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A discrete contact model for crowd motion

Bertrand Maury, Juliette Venel (2011)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The aim of this paper is to develop a crowd motion model designed to handle highly packed situations. The model we propose rests on two principles: we first define a spontaneous velocity which corresponds to the velocity each individual would like to have in the absence of other people. The actual velocity is then computed as the projection of the spontaneous velocity onto the set of admissible velocities (i.e. velocities which do not violate the non-overlapping constraint). We describe here the...

A discrete contact model for crowd motion

Bertrand Maury, Juliette Venel (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

The aim of this paper is to develop a crowd motion model designed to handle highly packed situations. The model we propose rests on two principles: we first define a spontaneous velocity which corresponds to the velocity each individual would like to have in the absence of other people. The actual velocity is then computed as the projection of the spontaneous velocity onto the set of admissible velocities (i.e. velocities which do not violate the non-overlapping constraint). We describe here...

Motor-Mediated Microtubule Self-Organization in Dilute and Semi-Dilute Filament Solutions

S. Swaminathan, F. Ziebert, I. S. Aranson, D. Karpeev (2010)

Mathematical Modelling of Natural Phenomena

We study molecular motor-induced microtubule self-organization in dilute and semi-dilute filament solutions. In the dilute case, we use a probabilistic model of microtubule interaction via molecular motors to investigate microtubule bundle dynamics. Microtubules are modeled as polar rods interacting through fully inelastic, binary collisions. Our model indicates that initially disordered systems of interacting rods exhibit an orientational instability...

On Carnot's theorem in time dependent impulsive mechanics.

Stefano Pasquero (2005)

Extracta Mathematicae

We show that the validity of the Carnot's theorem about the kinetic energy balance for a mechanical system subject to an inert impulsive kinetic constraint, once correctly framed in the time dependent geometric environment for Impulsive Mechanics given by the left and right jet bundles of the space-time bundle N, is strictly related to the frame of reference used to describe the system and then it is not an intrinsic property of the mechanical system itself. We analyze in details the class of frames...

On the Singularities of the Newtonian two dimensional N-body Problem

Carlo Marchioro, Mario Pulvirenti (1983)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si considera un sistema bidimensionale di N particelle interagenti tramite un potenziale di Newton o di Coulomb e si mostra che l’insieme delle condizioni iniziali che in un tempo finito possono condurre a delle singolarità possiede misura di Lebesgue nulla.

On weak solutions to the Lagrange-d'Alembert equation

Dmitry Treschev, Oleg Zubelevich (2013)

Applicationes Mathematicae

We consider nonholonomic systems with collisions and propose a concept of weak solutions to Lagrange-d'Alembert equations. Using this concept we describe the dynamics of collisions. Collisions of a rotating ball and a rough floor are considered.

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