## About

116

Publications

7,045

Reads

**How we measure 'reads'**

A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more

587

Citations

Introduction

I am a Professor of Mechanical Engineering at the Technical University of Belfort-Monbéliard, and a researcher in the Micro-Acoustics Team at the FEMTO-ST Laboratory. My research focuses on multi-scale modelling and control of distributed mechatronic systems with applications to micro and nano-system arrays. My previous position was as an associate professor in applied mathematics at the University of Franche-Comté.

Additional affiliations

September 2002 - present

September 1992 - September 2002

September 1992 - August 2002

## Publications

Publications (116)

Motivated by an ongoing project on computer aided derivation of asymptotic models governed by partial differential equations, we introduce a class of term transformations that consists of traversal strategies and insertion of contexts. We define unification and combination operations on this class which amount to merging transformations in order to...

In the domain of model-based design, the main challenge is to provide a model with a set of conditions and algorithms to ensure that the designed system produces correct results. A dataflow based model called Actors with Stretchable Access Patterns (ASAP) has been recently proposed, which takes the behavior of functional blocks on real architecture...

A periodic homogenization model of the electrostatic equation is constructed for a comb drive with a large number of fingers and whose mode of operation is in-plane and longitudinal. The model is obtained in the case where the distance between the rotor and the stator is of an order $\varepsilon ^{\alpha }$, $\alpha \geq 2$, where $\varepsilon$ den...

In this article, we propose a new framework based on dataflow graphs to abstract and analyze designs for hardware architectures. It is called Actors with Stretchable Access Patterns (ASAP). It can overcome some limitations of all Static Data Flow (SDF) based models like mandatory buffering between actors. This article details the fundamental contri...

Motivated by an ongoing project on the computer aided derivation of multiscale partial differential equation models, we introduce a class of term transformations that consists in navigation strategies and insertion of contexts. We define a unification and combination operations on this class which enjoy nice algebraic properties like associativity,...

MEMSALab is a software in development that will allow the generation of multiscale multi-physics model families based on their derivation. Here, we present a mini-language to express such models in a way that is both relatively simple and generates the tree structures necessary for derivations. For validation, it is used for the direct construction...

Micro-mirror arrays play an important role in our life. They are widely used in many fields such as optical devices, tunable lasers, hard disk storage, projectors and so on. Here we utilize the unfolding method to analyze the asymptotic behavior of a two-dimensional periodic micromirror array with two zones of different actuation. The mirrors are e...

A methodology for the simulation of large two-dimensional micro-mirror arrays (MMA) whose behavior is governed by the static electro-mechanical system is presented. The considered array is actuated by two different voltages in two subdomains. The proposed solution makes it possible to perform simulations of an arbitrarily large size array without r...

For computer-aided hardware design, models are usually used to evaluate the designed systems. But there is still a gap between models and their efficient implementations on a real architecture, like FPGAs. For example, some model characteristics may lead to a waste of resources, which can even make a design infeasible. In this paper, we focus on ho...

This study is based on the properties of Depth Image Based Rendering (DIBR), especially on the characteristics of holes caused by disocclusion. In order to recover the texture and the structure in missing areas and to improve the quality of rendered image, some research has been done on the hole-filling process for the virtual view image, starting...

Modeling the electric field in a matrix of micro-mirrors is presented as the first application of the MEMSALab software package. The latter is dedicated to semi-automated derivation of multiscale models by asymptotic methods and will complement simulation software as finite element software. It is designed according to a principle of reusability wh...

This paper reports recent progress in modeling and simulation of a one-dimensional Micro-Mirror Array actuated by an electrostatic force. We present results obtained through numerical simulations of a single cell: the analysis and the optimization of the pull-in voltage and the analysis of the bounces of the mirror in contact with the base when it...

We present two aspects of modeling and design of a Scanning Thermal Microscopy (SThM) probe built by microfabrication techniques. An optimized design based on a full parametrization of its geometry is calculated using a multi-criteria optimization technique after a drastic selection of the most sensitive geometrical parameters. The optimization is...

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. Thi...

In view of qualitative temperature measurement by scanning thermal microscopy, we introduce a model-based control law for a new microfabricated probe. The underlying model is the time-space two-scale electro-thermal model presented in [15], since it has the power to represent transcients of harmonic modulations. The control method accounts for an e...

This work is motivated by the challenging problem of the computer-aided generation of approximations (viewed as a series of transformations) of partial derivative equations. In this framework, the approximations posed over complex settings are incrementally constructed by extending an approximation posed on a simple setting and combining these exte...

This paper reports recent advances in the development of a symbolic asymptotic modeling software package, called MEMSALab, which will be used for automatic generation of asymptotic models for arrays of micro and nanosystems. More precisely, a model is a partial differential equation and an asymptotic method approximate it by another partial differe...

