Massimiliano Daniele Rosini
UMCS, Mathematics, Faculty Member
- Traffic Simulation, Nonlinear Elasticity, Nonlinear hyperbolic equations, Semiconductor Device Modeling and Simulation, Pedestrian flow, Crowd Simulation, and 7 morePedestrian and Evacuation Dynamics, Conservation Laws, Pedestrian flow modelling, Crowd Modeling, Pedestrian Simulation, Crowd dynamics, and Computer Scienceedit
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In this chapter we study the Cauchy problems for one-dimensional scalar conservation laws. In particular, we prove that the Cauchy problem is well posed in the class of entropy weak solutions, in the sense that it admits a unique entropy... more
In this chapter we study the Cauchy problems for one-dimensional scalar conservation laws. In particular, we prove that the Cauchy problem is well posed in the class of entropy weak solutions, in the sense that it admits a unique entropy weak solution. The existence of the solutions is proved by the method of wave front tracking. The uniqueness is proved by showing the Kružkov result of the L1 contractiveness of the flow generated by a scalar conservation law.
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Research Interests: Engineering, Computer Science, Mathematical Sciences, Valve, Riemann Problem, and 3 moreGas Flow, L, and B
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We deal with phase transition models for vehicular traffic on road networks. The models consider two different traffic regimes and are given by a scalar conservation law in the free phase and by a system of two conservation laws in the... more
We deal with phase transition models for vehicular traffic on road networks. The models consider two different traffic regimes and are given by a scalar conservation law in the free phase and by a system of two conservation laws in the congested phase. We focus on the Riemann problem at a junction as a preliminary step for the study of the Cauchy problem on a road network.
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In this paper we analyze the effects of a one‐way valve on the isothermal gas flow through a pipe. The valve keeps the flow at a constant value , if possible; otherwise it is closed. First, for fixed , we define a Riemann solver and... more
In this paper we analyze the effects of a one‐way valve on the isothermal gas flow through a pipe. The valve keeps the flow at a constant value , if possible; otherwise it is closed. First, for fixed , we define a Riemann solver and characterize the coherence of its initial data; coherence is a necessary condition for the construction of solutions to a general initial‐value problem based on a wave‐front tracking scheme. We also give an example of an invariant and coherent domain where the valve can be either open or closed. Second, for suitable compact sets of initial data we make precise the range of values that guarantee the coherence. At last, in the case of a real valve with finite reaction time, we show the chattering (rapid switch on and off) of the valve in correspondence with incoherent initial data.
Research Interests: Engineering, Computer Science, Mathematical Sciences, Solver, Valve, and 4 moreRiemann Problem, Gas Flow, L, and B
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This presentation will survey some recent results on models of pedestrian flows based on partial differential equations. The typical situation is that of a crowd trying to move quickly through an exit. First, the 1D model introduced in... more
This presentation will survey some recent results on models of pedestrian flows based on partial differential equations. The typical situation is that of a crowd trying to move quickly through an exit. First, the 1D model introduced in [1] will be presented. It consists of a scalar conservation law solved through suitable non-classical shocks and based on a new fundamental diagram, i.e. a flow- density relation, with 2 points of maximum. This feature was recently experimentally confirmed in [3, 5]. This model does not fit within the results on nonclassical solutions usually found in the literature. Nevertheless, the existence of global solutions with large total variation was proved in [2]. Then, a 2D model will be considered in greater detail. Based on the conservation of mass equation, it can be written as ∂tρ+ div ρ v(ρ) g(x, y) + ε1w(x, y) − ε2 gradψ(ρ)√ 1 + ‖ gradψ(ρ)‖2 = 0 (1) where
This chapter presents notations, terminologies and various mathematical basic results, which will be used in later chapters. © 2013 Springer International Publishing Switzerland
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In this chapter we apply the CR model to describe the evacuation of a corridor through an exit when panic arises. Two different situations are considered: first when the space between the pedestrians and the exit is free, then when before... more
In this chapter we apply the CR model to describe the evacuation of a corridor through an exit when panic arises. Two different situations are considered: first when the space between the pedestrians and the exit is free, then when before the exit there is a further door, through which the pedestrians have to move. According with empirical observations, the CR model confirms that placing such a door may reduce the time necessary for the evacuation. This displays the ability of the CR model to reproduce the so called Braess' paradox for pedestrian flows. © 2013 Springer International Publishing Switzerland
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In this paper optimization problems arising from vehicular traffic and crowd dynamics are considered from the analytical point of view
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We review recent results and present new ones on one-dimensional conservation laws with point constraints on the flux. Their application is, for instance, the modeling of traffic flow through bottlenecks, such as exits in the context of... more
We review recent results and present new ones on one-dimensional conservation laws with point constraints on the flux. Their application is, for instance, the modeling of traffic flow through bottlenecks, such as exits in the context of pedestrians’ traffic and tollgates in vehicular traffic. In particular, we consider nonlocal constraints, which allow to model, e.g., the irrational behavior (“panic”) near the exits observed in dense crowds and the capacity drop at tollbooths in vehicular traffic. Numerical schemes for the considered applications, based on finite volume methods, are designed, their convergence is proved, and their validations are done with explicit solutions. Finally, we complement our results with numerical examples, which show that constrained models are able to reproduce important features in traffic flow, such as capacity drop and self-organization.
