We use the methods of statistical physics and stochastic modeling to investigate behavior of complex systems out of equilibrium.
Using the methods of statistical physics and stochastic modelling we examine behavior of complex systems far from equilibrium. Generically we have in mind colloidal particles of diameters several tens nanometers to several micrometers moving in a liquid under the influence of external driving and hydrodynamic forces. The character of these forces is determined both by the movement of the particles themselves and dynamics of the fluid itself, as well as by geometric constraints as is the case of the flow in a narrow tube of complex shape. To be concrete, we can for example investigate directed movement of organic particles carrying a specific drug in blood vessel toward the site where it is to be applied.
Contrary to the well-studied Brownian motion, colloidal particles studied by us have often an "active" character, because they are driven by an external field, depending for example on the random orientation of coated particles. A crucial mechanism for establishing steady transport is the ratchet effect due to breakdown of space symmetries. Colloid particles behave like molecular motors . We also investigate systems of interacting colloidal particles, including effective interactions mediated by surrounding fluid. As model systems we use Brownian particles, as well as discrete models, where direct interaction of particles has the character of hard-core repulsion. This way we are able to model dynamical separation of colloid particles of different types.
Another theoretical and practical means for analysis of complex non-equilibrium systems is the technique of non-equilibrium linear response. It is used to study the reaction of the system on small external perturbations caused for example by applying mechanical probes,slow change of external temperature etc. The character of such mechanical or thermal response bears a fingerprint of thermodynamic and kinetic properties of the system and differs profoundly between systems close to and far from thermodynamic equilibrium. This is a useful methodology for analysis of systems where standard equilibrium techniques fail.