45987-AC6
Non-Perturbative Effects of Dynamical Inhomogeneities in Viscous Fluid Mixtures
Over the last year, the PRF funds have been applied towards the salary of post-doctoral Research Associate Ramses van Zon. This financial support has enabled us to continue our collaboration on the dynamics of glassy systems. The PRF support has enabled work to proceed along one of the central lines of interest in my research group, the role of collective motion in systems exhibiting rugged-energy landscapes. In addition, thanks to these funds, Dr. van Zon has been able to continue his work in the group while looking for a permanent position in Canada. During the funding period, work has been initiated on combining a model composed of infinitely thin, hard crosses with a mesoscopic model of a fluid. In model solvent, the fluid molecules are point particles with punctuated rotational interactions that lead to hydrodynamic motion of the fluid on a macroscopic scale. A number of computational techniques to extend the time scale accessible to simulation have been developed, including the extension of the hard interactions between crosses to include attractive interactions and softer repulsions while maintaining the advantages of event-driven simulations. Simulating irregularly shaped objects, such as long needles, is facilitated by using rigid bounding boxes to limit the number of interaction partners of a particular needle. The bounding boxes can be utilized to identify analytically the earliest time at which a given pair of needles can interact and thereby improve the efficiency of the simulation and glassiness of the systems studied. We have conducted investigations into the signature of slow orientational relaxation of long needles near the nematic ordering transition and observed similarities with simple glass formers in the form of the stretched-exponential relaxation of the auto-correlation function of the long-axis director of the needle. The orientational dynamics near the nematic transition is characterized by slow and highly cooperative collective motion of local ordering fields of the director, Of particular future interest are extensions of the cross model to include an arbitrary number of arms. The limit of rotors with infinitely many arms is especially intriguing, since the molecules would, on one hand, become a solid sphere, but on the other hand still would not have any excluded volume. The simulation of glassy systems requires efficient means of computing the time evolution of constituents of the system. In situations where the dynamics is not amenable to event-driven algorithms, symplectic sequential integration schemes offer superior stability and accuracy. Utilizing operator splitting algebra, we have developed the first methods of evolving rigid body systems that rigorously conserve a shadow Hamiltonian. The integration method is based on combining the exact free propagation of an arbitrary rigid body with updates of momenta and angular momenta to construct integrators of arbitrary order. We have demonstrated that while a second-order Verlet-like scheme is optimal if only static information is required, a simple variant of the Verlet scheme is optimal at accuracy levels typically required in the computation of dynamical correlations, as is the case in glassy systems. Furthermore, if very accurate trajectories of the system are desired, an advanced gradient-like fourth order scheme offers the most efficient implementation of the evolution. Along analytical lines, we have examined kinetically constrained spin models, in particular the Frederickson-Andersen model. We have been working towards formulating simple schemes, both numerical and analytical, of incorporating an arbitrary number of multilinear modes in order to get nonperturbative results, starting from the complete basis set in terms of down-spin domains. Formulating such schemes is facilitated by the fact that the coupling vertices are easily obtained analytically for these models. For instance, incorporating one down-spin domain of arbitrary size (nonperturbatively) in the theory, the spin-spin time auto-correlation function can be predicted in an analytic form up to fairly low values of the mobile spins. This can be seen as a resummation of the contributions of a specific infinite set of basis vectors. Improvements can be made by including several down-spin domains after one another. We are currently in the process of developing resummation schemes that include an arbitrary number of domains to produce non-perturbative results for the Frederickson-Andersen model.
