A Riemann solver at a junction compatible with a homogenization limit

We consider a junction regulated by a traffic lights, with n incoming roads and only one outgoing road. On each road the Phase Transition traffic model, proposed in [6], describes the evolution of car traffic. Such model is an extension of the classic Lighthill-Whitham-Richards one, obtained by assuming that different drivers may have different maximal speed. By sending to infinity the number of cycles of the traffic lights, we obtain a justification of the Riemann solver introduced in [9] and in particular of the rule for determining the maximal speed in the outgoing road.Comment: 19 page

Stability and Optimization in Structured Population Models on Graphs

We prove existence and uniqueness of solutions, continuous dependence from the initial datum and stability with respect to the boundary condition in a class of initial--boundary value problems for systems of balance laws. The particular choice of the boundary condition allows to comprehend models with very different structures. In particular, we consider a juvenile-adult model, the problem of the optimal mating ratio and a model for the optimal management of biological resources. The stability result obtained allows to tackle various optimal management/control problems, providing sufficient conditions for the existence of optimal choices/controls.Comment: 22 pages, 7 figure

The Godunov Method for a 2-Phase Model

We consider the Godunov numerical method to the phase-transition traffic model, proposed in [6], by Colombo, Marcellini, and Rascle. Numerical tests are shown to prove the validity of the method. Moreover we highlight the differences between such model and the one proposed in [1], by Blandin, Work, Goatin, Piccoli, and Bayen.Comment: 13 page

Differential Equations Modeling Crowd Interactions

Nonlocal conservation laws are used to describe various realistic instances of crowd behaviors. First, a basic analytic framework is established through an "ad hoc" well posedness theorem for systems of nonlocal conservation laws in several space dimensions interacting non locally with a system of ODEs. Numerical integrations show possible applications to the interaction of different groups of pedestrians, and also with other "agents".Comment: 26 pages, 5 figure

The Aw-Rascle traffic model with locally constrained flow

We consider solutions of the Aw-Rascle model for traffic flow fulfilling a constraint on the flux at $x=0$. Two different kinds of solutions are proposed: at $x=0$ the first one conserves both the number of vehicles and the generalized momentum, while the second one conserves only the number of cars. We study the invariant domains for these solutions and we compare the two Riemann solvers in terms of total variation of relevant quantities. Finally we construct ad hoc finite volume numerical schemes to compute these solutions.Comment: 24 page

On the optimization of conservation law models at a junction with inflow and flow distribution controls

The paper proposes a general framework to analyze control problems for conservation law models on a network. Namely we consider a general class of junction distribution controls and inflow controls and we establish the compactness in $L^1$ of a class of flux-traces of solutions. We then derive the existence of solutions for two optimization problems: (I) the maximization of an integral functional depending on the flux-traces of solutions evaluated at points of the incoming and outgoing edges; (II) the minimization of the total variation of the optimal solutions of problem (I). Finally we provide an equivalent variational formulation of the min-max problem (II) and we discuss some numerical simulations for a junction with two incoming and two outgoing edges.Comment: 29 pages, 14 figure

Polynomial Profits in Renewable Resources Management

A system of renewal equations on a graph provides a framework to describe the exploitation of a biological resource. In this context, we formulate an optimal control problem, prove the existence of an optimal control and ensure that the target cost function is polynomial in the control. In specific situations, further information about the form of this dependence is obtained. As a consequence, in some cases the optimal control is proved to be necessarily bang--bang, in other cases the computations necessary to find the optimal control are significantly reduced

The Cauchy problem at a node with buffer

International audienceWe consider the Lighthill-Whitham-Richards traffic flow model on a network composed by an arbitrary number of incoming and outgoing arcs connected together by a node with a buffer. Similar to [M. Herty, J.-P. Lebacque, and S. Moutari. A novel model for intersections of vehicular traffic flow. Netw. Heterog. Media, 4(4):813–826 (electronic), 2009], we define the solution to the Riemann problem at the node and we prove existence and well posedness of solutions to the Cauchy problem, by using the wave-front tracking technique and the generalized tangent vectors

Ichthyofaunistic composition of the Quilombo river, tributary of the Mogi-Guaçu river, upper Paraná river basin, southeastern Brazil

Um estudo sobre a composição ictiofaunística do rio Quilombo foi realizado com o intuito de identificar quais espécies de peixes habitam a bacia, com que freqüência tais espécies são encontradas e verificar variações na distribuição longitudinal desta ictiofauna. Foram demarcados quatro pontos de coletas distribuídos na bacia, os quais foram visitados 21 vezes ao longo de um ano e dez meses (entre setembro de 2003 e junho de 2005), abrangendo os períodos seco e úmido que ocorrem anualmente na região estudada. Para coleta dos peixes foram utilizadas diferentes artes de pesca: tarrafas, redes de espera, rede de arrasto, peneiras, linha e anzol. Os peixes foram fixados em formalina 10%, conservados em etanol 70%, identificados e encontram-se depositados na coleção de peixes do Laboratório de Ictiologia Sistemática do Departamento de Ecologia e Biologia Evolutiva da UFSCar. Foram coletados 2982 exemplares, os quais estão divididos em 6 ordens, 19 famílias, 52 gêneros e 68 espécies. As ordens Characiformes (57,3%) e Siluriformes (30,9%) tiveram maior participação no total de espécies em relação às ordens Gymnotiformes, Cyprinodontiformes, Perciformes e Synbranchiformes, que juntas somaram 11,8% da riqueza. A análise da constância permitiu verificar que a composição da ictiofauna desse rio variou ao longo do período, principalmente nos trechos médio e inferior. O índice de similaridade (Jaccard) evidenciou que os conjuntos de espécies são diferentes entre os pontos de coleta, mostrando particularidades em cada um deles.A study about fish composition in the Quilombo river, of the upper Paraná hydrographic system, is presented. We aimed to identify which species inhabit this small river, to verify the frequency they occur and to study the longitudinal distribution of the ichthyofauna. Fish were sampled for a period of one year and ten months (September 2003 to June 2005) at four collection sites defined through the river basin, comprising dry and wet seasonal periods. Trawlnet, gillnets, seine net, sieves and hooks were used for fish sample. Fish collected were immediately fixed in 10% formalin solution. In the laboratory specimens were preserved in ethanol 70%, identified and deposited in the fish collection of the Laboratório de Ictiologia Sistemática (LISDEBE) of the Departamento de Ecologia e Biologia Evolutiva of the Universidade Federal de São Carlos. An amount of 2982 specimens belonging to 6 orders, 19 families, 52 genera and 68 species were collected. The orders Characiformes (57.3%) and Siluriformes (30.9%) predominated in terms of species richness. The orders Gymnotiformes, Cyprinodontiformes, Perciformes and Synbranchiformes summed 11.8% of total fish richness. The analysis of constancy revealed that the ichthyofaunistic composition in the middle and lower sampled stretches suffered higher temporal variability in comparison to upper stretches of Quilombo river basin. The similarity (Jaccard index) among samples showed that each collection site have distinct assemblages of fish