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Nematic liquid crystals are characterized by the occurrence of disclination lines, topological defects where the average molecular orientation changes abruptly. Recent experiments have shown that, in addition to their application in displays, liquid crystals permit the detection of ligand-receptor binding by optical amplification. The optimal design of LC-based biosensors requires an understanding of the effects of the presence of biomolecules on the structure and dynamics of nematic liquid crystals. We present a multiscale approach that combines molecular simulations and mesoscale modeling: Monte Carlo simulations are used to study the interactions of diluite colloidal particles, as well as the structure of topological defects; these results compare satisfactorily with the corresponding theoretical calculations at the mesoscale level. The mesoscale modeling of a multi-particle sensor shows that adsorbed biomo- lecules modify the relaxation dynamics in the device: at low surface-coverage densities, the equilibrium structure is characterized by a slightly perturbed uniform nematic order; at a critical density, the dynamics exhibits a slowdown at late stages, characteristic of the inability of the nematic to achieve a uniform order. These results are compared with experimental observations of the nematic response in biosensors.

We review some recent results obtained by our group, on the general subject of polymers confined within narrow slits. First, we present a derivation of the free energy of compression of two- and three-dimensional networks between parallel walls. Then, we consider the problem of the adhesion between two parallel surfaces, produced by an ensemble of chains forming irreversible and randomly distributed bonds with the walls. We evaluate the free energy change and the elastic moduli of the polymer layer, corresponding to both tangential (shear) and normal (elongation and compression) deformations. Both calculations adopt different variants the phantom chain model, whereby polymer-polymer interactions are neglected.

The complex rotational and deformational behavior of polymer molecules in dilute solutions subjected to a shear flow as studied in non-equilibrium molecular dynamics computer simulations can be understood qualitatively within a simple dumbbell model. It allows a numerical test of a conjectured relation between the average angular velocity of a flexible polymer molecule and a ratio of components of the gyration tensor. The model involves a pseudo-friction coefficient which is chosen such that the peculiar kinetic energy is kept constant: Gaussian thermostat. The orbits show rotation, wagging and tumbling, depending on the shear rate, combined with radial stretching and compression. The angular velocity divided by minus the shear rate is equal to 1/2 at small shear rates, corresponding to a solid body like behavior. At high values of the shear rate the angular velocity decreases strongly with increasing shear rates. In both these regimes, the conjectured relation holds true. For intermediate shear rates, however, this relation between the true angular velocity and the corresponding expression inferred from the gyration tensor is violated. The behavior of the dumbbell is highly irregular for these shear rates, a sensitive dependence on the initial conditions and on the shear rate are noticed. The largest Lyapunov exponent is positive, indicating chaotic behavior for certain values of the shear rates. For certain shear rates, no unique assymtotic state exists. At some inermediate and at high shear rates, stable periodic orbits with long periods are observed. The irregular behavior of the angular velocity at intermediate shear rates persists when the Gaussian thermostat is replaced by a Nosé-Hoover thermostat and even when an additional thermostat is applied which controls the configurational temperature.

The theological properties of nematic liquid crystalline polymers are strongly affected by the dynamic behavior of the molecular alignment. Starting from a closed nonlinear inhomogeneous relaxation equation for the five components of the alignment tensor which, in turn, can be inferred from a generalized Fokker-Planck equation, it has recently been demonstrated (G. Rienäcker, M. Kröger, and S. Hess, Phys. Rev. E 66 , 040702(R) (2002); Physica A 315 , 537 (2002)) that the rather complex orientation behavior of tumbling nematics can even be chaotic in a certain range of the relevant control variables, viz. the shear rate and tumbling parameter. Here the theological consequences, in particular the shear stress and the normal stress differences, as well as the underlying dynamics of the alignment tensor are computed and discussed. For selected state points, long-time averages are evaluated both for imposed constant shear rate and constant shear stress. Orientational and theological properties are presented as function of the shear rate. The transitions between different dynamic states are detected and discussed. Representative examples of alignment orbits and theological phase portraits give insight into the dynamic behavior.

This article will review some of the progress made recently in developing parallel simulation techniques for macromolecules. It will start with simple methods for molecular dynamics, involving replicated data techniques; and go on to show how parallel performance can be improved by careful load-balancing and reduction of message passing. Domain decomposition MD methods are then presented as a way of reducing message passing further, so that effective parallelisation can occur with even the slowest of communication links ethernett). Finally, parallel techniques for conducting Monte Carlo are reviewed, and ways of combining parallel methods are presented. The latter looks like becoming an effective way of using massively parallel architectures for macro-molecules, without the need to simulate huge systems sizes.