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Computer simulations of Brownian motion of complex systems

Published online by Cambridge University Press:  26 April 2006

P. S. Grassia ,
E. J. Hinch  and
L. C. Nitsche
P. S. Grassia
Affiliation:
Department of Applied Mathematics and Theoretical Physics, The University of Cambridge, Silver Street, Cambridge CB3 9EW, UK
E. J. Hinch
Affiliation:
Department of Applied Mathematics and Theoretical Physics, The University of Cambridge, Silver Street, Cambridge CB3 9EW, UK
L. C. Nitsche
Affiliation:
Department of Chemical Engineering, The University of Illinois at Chicago, 810 South Clinton Street, Chicago, IL 60607, USA
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Abstract

Care is needed with algorithms for computer simulations of the Brownian motion of complex systems, such as colloidal and macromolecular systems which have internal degrees of freedom describing changes in configuration. Problems can arise when the diffusivity or the inertia changes with the configuration of the system. There are some problems in replacing very stiff bonds by rigid constraints. These problems and their resolution are illustrated by some artificial models; firstly in one dimension, then in the neighbourhood of an ellipse in two dimensions and finally for the trimer polymer molecule.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 282 , 10 January 1995 , pp. 373 - 403
Copyright
© 1995 Cambridge University Press

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References

Ermak, D. L. & Mccammon, J. A. 1978 Brownian dynamics with hydrodynamic interaction. J. Chem. Phys. 69, 1352–1360.Google Scholar
Fixman, M. 1978a Simulation of polymer dynamics. I. General theory. J. Chem. Phys. 69, 1527–1537.Google Scholar
Fixman, M. 1978b Simulation of polymer dynamics. II. Relaxation rates and dynamic viscosity. J. Chem. Phys. 69, 1539–1545.Google Scholar
Fixman, M. 1986 Construction of Langevin forces in simulations of hydrodynamic interactions. Macromolecules 19, 1204–1207.Google Scholar
Hassager, O. 1974 Kinetic theory and rheology of bead-rod model for macromolecular solution. I. Equilibria & steady flow properties. J. Chem. Phys. 60, 2111–2124.Google Scholar
Helfand, E. 1979 Flexible vs rigid constraints in statistical mechanics. J. Chem. Phys. 71, 5000–5007.Google Scholar
Helfand, E. Wasserman, Z. R. & Weber, T. A. 1980 Brownian dynamics study of polymer conformational transitions. Macromolecules 13, 526–533.Google Scholar
Heyes, D. M. & Melrose, J. R. 1993 Brownian dynamics simulations of model hard-sphere suspensions. J. Non-Newtonian Fluid Mech. 46, 1–28.Google Scholar
Hinch, E.J. 1994 Brownian motion with stiff bonds and rigid constraints. J. Fluid Mech. 271, 219–234.Google Scholar
Hinch, E.J. & Nitsche, L.C. 1993 Nonlinear drift interactions between fluctuating colloidal particles: oscillatory and stochastic motions. J. Fluid Mech. 256, 343–401.Google Scholar
Kampen, N. G. Van 1981 Statistical mechanics of trimers. Applied Sci. Res. 37, 67–75.Google Scholar
Kampen, N.G. Van & Lodder, J.J. 1984 Constraints. Am. J. Phys. 52, 419–424.Google Scholar
Kirkwood, J. G. 1949 The statistical mechanical theory of irreversible processes in solutions of flexible macromolecules. Visco-elastic behaviour. Rec. Trav. Chim. 68, 649–660.Google Scholar
Kramers, H. A. 1946 The behaviour of macromolecules in inhomogeneous flows. J. Chem. Phys. 14, 415–424.Google Scholar
Kubo, R., Toda, M & Hasitsume, N. 1985 Statistical Physics II §1.6. Springer.
Luty, B.A., Wade, R.C., Madura, J.D., Davis, M.E., Briggs, J.A. & McCammon, J.A. 1993 Brownian dynamics simulations of diffusional encounters between triose phosphate isomerase and glyceraldehyde phosphate: electrostatic steering of glyceraldehyde phosphate. J. Chem. Phys. 97, 233–237.CrossRefGoogle Scholar
Nambi, P., Wierzbicki, A. & Allison, S. A. 1992 Intermolecular interaction between bovine pancreatic trypsin inhibitor molecules probed by Brownian dynamics simulations. J. Chem. Phys. 95, 9595–9600.Google Scholar
Northrup, S. H. & Erickson, H. P. 1992 Kinetics of protein-protein association of diffusion-influenced biomolecular reactions. Proc. Natl. Acad. Sci. USA 89, 3338–3342.Google Scholar
Øskendal, B. 1985 Stochastic Differential Equations: An Introduction with Applications. Springer-Verlag.
Parnas, R. S. & Cohen, Y. 1991 Response of a terminally anchored polymer chain to a simple shear flow. Macromolecules 24, 4646–4656.Google Scholar
Pear, M. R. & Weiner, J. H. 1979 Brownian dynamics study of a polymer chain of linked rigid bodies. J. Chem. Phys. 71, 212–224.Google Scholar
Rallison, J. M. 1979 The role of rigidity constraints in the rheology of dilute polymer solutions. J. Fluid Mech. 93, 251–279.Google Scholar
Rey, A., Freire, J. J. & García de la Torre, J. 1989 Brownian dynamics of a flexible polymer. Internal modes and quasielastic scattering function. J. Chem. Phys. 90, 2035–2041.Google Scholar
Rigos, A. A. & Wilemski, G. 1992 Brownian dynamics simulations of an order-disorder transition in sheared sterically stabilized colloid suspensions. J. Chem. Phys. 96, 3981–3986.Google Scholar
Sherwood, J. D. 1992 Brownian dynamics simulation of a 2-D suspension of charged colloidal plates under shear. J. Non-Newtonian Fluid Mech. 43, 195–228.Google Scholar