An image system and surface singularity solutions for potential flow past an elliptical cylinder

The Milne-Thomson circle theorem is extended to give a simplegeneral expression for the image system in an elliptical cylinderintroduced into an otherwise specified unbounded potential flowwhich contains no singularities in the region to be occupiedby the ellipse. This image system is used to obtain an expressionfor the corresponding source-sink surface singularity distributionon the ellipse, thus providing new benchmark test cases forsource-sink solutions as obtained numerically by a panel method.Several typical examples are given to illustrate the generaltheoretical approach.     

Quantum effects in ice Ih

Quantum and classical simulations are carried out on ice Ih over a range of temperatures utilizing the TIP4P water model. The rigid-body centroid molecular dynamics method employed allows for the investigation of equilibrium and dynamical properties of the quantum system. The impact of quantization on the local structure, as measured by the radial and spatial distribution functions, as well as the energy is presented. The effects of quantization on the lattice vibrations, associated with the molecular translations and librations, are also reported. Comparison of quantum and classical simulation results indicates that shifts in the average potential energy are equivalent to rising the temperature about 80 K and are therefore non-negligible. The energy shifts due to quantization and the quantum mechanical uncertainties observed in ice are smaller than the values previously reported for liquid water. Additionally, we carry out a comparative study of melting in our classical and quantum simulations and show that there are significant differences between classical and quantum ice.     

Density functional theory investigations on the chemical basis of the selectivity filter in the K+ channel protein

The chemical-physical basis of loading and release of K(+) and Na(+) ions in and out of the selectivity filter of the K(+) channel has been investigated using the B3LYP method of density functional theory. We have shown that the difference between binding free energies of K(+) and Na(+) to the cavity end of the filter is smaller than the difference between the K(+) and Na(+) solvation free energies. Thus, the loading of K(+) ions into the cavity end of the selectivity filter from the solution phase is suggested to be selective prior to the subsequent conduction process. It is shown that the extracellular end of the filter is only optimal for K(+) ions, because K(+) ions prefer the coordination environment of eight carbonyl oxygens. Na(+) ions do not fit into the extracellular end of the filter, since they prefer the coordination environment of six carbonyl oxygens. Overall, the results suggest that the rigid C(4) symmetric selectivity filter is specifically designed for conduction of K(+) ions.