# Computer simulation of soft condensed matter and complex
systems

Our research deals with classical molecular dynamics and Monte Carlo computer simulation of liquids, especially liquid crystals, on massively parallel architectures; it includes the development of algorithms, code, force field parameters and OpenGL-based molecular graphics.

The oblate ellipsoids over the navigation bar are a coarse-grained model (Gay-Berne potential with Bates-Luckhurst extension, elongation = 0,2) of the isotropic phase formed by a discotic mesogen, e.g. a triphenylene derivative as one of those above. The colour of the molecules was chosen to depend on the orientation of their symmetry axis. The simulation was performed on a parallel computer at the NIC in Jülich with the domain decomposition molecular dynamics program GBmega, that we develop together with Prof. M. P. Allen from the University of Warwick. As the picture below it was made with the group's own OpenGL molecular graphics program QMGA.

The following equations show an extract from four centuries of development of classical mechanics, that is the base for our simulations: Newton's second law (17th century), the Lagrangian formulation with generalised coordinates, the principle of stationary or least action and the Euler-Lagrange equation (18th century), the Hamiltonian formulation with canonically conjugated momenta defined by a Legendre transformation and the canonical equations of motion, Poisson brackets, the Liouville operator (19th century), the Trotter factorization of the classical propagator leading to the velocity Verlet integrator, and the latter implemented in C++ (20th century).

Further keywords of our research are statistical mechanics, complex systems, scientific computing, orientation-dependent potentials for rigid bodies, transport phenomena, standard and anomalous diffusion, non-equilibrium thermodynamics, stochastic processes, stochastic differential equations, parabolic partial differential equations (Fokker-Planck), integral equations, continuous-time random walks, fractional calculus, path integrals, time series analysis, agent-based models, econophysics.

More information can be found in our publications.

"Piled Higher and Deeper", a grad student comic strip by Jorge Cham, www.phdcomics.com