Michel Lenczner

A Symbolic Transformation Language and its Application to a Multiscale Method

The context of this work is the design of a software, called MEMSALab, dedicated to the automatic derivation of multiscale models of arrays of micro- and nanosystems. In this domain a model is a partial differential equation. Multiscale methods approximate it by another partial differential equation which can be numerically simulated in a reasonable time. The challenge consists in taking into account a wide range of geometries combining thin and periodic structures with the possibility of multiple nested scales. In this paper we present a transformation language that will make the development of MEMSALab more feasible. It is proposed as a Maple package for rule-based programming, rewriting strategies and their combination with standard Maple code. We illustrate the practical interest of this language by using it to encode two examples of multiscale derivations, namely the two-scale limit of the derivative operator and the two-scale model of the stationary heat equation.

Homogenization of linear spatially periodic electronic circuits

In this paper we establish a simplified model of ngeneral spatially periodic linear electronic analog networks. It has a ntwo-scale structure. At the macro level it is an algebro-differential nequation and a circuit equation at the micro level. Its construction is nbased on the concept of two-scale convergence, introduced by the author in nthe framework of partial differential equations, adapted to vectors and nmatrices. Simple illustrative examples are detailed by hand calculation and na numerical simulation is reported.

Fuzzy holons for intelligent multi-scale design in cloud-based design for configurations

Cloud-based design for configurations can be referred to as a service-oriented networked design for configurations model. However, cloud-based models also pose challenges such as reliability, availability, capability, ability, adaptability of resources, and services across spatial boundaries. Multi-scale design can presumably stimulate greater intelligence in cloud-based models. Using the concepts of the fuzzy holon and the fuzzy attractor, this paper proposes the fuzzy holonic approach to address multi-scale design for configurations. A fuzzy design holon is defined through two basic holons: fuzzy function holon and fuzzy solution holon. A fuzzy attractor is defined as a fuzzy function holon or fuzzy function solution toward which a design tends to evolve. The proposed fuzzy holon model is driven by two conflicting drives: (a) completeness of fuzzy function holons and fuzzy solution holons, and (b) discrimination of fuzzy function holons and fuzzy solution holons. Through simulations, four possible states of behavior of fuzzy holon design are found: (a) the impossibility state characterized by the impossibility of fuzzy holon creation; (b) the creation and destruction state sometimes characterized by the creation of fuzzy holons and sometimes the destruction of fuzzy holons, (c) the development state characterized by a natural creation and development of fuzzy holons and (d) the failure state characterized by the interruption of the development of the fuzzy design holon and the destruction of already created fuzzy design holon. The model explains that design is not an orderly and well behaved phenomenon. It shows that fuzzy holon design is a discontinuous phenomenon.

Diffusive realizations for solutions of some operator equations: The one-dimensional case

In this paper we deal with the derivation of state-realizations of linear operators that are solutions to certain operator linear differential equations in one-dimensional bounded domains. We develop two approaches in the framework of diffusive representations: one with complex diffusive symbols; the other with real diffusive symbols. Then, we illustrate the theories and develop numerical methods for a Lyapunov equation arising from optimal control theory of the heat equation. A practical purpose of this approach is real-time computation on a semi-decentralized architecture with low granularity.

Influence of Functional Knowledge Structuring for Modular Design

This paper focuses on analyzing design methods on product modularity. Through an experimental case, the paper shows that design knowledge is of vital importance to conduct modular design. Modular design is consequence of combining different types of uncertain structured functional knowledge. The paper shows that it is not only the functional knowledge structure that drives the modular design, but also the ability of the designer to gain new functional knowledge, and dynamically, what designer does with that functional knowledge.

An Improved Algorithm Based on SURF for MR Infant Brain Image Registration

The correct diagnosis of brain diseases is crucial for children with brain disorders. But the complex characteristics of infant brain make the image analysis very complicated. Thus, an accurate image registration is a prerequisite for accurate analysis of MR infant brain images, and it provides valuable information for the diagnosis of doctors. This paper presents our research works on SURF registration algorithm of 2-D MR infant brain images. We firstly describe the original algorithm and analyze its advantages and drawbacks. Then an improved version is proposed, which uses 8-D descriptor vectors with the length of 128. The experiment results show, compared with the original version, our algorithm can achieve more accurate image registration with a little more time consumption. For all the images tested, the increase of correct matching rate varies from a minimum of 5.7 % to a maximum of 14.9 % compared with the classical one.

Fuzzy Functional Modelling in CAD Systems

Product modelling is essential during the conceptual design both in the functional and the structural design spaces. However, there is no adapted formal representation to support the functional modelling of products in CAD systems. Decompositions and grammars can be considered as formal powerful tools to describe products. Grammars can operate on sets of functions as well as on sets of shapes. Grammars operating on the set of the function are called Fuzzy Function Grammars; otherwise those operating on the set of shapes are called Fuzzy Shapes Grammars. The two grammars work simultaneously to model product. The evolution of the product model, from the functional structure to the physical structure, is done using axiomatic design. Using grammars and axiomatic design approach constitutes an effective tool for functional modelling of products in CAD system. The proposed design approach is validated by the application to a design case of industrial products. The results of the application validate the interest of proposed approach.