In Yakoubi [11] and Lenczner et al. [5] the authors developed a theoretical framework of diffusive realization for state-realizations of some linear operators. Those are solutions to certain linear operator differential equations posed in one-dimensional bounded domains. They illustrate the theory on a Lyapunov equation arising from the optimal con...

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 inte...

This article introduces the Ω counter, a frequency counter — or a frequency-to-digital converter, in a different jargon — based on the Linear Regression (LR) algorithm on time stamps. We discuss the noise of the electronics. We derive the statistical properties of the Ω counter on rigorous mathematical basis, including the weighted measure and the...

This article introduces the Parabolic Variance (PVAR), a wavelet variance similar to the Allan variance, based on the Linear Regression (LR) of phase data. The companion article arXiv:1506.05009 [physics.ins-det] details the frequency counter, which implements the LR estimate.
The PVAR combines the advantages of AVAR and MVAR. PVAR is good for lon...

This paper reports recent advances in the development of a symbolic asymptotic modeling software package MEMSALab which will be used for automatic generation of asymptotic models for arrays of micro and nanosystems. First, an asymptotic model for the stationary heat equation in a Micro-Mirror Array developed for astrophysics is presented together w...

We present a multi-scale model of a probe for scanning thermal microscopy. The probe is built by microfabrication techniques. In active mode, it is supplied by a source of harmonic and/or continuous current and the tip temperature is measured after a lock-in amplifier. The model distinguishes two time scales and two space scales. Simulation results...

This work is motivated by the wish to have the most precise measurement of a frequency ν and of the variance σ² of its fractional fluctuations in a given time τ, out of high-end general-purpose instruments. Thanks to the progress of digital electronics, new time-interval analyzers have been made available in the last few years. Such instruments mea...

This paper is the second part of a work devoted to the modelling of thin elastic plates with small, periodically distributed piezoelectric inclusions. We consider the equations of linear elasticity coupled with the electrostatic equation, with various kinds of electric boundary conditions. We derive the corresponding effective models when the thick...

We present a method for two-scale model derivation of the periodic homogenization of the one-dimensional wave equation in a bounded domain. It allows for analyzing the oscillations occurring on both microscopic and macroscopic scales. The novelty reported here is on the asymptotic behavior of high frequency waves and especially on the boundary cond...

Sustainable development should offer a holistic way of resolution of many sharp objective conflicting goals in design. In this context, the question about the stability of models can be raised. The design can be seen as a qualitative discontinuity phenomenon in a continuous background. Understanding and controlling the discontinuity is therefore an...

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 reasonabl...

This paper presents modelling, simulation and optimization results for a novel SThm probe. The model takes into account thermo-electro-mechanical equations. Moreover, a tip-surface contact model derived by taking into account microscopic multi-asperity contact is proposed and discussed. Results of multi-objective optimization are reported, and fina...

This paper discusses a new approximation method for operators that are solution to an operational Riccati
equation. The latter is derived from the theory of optimal control of linear problems posed in Hilbert spaces.
The approximation is based on the functional calculus of self-adjoint operators and the Cauchy formula.
Under a number of assumptions...

Vibrating mechanical structure characterization is demonstrated using contactless techniques best suited for mobile and rotating equipments. Fast measurement rates are achieved using Field Programmable Gate Array (FPGA) devices as real-time digital signal processors. Two kinds of algorithms are implemented on FPGA and experimentally validated in th...

We present a method for two-scale model derivation of the periodic
homogenization of the one-dimensional wave equation in a bounded domain. It
allows for analyzing the oscillations occurring on both microscopic and
macroscopic scales. The novelty reported here is on the asymptotic behavior of
high frequency waves and especially on the boundary cond...

This paper is the second part of a work devoted to the modelling of thin
elastic plates with small, periodically distributed piezoelectric inclusions.
We consider the equations of linear elasticity coupled with the electrostatic
equation, with various kinds of electric boundary conditions. We derive the
corresponding effective models when the thick...

The asymptotic behavior of a one-dimensional spectral problem with periodic
coefficient is addressed for high frequency modes by a method of Bloch wave
homogenization. The analysis leads to a spectral problem including both
microscopic and macroscopic eigenmodes. Numerical simulation results are
provided to corroborate the theory.

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 s...

Atomic force microscopes (AFM) provide high resolution images of surfaces. In this paper, we focus on an interferometry method for estimation of deflections in arrays of cantilever in quasi-static regime. We propose a novel complete solution with a least square based algorithm to determine interference fringe phases and its optimized FPGA implement...

In this paper, our attention is focused on a two-scale model based algorithm for deflection estimation of array of Atomic force microscopes (AFM) in quasi-static regime by interferometry. In a previous work, an algorithm based on three measurements by cantilever was introduced to compute their displacements in quasi-static regime. Here, we propose...

