Nematic reorientation in electric and magnetic fields

Homogeneous reorientation processes of two nematic liquid crystals in electric and magnetic fields have been observed using proton nuclear magnetic resonance spectroscopy (NMR). Using a recently developed experimental set-up, it is possible to study reorientation processes in liquid crystals by means of NMR experiments in a very flexible way. The time constant τ describing these processes has been determined as a function of the applied electric field. It emerges that the electric field cannot only be used to increase the reorientation time but also to slow the director reorientation by approximately one order of magnitude. Experimental data for 5CB and a fluorinated liquid crystal (BCH-5 FFF) are presented. The reorientation time measured as a function of the electric field can be used to calculate the rotational viscosity γ ₁. By repeating these experiments at different temperatures it was possible to investigate the temperature behaviour of γ ₁.     

Chaotic systems in complex phase space

This paper examines numerically the complex classical trajectories of the kicked rotor and the double pendulum. Both of these systems exhibit a transition to chaos, and this feature is studied in complex phase space. Additionally, it is shown that the short-time and long-time behaviours of these two PT-symmetric dynamical models in complex phase space exhibit strong qualitative similarities.     

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An Efficient Approximation Algorithm for Minimizing Makespan on Uniformly Related Machines

We give a new and efficient approximation algorithm for scheduling precedence-constrained jobs on machines with different speeds. The problem is as follows. We are given n jobs to be scheduled on a set of m machines. Jobs have processing times and machines have speeds. It takes p_j/s_i units of time for machine i with speed s_i to process job j with processing requirement p_j. Precedence constraints between jobs are given in the form of a partial order. If j k, processing of job k cannot start until job j's execution is completed. The objective is to find a non-preemptive schedule to minimize the makespan of the schedule. Chudak and Shmoys (1997, “Proceedings of the Eighth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA),” pp. 581–590) gave an algorithm with an approximation ratio of O(log m), significantly improving the earlier ratio of due to Jaffe (1980, Theoret. Comput. Sci.26, 1–17). Their algorithm is based on solving a linear programming relaxation. Building on some of their ideas, we present a combinatorial algorithm that achieves a similar approximation ratio but runs in O(n³) time. Our algorithm is based on a new and simple lower bound which we believe is of independent interest.     

Going beyond the self-consistent mean-field with the symmetry-restored generator coordinate method

Starting from successful self-consistent mean-field models, this paper discusses why and how to go beyond the mean field approximation. To include long-range correlations from fluctuations in collective degrees of freedom, one has to consider symmetry restoration and configuration mixing, which give access to ground-state correlations and spectroscopy.     

Iron speciation in natural hyperacid water investigated by Mössbauer spectroscopy

We have demonstrated the usefulness of the archetypical solid state-technique of Mössbauer spectroscopy to non-invasive studies of the redox and coordination chemistry of iron in a natural hyperacid solution from Iron Mountain, CA. Suitable fast cooling conditions were used to prepare a glass from the natural solution. Measurements of spectra at low temperatures (6 and 15 K) and in large external magnetic fields (6 T) of the glassy, frozen solution revealed a behaviour characteristic of slow paramagnetic relaxation of ferric ions. Analyses of the spectral components are in good agreement with dominance of hexaaquairon(III) ions.     

Dynamic clustering threshold reduces conformer ensemble size while maintaining a biologically relevant ensemble

Representing the 3D structures of ligands in virtual screenings via multi-conformer ensembles can be computationally intensive, especially for compounds with a large number of rotatable bonds. Thus, reducing the size of multi-conformer databases and the number of query conformers, while simultaneously reproducing the bioactive conformer with good accuracy, is of crucial interest. While clustering and RMSD filtering methods are employed in existing conformer generators, the novelty of this work is the inclusion of a clustering scheme (NMRCLUST) that does not require a user-defined cut-off value. This algorithm simultaneously optimizes the number and the average spread of the clusters. Here we describe and test four inter-dependent approaches for selecting computer-generated conformers, namely: OMEGA, NMRCLUST, RMS filtering and averaged-RMS filtering. The bioactive conformations of 65 selected ligands were extracted from the corresponding protein:ligand complexes from the Protein Data Bank, including eight ligands that adopted dissimilar bound conformations within different receptors. We show that NMRCLUST can be employed to further filter OMEGA-generated conformers while maintaining biological relevance of the ensemble. It was observed that NMRCLUST (containing on average 10 times fewer conformers per compound) performed nearly as well as OMEGA, and both outperformed RMS filtering and averaged-RMS filtering in terms of identifying the bioactive conformations with excellent and good matches (0.5 < RMSD < 1.0 Å). Furthermore, we propose thresholds for OMEGA root-mean square filtering depending on the number of rotors in a compound: 0.8, 1.0 and 1.4 for structures with low (1–4), medium (5–9) and high (10–15) numbers of rotatable bonds, respectively. The protocol employed is general and can be applied to reduce the number of conformers in multi-conformer compound collections and alleviate the complexity of downstream data processing in virtual screening experiments.