Catálogo de publicaciones - libros

Taking into account that a proper description of disordered systems should focus on distribution functions, the authors develop a powerful numerical scheme for the determination of the probability distribution of the local density of states (LDOS), which is based on a Chebyshev expansion with kernel polynomial refinement and allows the study of large finite clusters (up to 100). For the three-dimensional Anderson model it is demonstrated that the distribution of the LDOS shows a significant change at the disorder induced delocalisation-localisation transition. Consequently, the so-called typical density of states, defined as the geometric mean of the LDOS, emerges as a natural order parameter. The calculation of the phase diagram of the Anderson model proves the efficiency and reliability of the proposed approach in comparison to other localisation criteria, which rely, e.g., on the decay of the wavefunction or the inverse participation number.

Numerical solutions to the problem of seismic wave propagation, that allow simulations of complete wave fields through 3D structures, are currently revolutionizing seismology and related fields. So far - in order to calculate theoretical seismograms in the observed frequency bands - one had to resort to solution methods with severe limitations (e.g., ray theoretical approximations, one-dimensional structures, perturbation theory, etc.). Only in the past few years, computational power has allowed us to simulate wave fields that can be directly compared to observations. Even though the computations still require substantial resources, the methodologies developed in the past decade are beginning to enter routine processing steps in all branches ranging from exploration seismics to global seismology. Here we present recent examples in global seismology (spectral element modeling of global wave propagation) and earthquake scenario simulations, their relation to shaking hazard estimation, and associated problems. The next decade will see fundamental changes in the way data fitting (inverse problem, parameter estimation) is done in seismology with the potential of advances in several fields of Earth Sciences.

We study the scaling properties of the quantum projected (5) model in three dimensions by means of a highly accurate Quantum-Monte-Carlo analysis. Within the parameter regime studied (temperature and system size), we show that the scaling behavior is consistent with a (5)-symmetric critical behavior in the numerically accessible region. This holds both when the symmetry breaking is caused by quantum fluctuations only as well as when also the static (mean-field) symmetry is moderately broken. We argue that possible departure away from the (5) - symmetric scaling occurs only in an extremely narrow parameter regime, which is inaccessible both experimentally and numerically.

Inference of large phylogenetic trees using elaborate statistical models is computationally extremely intensive. Thus, progress is primarily achieved via algorithmic innovation rather than by brute-force allocation of all available computational resources. We present simple heuristics which yield accurate trees for synthetic (simulated) as well as real data and improve execution time compared to the currently fastest programs. The new heuristics are implemented in a sequential program (RAxML) which is available as open source code. Furthermore, we present a non-deterministic parallel version of our algorithm which in some cases yielded super-linear speedups for computations with 1000 organisms. We compare sequential RAxML performance with the currently fastest and most accurate programs for phylogenetic tree inference based on statistical methods using 50 synthetic alignments and 9 real-world alignments comprising up to 1000 sequences. RAxML outperforms those programs for real-world data in terms of speed and final likelihood values.

The quantum chemistry software , which implements various density functional methods to determine the electronic structure of molecular systems, has been ported to and optimized for the use on the Hitachi SR8000 supercomputer platform at Leibniz Rechenzentrum München. The effort focused on tuning the code and extending it by methods that allow the simulation of molecules in an environment, e.g., in solution or adsorbed at a solid surface or in a zeolite cavity.