A Game Theory Approach for the Groundwater Pollution Control

A differential game modeling the noncooperative outcome of pollution in groundwater is studied. Spatio-temporal objectives are constrained by a convection-diffusion-reaction equation ruling the spread of the pollution in the aquifer, and the velocity of the flow solves an elliptic partial differential equation. The existence of a Nash equilibrium is proved using a fixed point strategy. A uniqueness result for the Nash equilibrium is also proved under some additional assumptions. Some numerical illustrations are provided

Local Social Interaction and Urban Equilibria

In this paper we investigate the effect of local interaction in a simple urban economics model. Agents interact with others if and only if their interaction benefit outweights their travel cost and therefore meet others only within finite geographic windows. We show that two or more cites may co-exist at the equilibrium provided that they are sufficiently distant. For any interaction surplus function, there exists a unique spatial equilibrium on not too large city supports. The population density within a city is determined by a second order advance-delay differential equation, whose solutions are fully characterized for linear interaction surplus functions. Numerical analyses show that more localized interactions yield flatter population density and land rents over larger extents of the city support. They do not give support to the idea that multiple subcenters can be caused by small and finite geographic windows of interaction

Solving Internal Habit Formation Models Through Dynamic Programming in Infinite Dimension

In this paper, we study an economic model, where internal habits play a role. Their formation is described by a more general functional form than is usually assumed in the literature, because a finite memory effect is allowed. Indeed, the problem becomes the optimal control of a standard ordinary differential equation, with the past of the control entering both the objective function and an inequality constraint. Therefore, the problem is intrinsically infinite dimensional. To solve this model, we apply the dynamic programming approach and we find an explicit solution for the associated Hamilton–Jacobi–Bellman equation, which lets us write the optimal strategies in feedback form. Therefore, we contribute to the existing literature in two ways. Firstly, we fully develop the dynamic programming approach to a type of problem not studied in previous contributions. Secondly, we use this result to unveil the global dynamics of an economy characterized by generic internal habits

Approach to Design Behavioural Models for Traffic Network Users - Choice of transport mode

Our research work concerns the development of a multimodal urban traffic simulator designed to be a tool of decision-making aid similar to a game where in the user-player can test different scenarios by immersion in a 3D virtual city. Our approach is based on the activity-based model and the multi-agent technology. The implemented result is a hybrid simulator connecting numerical simulation and behavioural aspects coming from real data. This paper is focused on two points: firstly, we introduce how a final user (the traffic regulator) instantiates and assembles components so as to model a city and its urban traffic network, secondly, we present the use of Dempster-Shafer theory in the context of discrete choice modelling. Our approach manipulates input variables in order to test realistic representations of behaviours of agent categories in a decision-making process. The traffic modelling is based on a questionnaire elaborated from standard arrays of Taguchi. The significant variables and interactions are determined with the analysis of variance which suggests a reduced model describing the behaviour of a particular social category. The belief theory is used to take into account the doubt of some respondents as well as for the preferences redistribution if the number of alternatives changes. The effects of external traffic conditions are also quantified to choose a'robust'alternative and to use the agents'memory

L’apport de l’ancrage squelettique en orthodontie

Pour assurer au mieux les mouvements orthodontiques, l’orthodontie a besoin de s’appuyer sur un ancrage fiable, le plus fixe possible. Dans de nombreux cas, l’ancrage intra-buccal ou même extra-buccal ne peut répondre aux exigences d’ancrage du praticien orthodontiste. En assurant un ancrage fixe, l’ancrage squelettique permet la mise en oeuvre de mouvements complexes tels que ingressions ou déplacements d’un groupe de dents. Cet article décrit l’ancrage squelettique, son développement historique, ses différentes applications, les paramètres à considérer, ses avantages puis ses limitations. Un cas clinique est présenté afin de montrer les différentes étapes du traitement ainsi que le résultat obtenu. Orthodontistes et impantologistes ont là une occasion de collaborer plus étroitement que par le passé. Cette interaction devrait permettre des traitements et des résultats considérés jusque-là comme impossibles à mener et à obtenir

Distributed Optimal Control Models in Environmental Economics: A Review

We review the most recent advances in distributed optimal control applied to environmental economics, covering in particular problems where the state dynamics are governed by partial differential equations (PDEs). This is a quite fresh application area of distributed optimal control, which has already suggested several new mathematical research lines due to the specificities of the environmental economics problems involved. We enhance the latter through a survey of the variety of themes and associated mathematical structures beared by this literature. We also provide a quick tour of the existing tools in the theory of distributed optimal control that have been applied so far in environmental economics

The dispersion of age differences between partners and the asymptotic dynamics of the HIV epidemic

In this paper, the effect of a change in the distribution of age differences between sexual partners on the dynamics of the HIV epidemic is studied. In a gender- and age-structured compartmental model, it is shown that if the variance of the distribution is small enough, an increase in this variance strongly increases the basic reproduction number. Moreover, if the variance is large enough, the mean age difference barely affects the basic reproduction number. We, therefore, conclude that the local stability of the disease-free equilibrium relies more on the variance than on the mean