ABSTRACT: We examine the effect of interactions between the electrons on the
Landauer-B\\\"uttiker conductances of some systems of quantum wires with
different geometries. The systems include a wire with a stub in the
middle, and a wire containing a ring which can enclose a magnetic flux.
The electrons in each of the wires is taken to be weakly interacting,
and scattering matrices are introduced at all the junctions present in
the systems. Using a renormalization group method developed recently, we
compute the conductances of these systems as functions of the temperature
and the wire lengths. We present results for high, intermediate and low
temperatures which correspond respectively to the thermal coherence length
being smaller than, comparable to and larger than the smallest wire length
in the different systems, i.e., the length of the stub or each arm of the
ring. The renormalization group procedure and the formulae used to compute
the conductances are different in the three regimes. Our results show that
the Landauer-B\\\"uttiker conductances of various systems of experimental
interest depend on the temperature and lengths in a non-trivial way when
interactions are taken into account.