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     

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.     

Direct evidence for a three-dimensional magnetic flux rope flanked by two active magnetic reconnection X lines at Earth's magnetopause

We report the direct detection by three THEMIS spacecraft of a magnetic flux rope flanked by two active X lines producing colliding plasma jets near the center of the flux rope. The observed density depletion and open magnetic field topology inside the flux rope reveal important three-dimensional effects. There was also evidence for nonthermal electron energization within the flux rope core where the fluxes of 1-4 keV superthermal electrons were higher than those in the converging reconnection jets. The observed ion and electron energizations differ from current theoretical predictions.     

Light- and Manganese-Initiated Borylation of Aryl Diazonium Salts: Mechanistic Insight on the Ultrafast Time-Scale Revealed by Time-Resolved Spectroscopic Analysis

Manganese-mediated borylation of aryl/heteroaryl diazonium salts emerges as a general and versatile synthetic methodology for the synthesis of the corresponding boronate esters. The reaction proved an ideal testing ground for delineating the Mn species responsible for the photochemical reaction processes, that is, involving either Mn radical or Mn cationic species, which is dependent on the presence of a suitably strong oxidant. Our findings are important for a plethora of processes employing Mn-containing carbonyl species as initiators and/or catalysts, which have considerable potential in synthetic applications.     

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.     

Production of muon pairs in the continuum region by 39.5 GeV/cπ±, K±, p and p beams incident on a copper target

General features of the inclusive hadroproduction of muon pairs of mass greater than 1.5 GeV/c² are shown. For incident π^?, the data extend up to M=5.7 GeV/c² (i.e.M²/s≈0.4). The scaling cross section M³dσ/dM for π^?N reactions is much flatter than that for pN reactions and exceeds the latter by two to three orders of magnitude at large M²/s.     

Aspects of Dirac Operators in Analysis

We give a review of the analysis behind several examples of Dirac-type operators over manifolds arising in Clifford analysis. These include the Atiyah-Singer-Dirac operator acting on sections of a spin bundle over a spin manifold. It also includes several Dirac operators arising over conformally flat spin manifolds including hyperbolic space. Links to classical harmonic analysis are pointed out.

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Received: June 2007