Colloidal suspensions of Laponite clay platelets are studied by means of Brownian dynamics simulations. The platelets carry discrete charged sites which interact via a Yukawa potential. As in the paper by S. Kutter et al. [J. Chem. Phys. 112, 311 (2000)], two models are considered. In the first one all surface sites are identically negative charged, whereas in the second one, rim charges of opposite sign are included. These models mimic the behavior of the Laponite particles in different media. They are employed in a series of simulations for different Laponite concentrations and for two values of the Debye length. For the equilibrium states, the system structure is studied by center-to-center and orientational pair distribution functions. Long-time translational and rotational self-diffusion coefficients are computed by two different methods, which yield very similar results.
The problem of relating microscopic chaos to macroscopic behavior in a many-degrees-of-freedom system is numerically investigated by analyzing statistical properties associated to the position and momentum of a heavy impurity embedded in a chain of nearest-neighbor anharmonic Fermi-Pasta-Ulam oscillators. For this model we have found that the behavior of the relaxation time of the momentum autocorrelation function of the impurity is different depending on the dynamical regime (either regular or chaotic) of the lattice.
In this work we give an alternative method to calculate the transition probability densities (TPD) for the velocity space, phase space, and Smoluchowsky configuration space of a Brownian gas of charged particles in the presence of a constant magnetic field. Our proposal consists in transforming, by means of a rotation matrix, the Langevin equation of a charged particle in the velocity space into another velocity space where the behavior is quite similar to that of ordinary Brownian motion. A similar strategy is also applied to the phase-space. In consequence, in the transformed space both the Fokker-Planck and Fokker-Planck-Kramers equations are solved following Chandrasekhar's methodology. Our results are compared with those obtained by Czopnik and Garbaczewski [Phys. Rev. E 63, 021105 (2001)].
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