- 13-2 No Cuneo, Jean-Pierre Eckmann
- Controlling General Polynomial Networks
Jan 7, 13
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Abstract. We consider networks of massive particles connected by
non-linear springs. Some particles interact with heat baths at
different temperatures, which
are modeled as stochastic driving forces.
The structure of the network is
arbitrary, but the motion of each particle is 1D.
For polynomial interactions, we give sufficient conditions
for H rmander's ``bracket condition''
to hold, which implies the
uniqueness of the steady state (if it exists), as well as the
controllability of the associated system in control theory. These
conditions are constructive; they are formulated in terms of
inequivalence of the forces (modulo
translations) and/or conditions on the topology of the
connections. We illustrate our results with
examples, including ``conducting chains'' of variable cross-section.
This then extends the results for a simple chain obtained in Eckmann, Pillet, Rey-Bellet (1999).