Electrostatic forces on charged surfaces of bilayer lipid membranes

Simulating protein-membrane interactions is an important and dynamic area of research. A proper definition of electrostatic forces on membrane surfaces is necessary for developing electromechanical models of protein-membrane interactions. Here we modeled the bilayer membrane as a continuum with general continuous distributions of lipids charges on membrane surfaces. A new electrostatic potential energy functional was then defined for this solvated protein-membrane system. We investigated the geometrical transformation properties of the membrane surfaces under a smooth velocity field. These properties allows us to apply the Hadamard-Zolesio structure theorem, and the electrostatic forces on membrane surfaces can be computed as the shape derivative of the electrostatic energy functional

The superhydrophobicity of polymer surfaces: Recent developments

Superhydrophobicity is the extreme water repellence of highly textured surfaces. The field of superhydrophobicity research has reached a stage where huge numbers of candidate treatments have been proposed and jumps have been made in theoretically describing them. There now seems to be a move to more practical concerns and to considering the demands of individual applications instead of more general cases. With these developments, polymeric surfaces with their huge variety of properties have come to the fore and are fast becoming the material of choice for designing, developing, and producing superhydrophobic surfaces. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 49: 1203–1217, 201

Electronic States of Wires and Slabs of Topological Insulators: Quantum Hall Effects and Edge Transport

We develop a simple model of surface states for topological insulators, developing matching relations for states on surfaces of different orientations. The model allows one to write simple Dirac Hamiltonians for each surface, and to determine how perturbations that couple to electron spin impact them. We then study two specific realizations of such systems: quantum wires of rectangular cross-section and a rectangular slab in a magnetic field. In the former case we find a gap at zero energy due to the finite size of the system. This can be removed by application of exchange fields on the top and bottom surfaces, which lead to gapless chiral states appearing on the lateral surfaces. In the presence of a magnetic field, we examine how Landau level states on surfaces perpendicular to the field join onto confined states of the lateral surfaces. We show that an imbalance in the number of states propagating in each direction on the lateral surface is sufficient to stabilize a quantized Hall effect if there are processes that equilibrate the distribution of current among these channels.Comment: 14 pages, 9 figures include