Dynamiques territoriales et système de la mobilité : un modèle bayésien pour la Côte d'Azur

22 pagesLe système de la mobilité joue un rôle fondamental dans les dynamiques urbaines et territoriales. Dans le cas des espaces métropolitains méditerranéens, les impacts de ces dynamiques sont d'autant plus problématiques qu'ils ont lieu dans des milieux déjà fragilisés où l'espace est devenu une ressource rare. L'espace métropolitain azuréen est un très bon exemple de ces dynamiques et de ces contraintes : dans le cadre d'une forte croissance démographique et urbaine, la périurbanisation et la dépendance automobile se présentent aujourd'hui comme des enjeux importants dans un espace aux limites de la saturation. Dans cette contribution, la relation ville-transports-environnement sur la Côte d'Azur est analysée à l'aide de la technique des réseaux bayésiens. Après une brève introduction à la théorie des réseaux bayésiens, sera produit un modèle de fonctionnement de la relation ville-transports-environnement sur la Côte d'Azur, sous la forme d'un réseau bayésien constitué par 31 indicateurs territoriaux. Puis, le modèle trouvé est utilisé pour la mise en évidence de dynamiques territoriales bien déterminées, caractérisant les différents sous-espaces de la conurbation azuréenne et constituant des enjeux pour la durabilité de son développement

Dynamiques territoriales et système de la mobilité : un modèle bayésien pour la Côte d'Azur

22 pagesLe système de la mobilité joue un rôle fondamental dans les dynamiques urbaines et territoriales. Dans le cas des espaces métropolitains méditerranéens, les impacts de ces dynamiques sont d'autant plus problématiques qu'ils ont lieu dans des milieux déjà fragilisés où l'espace est devenu une ressource rare. L'espace métropolitain azuréen est un très bon exemple de ces dynamiques et de ces contraintes : dans le cadre d'une forte croissance démographique et urbaine, la périurbanisation et la dépendance automobile se présentent aujourd'hui comme des enjeux importants dans un espace aux limites de la saturation. Dans cette contribution, la relation ville-transports-environnement sur la Côte d'Azur est analysée à l'aide de la technique des réseaux bayésiens. Après une brève introduction à la théorie des réseaux bayésiens, sera produit un modèle de fonctionnement de la relation ville-transports-environnement sur la Côte d'Azur, sous la forme d'un réseau bayésien constitué par 31 indicateurs territoriaux. Puis, le modèle trouvé est utilisé pour la mise en évidence de dynamiques territoriales bien déterminées, caractérisant les différents sous-espaces de la conurbation azuréenne et constituant des enjeux pour la durabilité de son développement

Existence of periodic orbits near heteroclinic connections

We consider a potential $W:R^m\rightarrow R$ with two different global minima $a_-, a_+$ and, under a symmetry assumption, we use a variational approach to show that the Hamiltonian system \begin{equation} \ddot{u}=W_u(u), \hskip 2cm (1) \end{equation} has a family of $T$-periodic solutions $u^T$ which, along a sequence $T_j\rightarrow+\infty$, converges locally to a heteroclinic solution that connects $a_-$ to $a_+$. We then focus on the elliptic system \begin{equation} \Delta u=W_u(u),\;\; u:R^2\rightarrow R^m, \hskip 2cm (2) \end{equation} that we interpret as an infinite dimensional analogous of (1), where $x$ plays the role of time and $W$ is replaced by the action functional $$J_R(u)=\int_R\Bigl(\frac{1}{2}\vert u_y\vert^2+W(u)\Bigr)dy.$$ We assume that $J_R$ has two different global minimizers $\bar{u}_-, \bar{u}_+:R\rightarrow R^m$ in the set of maps that connect $a_-$ to $a_+$. We work in a symmetric context and prove, via a minimization procedure, that (2) has a family of solutions $u^L:R^2\rightarrow R^m$, which is $L$-periodic in $x$, converges to $a_\pm$ as $y\rightarrow\pm\infty$ and, along a sequence $L_j\rightarrow+\infty$, converges locally to a heteroclinic solution that connects $\bar{u}_-$ to $\bar{u}_+$.Comment: 36 pages, 4 figure

Motion of three-dimensional elastic films by anisotropic surface diffusion with curvature regularization

Short time existence for a surface diffusion evolution equation with curvature regularization is proved in the context of epitaxially strained three-dimensional films. This is achieved by implementing a minimizing movement scheme, which is hinged on the $H^{-1}$-gradient flow structure underpinning the evolution law. Long-time behavior and Liapunov stability in the case of initial data close to a flat configuration are also addressed.Comment: 44 page

Nondegenerate abnormality, controllability, and gap phenomena in optimal control with state constraints

