Effective Maxwell equations from time-dependent density functional theory

The behavior of interacting electrons in a perfect crystal under macroscopic external electric and magnetic fields is studied. Effective Maxwell equations for the macroscopic electric and magnetic fields are derived starting from time-dependent density functional theory. Effective permittivity and permeability coefficients are obtained.Comment: 36 page

Complex Monge-Amp\`ere equations on quasi-projective varieties

We introduce generalized Monge-Amp\`ere capacities and use these to study complex Monge-Amp\`ere equations whose right-hand side is smooth outside a divisor. We prove, in many cases, that there exists a unique normalized solution which is smooth outside the divisor

Strangeness production in heavy ion collisions at SPS and RHIC within two-source statistical model

The experimental data on hadron yields and ratios in central Pb+Pb and Au+Au collisions at SPS and RHIC energies, respectively, are analysed within a two-source statistical model of an ideal hadron gas. These two sources represent the expanding system of colliding heavy ions, where the hot central fireball is embedded in a larger but cooler fireball. The volume of the central source increases with rising bombarding energy. Results of the two-source model fit to RHIC experimental data at midrapidity coincide with the results of the one-source thermal model fit, indicating the formation of an extended fireball, which is three times larger than the corresponding core at SPS.Comment: Talk at "Strange Quarks in Matter" Conference (Strangeness'2001), September 2001, Frankfurt a.M., German

Applications of inverse simulation to a nonlinear model of an underwater vehicle

Inverse simulation provides an important alternative to conventional simulation and to more formal mathematical techniques of model inversion. The application of inverse simulation methods to a nonlinear dynamic model of an unmanned underwater vehicle with actuator limits is found to give rise to a number of challenging problems. It is shown that this particular problem requires, in common with other applications that include hard nonlinearities in the model or discontinuities in the required trajectory, can best be approached using a search-based optimization algorithm for inverse simulation in place of the more conventional Newton- Raphson approach. Results show that meaningful inverse simulation results can be obtained but that multi-solution responses exist. Although the inverse solutions are not unique they are shown to generate the required trajectories when tested using conventional forward simulation methods

Quantum fluctuations and isotope effects in ab initio descriptions of water

Nuclear quantum effects, such as zero-point energy and tunneling, cause significant changes to the structure and dynamics of hydrogen bonded systems such as liquid water. However, due to the current inability to simulate liquid water using an exact description of its electronic structure, the interplay between nuclear and electronic quantum effects remains unclear. Here we use simulations that incorporate the quantum mechanical nature of both the nuclei and electrons to provide a fully ab initio determination of the particle quantum kinetic energies, free energy change upon exchanging hydrogen for deuterium and the isotope fractionation ratio in water. These properties, which selectively probe the quantum nature of the nuclear degrees of freedom, allow us to make direct comparison to recent experiments and elucidate how electronic exchange and correlation and nuclear quantum fluctuations determine the structure of the hydrogen bond in water.Comment: 8 pages, 2 figures, 2 table