Hydrodynamic slip boundary condition at chemically patterned surfaces: A continuum deduction from molecular dynamics

We investigate the slip boundary condition for single-phase flow past a chemically patterned surface. Molecular dynamics (MD) simulations show that modulation of fluid-solid interaction along a chemically patterned surface induces a lateral structure in the fluid molecular organization near the surface. Consequently, various forces and stresses in the fluid vary along the patterned surface. Given the presence of these lateral variations, a general scheme is developed to extract hydrodynamic information from MD data. With the help of this scheme, the validity of the Navier slip boundary condition is verified for the chemically patterned surface, where a local slip length can be defined. Based on the MD results, a continuum hydrodynamic model is formulated using the Navier-Stokes equation and the Navier boundary condition, with a slip length varying along the patterned surface. Steady-state velocity fields from continuum calculations are in quantitative agreement with those from MD simulations. It is shown that, when the pattern period is sufficiently small, the solid surface appears to be homogeneous, with an effective slip length that can be controlled by surface patterning. Such a tunable slip length may have important applications in nanofluidics.Comment: 41 pages, 17 figure

Polymers Confined between Two Parallel Plane Walls

Single three dimensional polymers confined to a slab, i.e. to the region between two parallel plane walls, are studied by Monte Carlo simulations. They are described by $N$-step walks on a simple cubic lattice confined to the region $1 \le z \le D$. The simulations cover both regions $D > R_F$ (where $R_F \sim N^\nu$ is the Flory radius, with $\nu \approx 0.587$), as well as the cross-over region in between. Chain lengths are up to $N=80,000$, slab widths up to D=120. In order to test the analysis program and to check for finite size corrections, we actually studied three different models: (a) Ordinary random walks (mimicking $\Theta$-polymers); (b) Self-avoiding walks (SAW); and (c) Domb-Joyce walks with the self-repulsion tuned to the point where finite size corrections for free (unrestricted) chains are minimal. For the simulations we employ the pruned-enriched-Rosenbluth method (PERM) with Markovian anticipation. In addition to the partition sum (which gives us a direct estimate of the forces exerted onto the walls), we measure the density profiles of monomers and of end points transverse to the slab, and the radial extent of the chain parallel to the walls. All scaling laws and some of the universal amplitude ratios are compared to theoretical predictions.Comment: 8 pages, 14 figures include

Security of Continuous Variable Quantum Cryptography

We discuss a quantum key distribution scheme in which small phase and amplitude modulations of CW light beams carry the key information. The presence of EPR type correlations provides the quantum protection. We identify universal constraints on the level of shared information between the intended receiver (Bob) and any eavesdropper (Eve) and use this to make a general evaluation of security. We identify teleportation as an optimum eavesdropping technique.Comment: 6 figure