The two phase model for vehicular traffic flows recently appeared in goatin2006aw and BenyahiaRosini01 is endowed with a point constraint on the flow to allow for the modelling of phenomena such as the effects of toll booths along a road.... more
The two phase model for vehicular traffic flows recently appeared in goatin2006aw and BenyahiaRosini01 is endowed with a point constraint on the flow to allow for the modelling of phenomena such as the effects of toll booths along a road. We describe in this paper two Riemann solvers for this model upon which an ulterior study of the cauchy problem should rely.
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We reproduce the capacity drop phenomenon at a road merge by implementing a non-local point constraint at the junction in a first order traffic model. We call capacity drop the situation in which the outflow through the junction is lower... more
We reproduce the capacity drop phenomenon at a road merge by implementing a non-local point constraint at the junction in a first order traffic model. We call capacity drop the situation in which the outflow through the junction is lower than the receiving capacity of the outgoing road, as too many vehicles trying to access the junction from the incoming roads hinder each other. In this paper, we first construct an enhanced version of the locally constrained model introduced by Haut et al. (Proceedings 16th IFAC World Congress. Prague, Czech Republic 229 (2005) TuM01TP/3), then we propose its counterpart featuring a non-local constraint and finally we compare numerically the two models by constructing an adapted finite volumes scheme.
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Research Interests: Chemical Engineering, Mathematics, Applied Mathematics, Algorithms, Biomedical Engineering, and 13 moreTransportation, Modeling and Simulation, Medicine, Computational Mathematics, Probability, Entropy, Humans, Computer Simulation, Crowd dynamics, Theoretical Models, Riemann Problem, Capacity Drop, and Cell Membrane
In this chapter we study the Cauchy problems for one-dimensional scalar conservation laws. In particular, we prove that the Cauchy problem is well posed in the class of entropy weak solutions, in the sense that it admits a unique entropy... more
In this chapter we study the Cauchy problems for one-dimensional scalar conservation laws. In particular, we prove that the Cauchy problem is well posed in the class of entropy weak solutions, in the sense that it admits a unique entropy weak solution. The existence of the solutions is proved by the method of wave front tracking. The uniqueness is proved by showing the Kružkov result of the L1 contractiveness of the flow generated by a scalar conservation law. © 2013 Springer International Publishing Switzerland
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Información del artículo Well Posedness of Balance Laws with Non-Characteristic Boundary.
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Abstract. In this paper we study the stability of transonic strong shock so-lutions of the steady state one-dimensional unipolar hydrodynamic model for semiconductors in the isentropic case. The approach is based on the construc-tion of a... more
Abstract. In this paper we study the stability of transonic strong shock so-lutions of the steady state one-dimensional unipolar hydrodynamic model for semiconductors in the isentropic case. The approach is based on the construc-tion of a pseudo-local symmetrizer and on the paradierential calculus with parameters, which combines the work of Bony-Meyer and the introduction of a large parameter. Contents
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In this paper we study the stability of transonic strong shock so- lutions of the steady state one-dimensional unipolar hydrodynamic model for semiconductors in the isentropic case. The approach is based on the construc- tion of a... more
In this paper we study the stability of transonic strong shock so- lutions of the steady state one-dimensional unipolar hydrodynamic model for semiconductors in the isentropic case. The approach is based on the construc- tion of a pseudo-local symmetrizer and on the paradieren tial calculus with parameters, which combines the work of Bony-Meyer and the introduction of a large parameter.
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In this paper, we consider the two phases macroscopic traffic model introduced in [P. Goatin, The Aw-Rascle vehicular traffic flow with phase transitions, Mathematical and Computer Modeling 44 (2006) 287-303]. We first apply the... more
In this paper, we consider the two phases macroscopic traffic model introduced in [P. Goatin, The Aw-Rascle vehicular traffic flow with phase transitions, Mathematical and Computer Modeling 44 (2006) 287-303]. We first apply the wave-front tracking method to prove existence and a priori bounds for weak solutions. Then, in the case the characteristic field corresponding to the free phase is linearly degenerate, we prove that the obtained weak solutions are in fact entropy solutions \`a la Kruzhkov. The case of solutions attaining values at the vacuum is considered. We also present an explicit numerical example to describe some qualitative features of the solutions.