A 10000 particle molecular dynamics model with long range forces

A technique is described for the computer simulation of the motion of 10000 simulated molecules. The number of computer operations per time-step is proportional to the number of simulated particles even though the force of interaction may be long range and no force cut-off is employed.     

Spectral tolerance determination for multivariate optical element design

Recent reports from our laboratory have described a method for all-optical multivariate chemometric prediction from optical spectroscopy. The concept behind this optical approach is that a spectral pattern (a regression vector) can be encoded into the spectrum of an optical filter. The key element of these measurement schemes is the multivariate optical element (MOE), a multiwavelength interference-based spectral discriminator that is tied to the regression vector of a particular measurement. The fabrication of these MOEs is a complex operation that requires precise techniques. However, to date, no quantitative means of determining the allowable design/ manufacturing errors for MOEs has existed. The purpose of the present report is to show how the spectroscopy of a sample is used to define the accuracy with which MOEs must be designed and manufactured. We conclude this report with a general treatment of spectral tolerance and a worked example. The worked example is based on actual experimental measurements. We show how the spectral bandpass is defined operationally in a real problem, and how the statistics of the theoretical regression vector influence both the bandpass and the minimum tolerances. In the experimental example, we demonstrate that tolerances range continuously between 1 (totally tolerant) to approximately 10^–3 (0.1% T) in this problem. Received: 21 August 2000 / Revised: 30 October 2000 / Accepted: 4 November 2000     

Electrochemical oxidation of a carbon black loaded polymer electrode in aqueous electrolytes

The suitability of a polymeric composite material for use as part of an anode structure in a cathodic protection system has been examined. The composite material was a conductive blend (volume resistivity typically 1.5 Ω cm) of carbon black in a polyethylene binder. A long operational lifetime for the material demands that the rate of carbon loss must be low. In the work reported here, electrochemical and in situ analytical techniques were employed to characterise the performance of the material over a wide range of anodic current densities in a variety of aqueous electrolytes. The predominant anodic electrochemical reaction on the polymeric material is CO₂ formation in acid and neutral solutions, which causes loss of carbon from the surface and the development of a non-conducting layer of polyethylene. The characteristics of the reaction suggest that it occurs via the discharge of H₂O. In alkaline pH, however, the anodic reactions are more complex. A high OH⁻ concentration (pH 12 or higher) favours the formation of oxygen rather than CO₂, particularly at low anodic potentials. The presence of CO₃ ²⁻ in the electrolyte catalyses the evolution of oxygen at pH values as low as 9. The electrochemical formation of oxygen always occurs in parallel with the generation of some humic acid in the solution. Received: 23 July 1998 / Accepted: 17 November 1998     

Simulation studies of the fidelity of biomolecular structure ensemble recreation

We examine the ability of Bayesian methods to recreate structural ensembles for partially folded molecules from averaged data. Specifically we test the ability of various algorithms to recreate different transition state ensembles for folding proteins using a multiple replica simulation algorithm using input from "gold standard" reference ensembles that were first generated with a Go-like Hamiltonian having nonpairwise additive terms. A set of low resolution data, which function as the "experimental" phi values, were first constructed from this reference ensemble. The resulting phi values were then treated as one would treat laboratory experimental data and were used as input in the replica reconstruction algorithm. The resulting ensembles of structures obtained by the replica algorithm were compared to the gold standard reference ensemble, from which those "data" were, in fact, obtained. It is found that for a unimodal transition state ensemble with a low barrier, the multiple replica algorithm does recreate the reference ensemble fairly successfully when no experimental error is assumed. The Kolmogorov-Smirnov test as well as principal component analysis show that the overlap of the recovered and reference ensembles is significantly enhanced when multiple replicas are used. Reduction of the multiple replica ensembles by clustering successfully yields subensembles with close similarity to the reference ensembles. On the other hand, for a high barrier transition state with two distinct transition state ensembles, the single replica algorithm only samples a few structures of one of the reference ensemble basins. This is due to the fact that the phi values are intrinsically ensemble averaged quantities. The replica algorithm with multiple copies does sample both reference ensemble basins. In contrast to the single replica case, the multiple replicas are constrained to reproduce the average phi values, but allow fluctuations in phi for each individual copy. These fluctuations facilitate a more faithful sampling of the reference ensemble basins. Finally, we test how robustly the reconstruction algorithm can function by introducing errors in phi comparable in magnitude to those suggested by some authors. In this circumstance we observe that the chances of ensemble recovery with the replica algorithm are poor using a single replica, but are improved when multiple copies are used. A multimodal transition state ensemble, however, turns out to be more sensitive to large errors in phi (if appropriately gauged) and attempts at successful recreation of the reference ensemble with simple replica algorithms can fall short.     

Super-Alfvénic propagation of substorm reconnection signatures and Poynting flux

The propagation of reconnection signatures and their associated energy are examined using kinetic particle-in-cell simulations and Cluster satellite observations. It is found that the quadrupolar out-of-plane magnetic field near the separatrices is associated with a kinetic Alfvén wave. For magnetotail parameters, the parallel propagation of this wave is super-Alfvénic (V(∥) ～ 1500-5500 km/s) and generates substantial Poynting flux (S ～ 10(-5)-10(-4) W/m(2)) consistent with Cluster observations of magnetic reconnection. This Poynting flux substantially exceeds that due to frozen-in ion bulk outflows and is sufficient to generate white light aurora in Earth's ionosphere.     

Papieruntersuchung

Ohne Zusammenfassung     

Zero-energy Fields on Real Projective Space

A smooth 1-form on real projective space with vanishing integral along all geodesics is said to have zero energy. Such a 1-form is necessarily the exterior derivative of a smooth function. We formulate a general version of this theorem for tensor fields on real projective space and prove it using methods of complex analysis. A key ingredient is the cohomology of involutive structures.     

Examples of unbounded homogeneous domains in complex space

We present several examples of homogeneous domains in complex space that do not have bounded realisations. The domains are equivalent to tubes over affinely homogeneous domains in real space.