Catálogo de publicaciones - libros

Parallel multigrid methods belong to the most prominent tools for solving huge systems of (non-)linear equations arising from the discretisation of PDEs, as for instance in Computational Fluid Dynamics (CFD). However, the quality of (parallel) multigrid methods in regard of numerical and computational complexity mainly stands and falls with the smoothing algorithms (“smoother”) used. Since the inherent highly recursive character of many global smoothers (SOR, ILU) often impedes a direct parallelisation, the application of block smoothers is an alternative. However, due to the weakened recursive character, the resulting parallel efficiency may decrease in comparison to the sequential performance, due to a weaker total numerical efficiency. Within this paper, we show the consequences of such a strategy for the resulting total efficiency on the Hitachi SR8000-F1 if incorporated into the parallel CFD solver for 3D incompressible flow. Moreover, we analyse the numerical losses of parallel efficiency due to communication costs and numerical efficiency on several modern parallel computer platforms.

Enzymes play a key role in modern pharmaceutical research because they represent targets for the design of new drugs. In addition to the classical approach of inhibiting an enzyme by blocking its binding site with an inhibitor, the level of gene expression is now moving into the focus of interest. An important system for the investigation of mechanisms of transcriptional control is the Tet repressor/ operator (TetR/) system. We employ a combined classical/quantum mechanical approach to model the structure and the spectroscopic properties of the TetR-tetracycline complex. As our methods are based on semiempirical molecular orbital theory, we have also developed a parallel pseudodiagonalization technique for the major computational step in such calculations. The parallel pseudodiagonalizer gives acceptable performance for up to about eight processors.

Enzymes play a key role in research of the pharmaceutical industry because they represent targets for the design of new drugs. Therefore, the determination of the mode of action of enzymes is one of the great challenges of modern chemistry and an important task in . The situation is aggravated by the fact that the number of enzymes with known three-dimensional structure is small compared to the number of pharmaceutically relevant enzymes. Therefore, approaches for searching for a new depend on the information available about the protein structure and the ligands binding to a particular target. In this article we present a methodology based on a ligand-based approach. It can also be employed if the three-dimensional structure of the target of interest is not known. The structures of a set of molecules are superimposed based on a of a (GA) to evaluate their . This is an important step in the identification of a for molecules that bind to the same receptor. With this method it is possible to determine a complementary map of the receptor binding pocket.

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.

In deformations of polynomial functions one may encounter “singularity exchange at infinity” when singular points disappear from the space and produce “virtual” singularities which have an influence on the topology of the limit polynomial. We find several rules of this exchange phenomenon, in which the total quantity of singularity turns out to be not conserved in general.

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.

In this paper, we study numerically the renormalization of the electron-spin (el-sp) interaction or vertex due to Coulomb correlations in a two-dimensional one-band Hubbard model with spin-fluctuation momentum transfer q = (π, π). Our simulations are based on a new numerically exact technique to extract the vertex, which is especially important for the physically relevant case, i.e., strong correlations, which cannot be controlled perturbatively. We find that the renormalized el-sp vertex decreases quite generally with increasing doping from the underdoped to the overdoped region. In the underdoped region, the corresponding effective pairing interaction increases strongly with lowering temperature in the weak- to intermediate-correlation regime. In contrast to this, it depends weakly on temperature in the strong-correlation regime. This behavior in the physically relevant strong-correlation case is due to a near cancellation between the temperature-driven enhancement of the spin susceptibility χ and the reduction of the el-sp interaction vertex. Thus, the spin-mediated d-wave attraction, which is peaked in weak coupling due to χ, is strongly reduced due to the el-sp vertex corrections for strong correlations.

We discuss single particle dynamics of the half-filled 2 Hubbard model at → 0 calculated within the dynamical cluster approximation, using numerical renormalization group as non-perturbative cluster solver, which requires the use of parallel architectures with large number of processors and memory. In addition, fast temporal storage for large out-of-core matrices is needed. The results obtained indicate that the half-filled 2 Hubbard model at → 0 is a paramagnetic insulator for values of the Coulomb interaction in strong contrast to weak-coupling theories.

We compare the results of different ab-initio density-functional methods (97, VASP, ABINIT, ) and approximations for the electronic, structural, and dynamical properties of a variety of single crystals, namely the ionic conductors CaF, BaF, ZrO, and LaF, and the semiconductors CdS and CdSe. In particular, we have ported the code to the Hitachi computer. These results are basic for the more extensive and current calculations of the static and lattice-dynamical properties of these systems as well as of systems like ZrO and mixed-crystal systems like CdSSe. We also report preliminary neutron scattering data at various temperatures for the structure of LaF.

We report on the successful numerical implementation of an original method for the accurate quantum treatment of helium under electromagnetic driving. Our approach is the first to allow for a description of the highly complex quantum dynamics of this system, in the entire non-relativistic parameter regime, i.e., it provides full spectral and dynamical information on the ionization of the atomic ground state by optical fields, as well as on the dynamics of doubly excited Rydberg states under radiofrequency driving. As a by-product, the non-trivial role of the dimension of configuration space for the field-free dynamics of doubly excited helium is elucidated.