Relative directed homotopy theory of partially ordered spaces

Algebraic topological methods have been used successfully in concurrency theory, the domain of theoretical computer science that deals with distributed computing. L. Fajstrup, E. Goubault, and M. Raussen have introduced partially ordered spaces (pospaces) as a model for concurrent systems. In this paper it is shown that the category of pospaces under a fixed pospace is both a fibration and a cofibration category in the sense of H. Baues. The homotopy notion in this fibration and cofibration category is relative directed homotopy. It is also shown that the category of pospaces is a closed model category such that the homotopy notion is directed homotopy.Comment: 20 page

Wigner crystals for a planar, equimolar binary mixture of classical, charged particles

We have investigated the ground state configurations of an equimolar, binary mixture of classical charged particles (with nominal charges $Q_1$ and $Q_2$) that condensate on a neutralizing plane. Using efficient Ewald summation techniques for the calculation of the ground state energies, we have identified the energetically most favourable ordered particle arrangements with the help of a highly reliable optimization tool based on ideas of evolutionary algorithms. Over a large range of charge ratios, $q = Q_2 / Q_1$, we identify six non-trivial ground states, some of which show a remarkable and unexpected structural complexity. For $0.59 \lesssim q < 1$ the system undergoes a phase separation where the two charge species populate in a hexagonal arrangement spatially separated areas.Comment: 14 pages, 8 figure