We determine the scaling exponents of polymer translocation ͑PT͒ through a nanopore by extensive computer simulations of various microscopic models for chain lengths extending up to N = 800 in some cases. We focus on the scaling of the average PT time ϳ N ␣ and the mean-square change of the PT coordinate, ͗s 2 ͑t͒͘ ϳ t ␤ . We find ␣ =1+2 and ␤ =2/ ␣ for unbiased PT in two dimensions ͑2D͒ and three dimensions ͑3D͒. The relation ␣␤ = 2 holds for driven PT in 2D, with a crossover from ␣ Ϸ 2 for short chains to ␣ Ϸ 1+ for long chains. This crossover is, however, absent in 3D where ␣ = 1.42Ϯ 0.01 and ␣␤ Ϸ 2.2 for N Ϸ 40− 800.

We develop and test numerically a lattice-Boltzmann (LB) model for nonideal fluids that incorporates thermal fluctuations. The fluid model is a momentum-conserving thermostat, for which we demonstrate how the temperature can be made equal at all length scales present in the system by having noise both locally in the stress tensor and by shaking the whole system in accord with the local temperature. The validity of the model is extended to a broad range of sound velocities. Our model features a consistent coupling scheme between the fluid and solid molecular dynamics objects, allowing us to use the LB fluid as a heat bath for solutes evolving in time without external Langevin noise added to the solute. This property expands the applicability of LB models to dense, strongly correlated systems with thermal fluctuations and potentially nonideal equations of state. Tests on the fluid itself and on static and dynamic properties of a coarse-grained polymer chain under strong hydrodynamic interactions are used to benchmark the model. The model produces results for singlechain diffusion that are in quantitative agreement with theory.

Abstract. We address the problem of the consistency of different measures of the hydrodynamic radius of solid point and composite solute particles incorporated into the hybrid lattice Boltzmannmolecular dynamics (LBMD) multiscale method. The coupling between the fluid and the particle phase is naturally implemented through a Stokesian type of frictional force proportional to the local velocity difference between the two. Using deterministic flow tests such as measuring the Stokes drag, hydrodynamic torques, and forces we first demonstrate that in this case the hydrodynamic size of the particles is ill-defined in the existing LBMD schemes. We then show how it is possible to effectively achieve the no-slip limit in a discrete simulation with a finite coefficient of the frictional force by demanding consistency of all these measures, but this requires a somewhat modified LB algorithm for numerical stability. Having fulfilled the criteria, we further show that in our consistent coupling scheme particles also obey the macroscopically observed fluctuation-dissipation theorem for the diffusion coefficient of a single particle without any adjustable parameters. In addition, we explicitly show that diffusion alone is not a good criterion for calibration of the frictional coupling.

We derive new analytical results for the hydrodynamic force exerted on a sinusoidally oscillating porous shell and a sphere of uniform density in the Stokes limit. The coupling between the spherical particle and the solvent is done using the Debye-Bueche-Brinkman (DBB) model, i.e. by a frictional force proportional to the local velocity difference between the permeable particle and the solvent. We compare our analytical results and existing dynamic theories to Lattice-Boltzmann simulations of full Navier-Stokes equations for the oscillating porous particle. We find our analytical results to agree with simulations over a broad range of porosities and frequencies