We develop a formalism to describe the equilibrium distributions for segments
of confined branched networks consisting of stiff filaments. This is applicable
to certain situations of cytoskeleton in cells, such as for example actin
filaments with branching due to the Arp2/3 complex. We develop a grand ensemble
formalism that enables the computation of segment density and polarisation
profiles within the confines of the cell. This is expressed in terms of the
solution to nonlinear integral equations for auxiliary functions. We find three
specific classes of behaviour depending on filament length, degree of branching
and the ratio of persistence length to the dimensions of the geometry. Our
method allows a numerical approach for semi-flexible filaments that are
networked.Comment: 15 pages, revise