We introduce a framework for computer-aided derivation of multi-scale models dedicated to arrays of microsystems. It relies on a combination of a asymptotic methods used in the field of partial differential equations with term rewriting techniques coming from computer science. In our approach, a multi-scale model derivation is characterized by the...

We introduce a framework for computer-aided derivation of multi-scale models.
It relies on a combination of an asymptotic method used in the field of partial
differential equations with term rewriting techniques coming from computer
science.
In our approach, a multi-scale model derivation is characterized by the
features taken into account in the a...

This paper proposes a holonic approach to address multi-scale sustainable design for configuration of cities. It is believed that multi-scale design can presumably stimulate greater environmental awareness. Assuming the city is a living organism, this paper defines the city as a cell based holon. It means designing "city cells within a city cell"....

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 knowle...

In this paper, our attention is focused on a two-scale model based algorithm for deflection estimation of array of Atomic force microscopes (AFM) in quasi-static regime by interferometry. In a previous work, an algorithm based on three measurements by cantilever was introduced to compute their displacements in quasi-static regime. Here, we propose...

We present a simplified model of the mechanical behavior of large arrays of cantilevers in the dynamic operating regime. The supporting base is assumed to be elastic thus cross-talk effect between the cantilevers is taken into account. Beforehand, the model has been mathematically justified starting from a thin plate model, using the two-scale appr...

This paper describes the design, prototyping and control of a 2D modular and self-reconfigurable robot for conveying microparts. The elementary block is designed to have a package dimension under 1cm$^3$ and will include the actuators, the electronics and the micro-controller. Electro-permanent (EP) magnets are used for both the linkage and the tra...

Multiphysics models of large arrays of micro- and nanosystems are too complex to be efficiently simulated by existing simulation software. Fortunately, asymptotic methods such as those based on two-scale convergence are applicable to homogenization of thin or periodic (i.e. array) structures. They generate simpler models tractable to simulation, bu...

Atomic force microscopes (AFM) provide high resolution images of surfaces. In this paper, we focus our attention on an inter ferometry method for deflection estimation of cantilever arrays in quasi-static regime. In its original form, spline interpolation was used to determine interference fringe phase, and thus the deflections. Computations were p...

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 illu...

We apply the method of semi-decentralized approximation, introduced in Lenczner and Yakoubi [2009] and Yakoubi [2010], to the linear quadratic regulation of a one-dimensional array of cantilevers with regularly spaced actuators and sensors. It is based on two mathematical concepts, namely on functions of operators, and on the Cauchy integral formul...

In this paper, we present new tools and results developed for Arrays of Microsystems and especially for Atomic Force Microscope (AFM) array design. For modeling, we developed a two-scale model of cantilever arrays in elastodynamics. A robust optimization toolbox is interfaced to aid for design before the microfabrication process. A model based algo...

We are currently developing software dedicated to multiscale and multiphysics modeling of arrays of micro and nanosystems. Unlike traditional software that is based on models built once and for all, here this is the software that constructs models. It is based on the mathematical Two-Scale Transform, a technique for asymptotic methods, together wit...

This work is motivated by a challenging problem of computer-aided 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. The challenge is to formalize these
approximating methods within a computer alge...

We present a model for two-dimensional arrays of micro-cantilevers in elasto-dynamical regime. It has been derived by a two-scale approximation method related to strongly heterogeneous system. We also report validation results regarding its modal structure compared with the one of a direct Finite Element Model (FEM).

We present a model for two-dimensional arrays of micro-cantilevers in elasto-dynamical regime. It has been derived by a two-scale approximation method related to strongly heterogeneous system. We also report validation results regarding its modal structure compared with the one of a direct Finite Element Model (FEM).

In this paper, we present a two-scale model including an optimal active control for a one-dimensional cantilever array with regularly spaced actuators and sensors. With the purpose of imple-menting the control in real time, we propose an approximation that may be realized by an analog dis-tributed electronic circuit. More precisely, our analog proc...

We focus on the question of real-time computation for optimal distributed filtering or control applicable to MEMS Arrays. We present an algorithm for the realization of a linear operator solution to a functional equation through its application to a Lyapunov operatorial equation associated to the heat equation in one dimension. It is based on the d...

In this paper, we present a two-scale model including an optimal active control for a one-dimensional cantilever array with regularly spaced actuators and sensors. With the purpose of implementing the control in real time, we propose an approximation that may be realized by an analog distributed electronic circuit. More precisely, our analog proces...

We present a new mathematical object designed to analyze the oscillations occurring on both microscopic and macroscopic scales in a wave equation with oscillating coefficients and data. Through a Bloch wave homogenization method, our study addresses typical problems of two-scale convergence in the interior of the domain, and sheds some light on the...

Introduction Modeling and identification of a cantilever array Semi-decentralized approximation of optimal control applied to a cantilever array Simulation of large-scale periodic circuits by a homogenization method Bibliography Appendix