Condensed Matter Theory

Abstract:

We numerically solve the hydrodynamic equations of motion for a cholesteric liquid crystal under an imposed Poiseuille flow, by means of lattice Boltzmann simulations. The elasticity of the cholesteric helix couples to the external flow to give rise to a highly viscoelastic flow. This is a technically difficult problem for standard flow solvers due to its fully two-dimensional nature. We consider a helix with axis parallel to the boundaries, and at the same time to either the primary flow or the vorticity direction (we identify these two flow modes as permeation and vorticity mode respectively). We quantify the large difference found in the steady state director and velocity profiles, and in the apparent viscosities obtained in the two cases.

Abstract:

A promising new method from the field of representations of Lie groups is applied to calculate integrals over unitary groups, which are important for multiantenna communications. To demonstrate the power and simplicity of this technique, a number of recent results are rederived, using only a few simple steps. In particular, we derive the joint probability distribution of eigenvalues of the matrix GG† with G a nonzero mean or a semicor-related Gaussian random matrix. These joint probability distribution functions can then be used to calculate the moment generating function of the mutual information for Gaussian multiple-input multiple-output (MIMO) channels with these probability distribution of their channel matrices G. We then turn to the previously unsolved problem of calculating the moment generating function of the mutual information of MIMO channels, which are correlated at both the receiver and the transmitter. From this moment generating function we obtain the ergodic average of the mutual information and study the outage probability. These methods can be applied to a number of other problems. As a particular example, we examine unitary encoded space-time transmission of MIMO systems and we derive the received signal distribution when the channel matrix is correlated at the transmitter end. © 2006 IEEE.

Abstract:

We present a combined experimental and numerical investigation of the coiling of a liquid "rope" falling on a solid surface, focusing on three little-explored aspects of the phenomenon: The time dependence of "inertio-gravitational" coiling, the systematic dependence of the radii of the coil and the rope on the experimental parameters, and the "secondary buckling" of the columnar structure generated by high-frequency coiling. Inertio-gravitational coiling is characterized by oscillations between states with different frequencies, and we present experimental observations of four distinct branches of such states in the frequency-fall height space. The transitions between coexisting states have no characteristic period, may take place with or without a change in the sense of rotation, and usually (but not always) occur via an intermediate "figure of eight" state. We present extensive laboratory measurements of the radii of the coil and of the rope within it, and show that they agree well with the predictions of a "slender-rope" numerical model. Finally, we use dimensional analysis to reveal a systematic variation of the critical column height for secondary buckling as a function of (dimensionless) flow rate and surface tension parameters.