We measured size evolution with time through Transmission Electron Microscopy of precipitates at 700°C ageing temperature. As a further result, we could calculate from these measurements the activation energy for precipitate growth

Optimal Control of Industrial Assembly Lines

This paper discusses the problem of assembly line control and introduces an optimal control formulation that can be used to improve the performance of the assembly line, in terms of cycle time minimization, resources' utilization, etc. A deterministic formulation of the problem is introduced, based on mixed-integer linear programming. A simple numerical simulation provides a first proof of the proposed concept