Triangular Trimers on the Triangular Lattice: an Exact Solution

A model is presented consisting of triangular trimers on the triangular lattice. In analogy to the dimer problem, these particles cover the lattice completely without overlap. The model has a honeycomb structure of hexagonal cells separated by rigid domain walls. The transfer matrix can be diagonalised by a Bethe Ansatz with two types of particles. This leads two an exact expression for the entropy on a two-dimensional subset of the parameter space.Comment: 4 pages, REVTeX, 5 EPS figure

Bethe Ansatz solution of triangular trimers on the triangular lattice

Details are presented of a recently announced exact solution of a model consisting of triangular trimers covering the triangular lattice. The solution involves a coordinate Bethe Ansatz with two kinds of particles. It is similar to that of the square-triangle random tiling model, due to M. Widom and P. A. Kalugin. The connection of the trimer model with related solvable models is discussed.Comment: 33 pages, LaTeX2e, 13 EPS figures, PSFra

Cost objective PLM and CE

Concurrent engineering taking into account product life-cycle factors seems to be one of the industrial challenges of the next years. Cost estimation and management are two main strategic tasks that imply the possibility of managing costs at the earliest stages of product development. This is why it is indispensable to let people from economics and from industrial engineering collaborates in order to find the best solution for enterprise progress for economical factors mastering. The objective of this paper is to present who we try to adapt costing methods in a PLM and CE point of view to the new industrial context and configuration in order to give pertinent decision aid for product and process choices. A very important factor is related to cost management problems when developing new products. A case study is introduced that presents how product development actors have referenced elements to product life-cycle costs and impacts, how they have an idea bout economical indicators when taking decisions during the progression of the project of product development.

Topological model for machining of parts with complex shapes

Complex shapes are widely used to design products in several industries such as aeronautics, automotive and domestic appliances. Several variations of their curvatures and orientations generate difficulties during their manufacturing or the machining of dies used in moulding, injection and forging. Analysis of several parts highlights two levels of difficulties between three types of shapes: prismatic parts with simple geometrical shapes, aeronautic structure parts composed of several shallow pockets and forging dies composed of several deep cavities which often contain protrusions. This paper mainly concerns High Speed Machining (HSM) of these dies which represent the highest complexity level because of the shapes' geometry and their topology. Five axes HSM is generally required for such complex shaped parts but 3 axes machining can be sufficient for dies. Evolutions in HSM CAM software and machine tools lead to an important increase in time for machining preparation. Analysis stages of the CAD model particularly induce this time increase which is required for a wise choice of cutting tools and machining strategies. Assistance modules for prismatic parts machining features identification in CAD models are widely implemented in CAM software. In spite of the last CAM evolutions, these kinds of CAM modules are undeveloped for aeronautical structure parts and forging dies. Development of new CAM modules for the extraction of relevant machining areas as well as the definition of the topological relations between these areas must make it possible for the machining assistant to reduce the machining preparation time. In this paper, a model developed for the description of complex shape parts topology is presented. It is based on machining areas extracted for the construction of geometrical features starting from CAD models of the parts. As topology is described in order to assist machining assistant during machining process generation, the difficulties associated with tasks he carried out are analyzed at first. The topological model presented after is based on the basic geometrical features extracted. Topological relations which represent the framework of the model are defined between the basic geometrical features which are gathered afterwards in macro-features. Approach used for the identification of these macro-features is also presented in this paper. Detailed application on the construction of the topological model of forging dies is presented in the last part of the paper

Framework for Product Lifecycle Management integration in Small and Medium Enterprises networks

In order to improve the performance of extended enterprises, Small and Medium Enterprises (SMEs) must be integrated into the extended networks. This integration must be carried out on several levels which are mastered by the Product Lifecycle Management (PLM). But, PLM is underdeveloped in SMEs mainly because of the difficulties in implementing information systems. This paper aims to propose a modeling framework to facilitate the implementation of PLM systems in SMEs. Our approach proposes a generic model for the creation of processes and data models. These models are explained, based on the scope and framework of the modeling, in order to highlight the improvements provided

Flag varieties and the Yang-Baxter equation

We investigate certain bases of Hecke algebras defined by means of the Yang-Baxter equation, which we call Yang-Baxter bases. These bases are essentially self-adjoint with respect to a canonical bilinear form. In the case of the degenerate Hecke algebra, we identify the coefficients in the expansion of the Yang-Baxter basis on the usual basis of the algebra with specializations of double Schubert polynomials. We also describe the expansions associated to other specializations of the generic Hecke algebra.Comment: 14 pages, latex. To appear in Lett. Math. Phy

Exponential transform of quadratic functional and multiplicative ergodicity of a Gauss-Markov process

The Laplace transform of partial sums of the square of a non-centered Gauss-Markov process, conditioning on its starting point, is explicitly computed. The parameters of multiplicative ergodicity are deduced