Condensed Matter Theory

Abstract:

Using a character expansion method, we calculate exactly the eigenvalue density of random matrices of the form M dagger M where M is a complex matrix drawn from a normalized distribution P(M) approximately exp(-Tr [AMB M dagger]) with A and B positive definite (square) matrices of arbitrary dimensions. Such so-called correlated Wishart matrices occur in many fields ranging from information theory to multivariate analysis.

Abstract:

The electrostatic contribution to the twist rigidity of DNA is studied, and it is shown that the Coulomb self-energy of the double-helical sugar-phosphate backbone makes a considerable contribution-the electrostatic twist rigidity of DNA is found to be C(elec) approximately 5 nm, which makes up about 7% of its total twist rigidity ( C(DNA) approximately 75 nm). The electrostatic twist rigidity is found, however, to depend only weakly on the salt concentration, because of a competition between two different screening mechanisms: (1) Debye screening by the salt ions in the bulk, and (2) structural screening by the periodic charge distribution along the backbone of the helical polyelectrolyte. It is found that, depending on the parameters, the electrostatic contribution to the twist rigidity could stabilize or destabilize the structure of a helical polyelectrolyte.

Abstract:

We propose a very simple one-dimensional swimmer consisting of three spheres that are linked by rigid rods whose lengths can change between two values. With a periodic motion in a nonreciprocal fashion, which breaks the time-reversal symmetry as well as the translational symmetry, we show that the model device can swim at low Reynolds number. This model system could be used in constructing molecular-sized machines.

Abstract:

We use lattice Boltzmann simulations to solve the Beris-Edwards equations of motion for a cholesteric liquid crystal subjected to Poiseuille flow along the direction of the helical axis (permeative flow). The results allow us to clarify and extend the approximate analytic treatments currently available. We find that if the cholesteric helix is pinned at the boundaries there is an enormous viscosity increase. If, instead, the helix is free the velocity profile is flattened, but the viscosity is essentially unchanged. We highlight the importance of secondary flows, and, for higher flow velocities, we identify a flow-induced double twist structure in the director field--reminiscent of the texture characteristic of blue phases.