Fractals and dynamical chaos in a two-dimensional Lorentz gas with sinks
Abstract
We consider a two-dimensional periodic reactive Lorentz gas, in which a moving point particle undergoes elastic collisions on fixed hard disks and annihilates on absorbing disks, called sinks. We present clear evidence of the existence of a fractal repeller in this open system. Moreover, we establish a relation between the reaction rate, describing the macroscopic evolution of the system, and two characteristic quantities of the microscopic chaos: the average Lyapunov exponent and the Hausdorff codimension of the fractal repeller.
- Publication:
-
Physical Review E
- Pub Date:
- March 2001
- DOI:
- 10.1103/PhysRevE.63.036227
- Bibcode:
- 2001PhRvE..63c6227C
- Keywords:
-
- 05.45.Df;
- 05.60.-k;
- Fractals;
- Transport processes