Cours ERASMUS

Active systems.

Examples of active systems are given : suspension of Quincke particles, ensemble of magnetotactic bacteria in a rotating field, swarming of magnetotactic bacteria – Stress tensor of active system – Pullers and pushers – Effective viscosity of bacterial suspensions.

Proposed personal work. Trajectories of magnetotactic bacteria submitted to a rotating field, in the non-synchronous regime.

Necessary background : basics in ordinary and partial differential equations, basics in hydrodynamics and elasticity. Some experience in MatLab or Mathematica may be helpful.

Self-propulsion of micro-organisms.

Main mechanisms of self-propulsion of microorganisms : rotating helice, flexible tail – Mobility matrix and its properties – Derivation of the self-propulsion velocity in terms of propagation of bending deformations along a flexible tail. As a particular example the self- propelling motion of very fast sulphur oxidizing bacteria is described.

Proposed personal work. Self-propulsion of a sheet thanks to propogating bending deformations.

Elastic-rod as a model of biopolymers.

Elastic-rod model formulation – Buckling of biopolymers – Formulation of the boundary value problem corresponding to the Euler instability of elastic-rod – Description of the numerical algorithm to solve it and its implementation with MatLab – Networks of semi- flexible filaments and their thermal fluctuations – Relation to the network elastic properties.

Proposed personal work. Buckled shapes of elastic rod under the action of compression by MatLab.

Fluctuation-dissipation theorem and its application in microrheology.

Complex susceptibility and response to external perturbation – Concepts of active and passive methods in microrheology – Fluctuation-dissipation theorem and its illustration for different examples :

• Brownian motion in viscous fluid ;
• Thermal power spectrum of the bead fluctuations in laser tweezers ;
• Brownian motion of particle in viscoelastic media ;
• Brownian motion in the network of semi-flexible biopolymers.

Proposed personal work. Deformation of semi-infinite elastic rod in viscous fluid under the action of the normal force applied at its end.

Short CV :

Prof. A. Cebers is graduated State University of Latvia in 1971. He obtained his degrees : Candidate of physical-mathematical sciences, Moscow State University, in 1977, Doctor of physico-mathematical sciences, Moscow State University,1987 and Dr.hab.phys., Scientific Council of Latvia in 1992. From 1997 he is Professor in theoretical physics of University of Latvia, head of department of theoretical physics. Starting from 1992 he has been many times invited professor of Univ. Paris 6, Univ. Paris 7, Univ. of Nice and Sophia Antipolis, visiting researcher in Penn Univ. and in Paris 11 Univ.. He is True Member of Academy of Sciences of Latvia (from 1993), True Member of Academy Europaea (2005). He is editor in chief of international journal Magnetohydrodynamics (from 2000).
He has 231 papers, 3 books. Hirsh factor is 23.