Fractal Fract

This article deals with the Random Sequential Adsorption (RSA) of 2D disks of same size on fractal surfaces with Hausdorff dimension $$1<d<2$$1<d<2. According to literature and confirmed by numerical simulations in the paper, the high coverage regime exhibits fractional dynamics, i.e. dynamics in $$t^{-1/d}$$t-1/dwhere d is the fractal dimension of the surface. As main contribution, this paper proposes to capture this behavior with a particular class of nonlinear model: a driftless control affine model

Immunophenotyping Reveals the Diversity of Human Dental Pulp Mesenchymal Stromal Cells In vivo and Their Evolution upon In vitro Amplification

International audienceMesenchymal stromal/stem cells (MSCs) from human dental pulp (DP) can be expanded in vitro for cell-based and regenerative dentistry therapeutic purposes. However, their heterogeneity may be a hurdle to the achievement of reproducible and predictable therapeutic outcomes. To get a better knowledge about this heterogeneity, we designed a flow cytometric strategy to analyze the phenotype of DP cells in vivo and upon in vitro expansion with stem cell markers. We focused on the CD31 − cell population to exclude endothelial and leukocytic cells. Results showed that the in vivo CD31 − DP cell population contained 1.4% of CD56 + , 1.5% of CD146 + , 2.4% of CD271 + and 6.3% of MSCA-1 + cells but very few Stro-1 + cells (≤1%). CD56 + , CD146 + , CD271 + , and MSCA-1 + cell subpopulations expressed various levels of these markers. CD146 + MSCA-1 + , CD271 + MSCA-1 + , and CD146 + CD271 + cells were the most abundant DP-MSC populations. Analysis of DP-MSCs expanded in vitro with a medicinal manufacturing approach showed that CD146 was expressed by about 50% of CD56 + , CD271 + , MSCA-1 + , and Stro-1 + cells, and MSCA-1 by 15-30% of CD56 + , CD146 + , CD271 + , and Stro-1 + cells. These ratios remained stable with passages. CD271 and Stro-1 were expressed by <1% of the expanded cell populations. Interestingly, the percentage of CD56 + cells strongly increased from P1 (25%) to P4 (80%) both in all sub-populations studied. CD146 + CD56 + , MSCA-1 + CD56 + , and CD146 + MSCA-1 + cells were the most abundant DP-MSCs at the end of P4. These results established that DP-MSCs constitute a heterogeneous mixture of cells in pulp tissue in vivo and in culture, and that their phenotype is modified upon in vitro expansion. Further studies are needed to determine whether co-expression of specific MSC markers confers DP cells specific properties that could be used for the regeneration of human tissues, including the dental pulp, with standardized cell-based medicinal products

Méthodes d'analyse et de synthèse robustes pour les systèmes linéaires périodiques

This thesis addresses robustness problems for a linear periodic systems. These correspond to a special case of linear time-varying systems with periodic dynamics. Such periodic processes arise in numerous domains such as aeronautics, celestial mechanics or communication systems. Systematic procedures for robust analysis and synthesis are proposed. The adopted framework is based on the Lyapunov theory and uses the linear matrix inequalities (LMI) formalism. Uncertainties are supposed to affect not only the system but the controller itself. This last problem is treated by the synthesis of convex sets of controllers ensuring a given level of performances for the closed-loop system. The question of the time structure of the controller is formulated. Does the controller need to be of the same periodicity as the system? Is it possible to reduce the number of parameters to be stored inside the controller? The class of time-structured controller is defined and dedicated synthesis methods are developed. Theoretical results are illustrated on the problem of the stationkeeping for a spacecraft on a low earth orbit subject to different disturbance accelerations (atmospheric drag, effect of the non spheric mass repartition of the Earth). Different feedback control laws are computed with performance requirements such as minimizing the amount of maneuvering propellant or the effect of additional unknown disturbance accelerations. Their efficiency is evaluated by the mean of non linear simulations.Cette thèse porte sur la commande robuste des systèmes linéaires périodiques qui constituent une classe particulière de systèmes variant dans le temps. Des dynamiques périodiques apparaissent dans de nombreux domaines des sciences de l'ingénieur tels que l'aéronautique, l'espace ou les systèmes de télécommunication. Des méthodes systématiques pour l'analyse et la synthèse robuste de ces systèmes sont proposées. Le cadre de travail choisi est celui de la théorie de Lyapunov et fait appel principalement à des outils numériques de type inégalités matricielles linéaires (LMI). La robustesse est envisagée de manière duale par la prise en compte d'incertitudes pouvant non seulement affecter le système à commander mais également le correcteur lui même. Ce dernier problème est traité par la synthèse d'ensembles convexes de correcteurs assurant un certain niveau de performances garanties vis-à-vis du système bouclé. La question de la structure temporelle du correcteur est également posée. Le correcteur doit il nécessairement être de même périodicité que le système? Est-il possible de réduire le nombre de paramètres à mémoriser? Pour répondre à ces différentes questions, nous avons défini la classe des correcteurs périodiques structurés dans le temps et développé des méthodes de synthèse adaptées. Les résultats théoriques sont illustrés sur le problème du maintien à poste autonome d'un satellite en orbite basse consistant à maintenir un satellite sur une orbite de référence excentrique malgré les différentes forces perturbatrices pouvant l'en écarter (frottement atmosphérique, effet de la distribution non-sphérique de la masse de la Terre). Différentes lois de commande minimisant certains critères de performances tels que la quantité de carburant consommée ou l'influence d'accélérations perturbatrices sont calculées. Leur qualité est ensuite évaluée à l'aide de simulations non-linéaires

Time-Domain Fractional Behaviour Modelling with Rational Non-Singular Kernels

This paper proposes a solution to model fractional behaviours with a convolution model involving non-singular kernels and without using fractional calculus. The non-singular kernels considered are rational functions of time. The interest of this class of kernel is demonstrated with a pure power law function that can be approximated in the time domain by a rational function whose pole and zeros are interlaced and linked by geometric laws. The Laplace transform and frequency response of this class of kernel is given and compared with an approximation found in the literature. The comparison reveals less phase oscillation with the solution proposed by the authors. A parameter estimation method is finally proposed to obtain the rational kernel model for general fractional behaviour. An application performed with this estimation method demonstrates the interest in non-singular rational kernels to model fractional behaviours. Another interest is the physical interpretation fractional behaviours that can be implemented with delay distributions

Initial Value Problem Should Not Be Associated to a Fractional Model Description Whatever the Derivative Definition Used

The paper shows that the Caputo definition of fractional differentiation is problematic if it is used in the definition of a fractional model and if initial conditions are taken into account. The demonstration is done using simple examples (or counterexamples). The analysis is extended to the Riemann-Liouville and Grünwald-Letnikov definitions. These results thus question the validity of results produced in the field of fractional model analysis in which initial conditions are involved