Mathematical model for diamond-type crystals with impurities or defects.
Mathematical models of suspension bridges
In this work we try to explain various mathematical models describing the dynamical behaviour of suspension bridges such as the Tacoma Narrows bridge. Our attention is concentrated on the derivation of these models, an interpretation of particular parameters and on a discussion of their advantages and disadvantages. Our work should be a starting point for a qualitative study of dynamical structures of this type and that is why we have a closer look at the models, which have not been studied in literature...
Mathematical models of suspension bridges: existence of unique solutions
Measure-differential inclusions in percussional dynamics.
Mécanique et géométrie dans les écrits de Mécanique de John Wallis. Le calcul du centre de gravité
John Wallis publie entre 1669 et 1671 les trois parties de son traité de Mécanique, qu’il caractérise lui-même comme un traité de géométrie. La mécanique est située à l’intérieur de la géométrie, dont elle partage les méthodes, puisque les propriétés du mouvement sont démontrées more geometrico. Wallis veut fonder la mécanique sur de nouvelles bases. Pour cela, il y applique une méthode qu’il a élaborée dans l’Arithmetica infinitorum, en partant de la méthode des indivisibles de Cavalieri, et qu’il...
Mechanical Lagrangian systems with external forces.
Mechanical oscillators with dampers defined by implicit constitutive relations
We study the vibrations of lumped parameter systems, the spring being defined by the classical linear constitutive relationship between the spring force and the elongation while the dashpot is described by a general implicit relationship between the damping force and the velocity. We prove global existence of solutions for the governing equations, and discuss conditions that the implicit relation satisfies that are sufficient for the uniqueness of solutions. We also present some counterexamples...
Mémoire sur la rotation de la lune
Mémoire sur le développement algébrique de la fonction perturbatrice.
Mémoire sur le mouvement vibratoire d'une membrane de forme elliptique.
Mémoire sur les équations du mouvement d'un système de corps.
Mémoire sur les inégalités séculaires des grands axes des orbites des planètes.
Méthode unitaire d'étude des différentes classes de problémes "bien posés" concernant certains systémes intégro-différentiels non linéaires aux opérateurs polyvibrants et aux autocontroles dans les limites d'integration.
Microscopic Modelling of Active Bacterial Suspensions
We present two-dimensional simulations of chemotactic self-propelled bacteria swimming in a viscous fluid. Self-propulsion is modelled by a couple of forces of same intensity and opposite direction applied on the rigid bacterial body and on an associated region in the fluid representing the flagellar bundle. The method for solving the fluid flow and the motion of the bacteria is based on a variational formulation written on the whole domain, strongly...
Minimization properties of Hill's orbits and applications to some N-body problems
Miss analysis in Lambert interceptions with application to a new guidance law.
Modeling, chaotic behavior, and control of dissipation properties of hysteretic systems.
Modélisation de la transition vers la turbulence
Modelling and control in pseudoplate problem with discontinuous thickness
This paper concerns an obstacle control problem for an elastic (homogeneous) and isotropic) pseudoplate. The state problem is modelled by a coercive variational inequality, where control variable enters the coefficients of the linear operator. Here, the role of control variable is played by the thickness of the pseudoplate which need not belong to the set of continuous functions. Since in general problems of control in coefficients have no optimal solution, a class of the extended optimal control...
Models for quadratic algebras associated with second order superintegrable systems in 2D.