Supramolecular dendrimer chemistry: using dendritic crown ethers to reversibly generate functional assemblies

A series of crown ether derivatives functionalised with dendritic branching based on l-lysine repeat units has been synthesised. The ability of these receptors to interact with cationic guests has been investigated using NMR and mass spectrometric techniques. Binding constants have been evaluated, some using competitive binding assays, and these indicate that the strength of interaction between the encapsulated crown-ether and cationic guests decreases with increasing dendritic functionalisation. The interaction of these dendritic branches with ditopic ammonium cation functionalised templates has been investigated, and Job plot analysis indicates the formation of 2:1 (branch/template) stoichiometric complexes in MeOH solution. These supramolecular assemblies have been disassembled by the addition of potassium cations, hence achieving controlled release of the template back into solution. This process has been investigated by NMR methods and the effect of counteranion on these studies is reported. The use of ditopic ammonium cations possessing long alkyl spacer chains as templates has also been investigated, and in this case, the 2:1 assembly that forms, goes on to achieve higher order levels of organisation, hence gelating the solvent. This particular system is therefore a rare example in which discrete, characterisable dendritic supermolecules possess an inherent potential for further supramolecular assembly, to yield new materials.     

Electronic Resources: The Ohio State University EESEE Project

Electronic resources aid in the teaching and learning of statistics by providing data that may be used interactively by teachers and students. By interacting with the data students are encouraged to discover knowledge and thereby gain a deeper understanding of statistical concepts. The Electronic Encyclopedia of Statistical Examples and Exercises (EESEE) is an electronic resource that includes over 80 'real-world' examples about the uses and abuses of statistics. These examples are drawn from published and printed media and the diverse range of subject-matter areas make it suitable for use in any statistics course.     

A mathematical description of the acoustic coupling of the mass/spring model

This paper describes hybrid mathematical model which couples the mechanics of the mass/spring model to the acoustic wave propagation model for use in generating the acoustic signal emitted by complex structures of paper fibres under strain. A discussion of the coupling method is presented including remarks on the errors encountered intrinsic to the discretisation scheme. The numerical results of a vibrating rubber band and a vibrating paper fibre are compared to their experimental counterparts. The fundamental frequencies of the acoustic signals are compared showing a close agreement between the experimental and numerical results.     

Ergodic control of reflected diffusions with jumps

We discuss ergodicity properties of a controlled jumps diffusion process reflected from the boundary of a bounded domain. The control parameters act on the drift term and on a first-order-type jump density. The controlled process is generated via a Girsanov change of probability, and a long-run average criterion is optimized. An optimal stationary feedback is constructed by means of the Hamilton-Jacobi-Bellman equation.     

CIRCE: a dedicated storage ring for coherent THz synchrotron radiation

We present the concepts for an electron storage ring dedicated to and optimized for the production of stable coherent synchrotron radiation (CSR) over the far-infrared terahertz wavelength range from 200 μm to about 1 cm. CIRCE (Coherent InfraRed CEnter) will be a 66 m circumference ring located on top of the ALS booster synchrotron shielding tunnel and using the existing ALS injector. This location provides enough floor space for both the CIRCE ring, its required shielding, and numerous beamlines. We briefly outline a model for CSR emission in which a static bunch distortion induced by the synchrotron radiation field is used to significantly extend the stable CSR emission towards higher frequencies. This model has been verified with experimental CSR results. We present the calculated CIRCE photon flux where a gain of 6–9 orders of magnitude is shown compared to existing far-IR sources. Additionally, the particular design of the dipole vacuum chamber has been optimized to allow an excellent transmission of these far-infrared wavelengths. We believe that the CIRCE source can be constructed for a modest cost.