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Microscopic Modelling of Active Bacterial Suspensions

A. Decoene, S. Martin, B. Maury (2011)

Mathematical Modelling of Natural Phenomena

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...

Modelling and control in pseudoplate problem with discontinuous thickness

Ján Lovíšek (2009)

Applications of Mathematics

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...

Motion with friction of a heavy particle on a manifold - applications to optimization

Alexandre Cabot (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Let Φ : H → R be a C2 function on a real Hilbert space and ∑ ⊂ H x R the manifold defined by ∑ := Graph (Φ). We study the motion of a material point with unit mass, subjected to stay on Σ and which moves under the action of the gravity force (characterized by g>0), the reaction force and the friction force ( γ > 0 is the friction parameter). For any initial conditions at time t=0, we prove the existence of a trajectory x(.) defined on R+. We are then interested in the asymptotic behaviour of...

Motion with friction of a heavy particle on a manifold. Applications to optimization

Alexandre Cabot (2002)

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

Let Φ : H → ℝ be a 𝒞 2 function on a real Hilbert space and Σ ⊂ H × ℝ the manifold defined by Σ : = Graph ( Φ ) . We study the motion of a material point with unit mass, subjected to stay on Σ and which moves under the action of the gravity force (characterized by g > 0 ), the reaction force and the friction force ( γ > 0 is the friction parameter). For any initial conditions at time t = 0 , we prove the existence of a trajectory x ( . ) defined on ℝ + . We are then interested in the asymptotic behaviour of the trajectories when t → + ∞ . More precisely,...

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...

Multibody System Mechanics: Modelling, Stability, Control, and Robustness by V. A. Konoplev and A. Cheremensky

Konoplev, V., Cheremensky, A. (2002)

Serdica Mathematical Journal

The Union of Bulgarian Mathematicians starts a new series of publica- tions: Mathematics and Its Applications. The first issue of the series is “Multi- body System Mechanics: Modelling, Stability, Control and Robustness”. The authors are well known mathematicians with various published books and articles. Professor Vladimir Konoplev works in the Institute of Problems of Mechanical Engineering, Russian Academy of Sciences (St. Petersburg, Russia), while Professor Alexander Cheremensky works...

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