27 research outputs found
Critical mass and the dependency of research quality on group size
Academic research groups are treated as complex systems and their cooperative
behaviour is analysed from a mathematical and statistical viewpoint. Contrary
to the naive expectation that the quality of a research group is simply given
by the mean calibre of its individual scientists, we show that intra-group
interactions play a dominant role. Our model manifests phenomena akin to phase
transitions which are brought about by these interactions, and which facilitate
the quantification of the notion of critical mass for research groups. We
present these critical masses for many academic areas. A consequence of our
analysis is that overall research performance of a given discipline is improved
by supporting medium-sized groups over large ones, while small groups must
strive to achieve critical mass.Comment: 16 pages, 6 figures consisting of 16 panels. Presentation and
reference list improved for version
Monte Carlo study of the evaporation/condensation transition on different Ising lattices
In 2002 Biskup et al. [Europhys. Lett. 60, 21 (2002)] sketched a rigorous
proof for the behavior of the 2D Ising lattice gas, at a finite volume and a
fixed excess \delta M of particles (spins) above the ambient gas density
(spontaneous magnetisation). By identifying a dimensionless parameter \Delta
(\delta M) and a universal constant \Delta_c, they showed in the limit of large
system sizes that for \Delta < \Delta_c the excess is absorbed in the
background (``evaporated'' system), while for \Delta > \Delta_c a droplet of
the dense phase occurs (``condensed'' system).
To check the applicability of the analytical results to much smaller,
practically accessible system sizes, we performed several Monte Carlo
simulations for the 2D Ising model with nearest-neighbour couplings on a square
lattice at fixed magnetisation M. Thereby, we measured the largest minority
droplet, corresponding to the condensed phase, at various system sizes (L=40,
>..., 640). With analytic values for for the spontaneous magnetisation m_0, the
susceptibility \chi and the Wulff interfacial free energy density \tau_W for
the infinite system, we were able to determine \lambda numerically in very good
agreement with the theoretical prediction.
Furthermore, we did simulations for the spin-1/2 Ising model on a triangular
lattice and with next-nearest-neighbour couplings on a square lattice. Again,
finding a very good agreement with the analytic formula, we demonstrate the
universal aspects of the theory with respect to the underlying lattice. For the
case of the next-nearest-neighbour model, where \tau_W is unknown analytically,
we present different methods to obtain it numerically by fitting to the
distribution of the magnetisation density P(m).Comment: 14 pages, 17 figures, 1 tabl