In optimal control theory, infimum gap means that there is a gap between the infimum values of a given minimum problem and an extended problem, obtained by enlarging the set of original solutions and controls. The gap phenomenon is somewhat "dual" to the problem of the controllability of the original control system to an extended solution. In this paper we present sufficient conditions for the absence of an infimum gap and for controllability for a wide class of optimal control problems subject to endpoint and state constraints. These conditions are based on a nondegenerate version of the nonsmooth constrained maximum principle, expressed in terms of subdifferentials. In particular, under some new constraint qualification conditions, we prove that: (i) if an extended minimizer is a nondegenerate normal extremal, then no gap shows up; (ii) given an extended solution verifying the constraints, either it is a nondegenerate abnormal extremal, or the original system is controllable to it. An application to the impulsive extension of a free end-time, non-convex optimization problem with control-polynomial dynamics illustrates the results

Impulsive optimal control problems with time delays in the drift term

We introduce a notion of bounded variation solution for a new class of nonlinear control systems with ordinary and impulsive controls, in which the drift function depends not only on the state, but also on its past history, through a finite number of time delays. After proving the well posedness of such solutions and the continuity of the corresponding input output map with respect to suitable topologies, we establish necessary optimality conditions for an associated optimal control problem. The approach, which involves approximating the problem by a non impulsive optimal control problem with time delays and using Ekeland principle combined with a recent, nonsmooth version of the Maximum Principle for conventional delayed systems, allows us to deal with mild regularity assumptions and a general endpoint constraint

No Infimum Gap and Normality in Optimal Impulsive Control Under State Constraints

In this paper we consider an impulsive extension of an optimal control problem with unbounded controls, subject to endpoint and state constraints. We show that the existence of an extended-sense minimizer that is a normal extremal for a constrained Maximum Principle ensures that there is no gap between the infima of the original problem and of its extension. Furthermore, we translate such relation into verifiable sufficient conditions for normality in the form of constraint and endpoint qualifications. Links between existence of an infimum gap and normality in impulsive control have previously been explored for problems without state constraints. This paper establishes such links in the presence of state constraints and of an additional ordinary control, for locally Lipschitz continuous data

The Nine Forms of the French Riviera: Classifying Urban Fabrics from the Pedestrian Perspective

[EN] Recent metropolitan growth produces new kinds of urban fabric, revealing different logics in the organization of urban space, but coexisting with more traditional urban fabrics in central cities and older suburbs. Having an overall view of the spatial patterns of urban fabrics in a vast metropolitan area is paramount for understanding the emerging spatial organization of the contemporary metropolis. The French Riviera is a polycentric metropolitan area of more than 1200 km2 structured around the old coastal cities of Nice, Cannes, Antibes and Monaco. XIX century and early XX century urban growth is now complemented by modern developments and more recent suburban areas. A large-scale analysis of urban fabrics can only be carried out through a new geoprocessing protocol, combining indicators of spatial relations within urban fabrics, geo-statistical analysis and Bayesian data-mining. Applied to the French Riviera, nine families of urban fabrics are identified and correlated to the historical periods of their production. Central cities are thus characterized by the combination of different families of pre-modern, dense, continuous built-up fabrics, as well as by modern discontinuous forms. More interestingly, fringe-belts in Nice and Cannes, as well as the techno-park of Sophia-Antipolis, combine a spinal cord of connective artificial fabrics having sparse specialized buildings, with the already mentioned discontinuous fabrics of modern urbanism. Further forms are identified in the suburban and “rurban” spaces around central cities. The proposed geoprocessing procedure is not intended to supersede traditional expert-base analysis of urban fabric. Rather, it should be considered as a complementary tool for large urban space analysis and as an input for studying urban form relation to socioeconomic phenomena.This research was carried out thanks to a research grant of the Nice-Côte d’Azur Chamber of Commerce and Industry (CIFRE agreement with UMR ESPACE).Fusco, G.; Araldi, A. (2018). The Nine Forms of the French Riviera: Classifying Urban Fabrics from the Pedestrian Perspective. En 24th ISUF International Conference. Book of Papers. Editorial Universitat Politècnica de València. 1313-1325. https://doi.org/10.4995/ISUF2017.2017.52191313132

Platonic polyhedra, periodic orbits and chaotic motions in the N-body problem with non-Newtonian forces

We consider the $N$-body problem with interaction potential $U_alpha=rac{1}{ert x_i-x_jert^alpha}$ for alpha>1. We assume that the particles have all the same mass and that $N$ is the order $ertmathcal{R}ert$ of the rotation group $mathcal{R}$ of one of the five Platonic polyhedra. We study motions that, up to a relabeling of the $N$ particles, are invariant under $mathcal{R}$. By variational techniques we prove the existence of periodic and chaotic motions