Construction of sundials via vectors

A method based on oblique projection is presented for construction of sundials. The derived formulas are classical, but usage of vectors and projections renders a coherent presentation rather than a number of special cases. The presented work is aimed to be useful for those taking a beginning module on vector algebra.     

An elementary algorithm to evaluate trigonometric functions to high precision

Evaluation of the cosine function is done via a simple Cordic-like algorithm, together with a package for handling arbitrary-precision arithmetic in the computer program Matlab. Approximations to the cosine function having hundreds of correct decimals are presented with a discussion around errors and implementation.     

Sticking efficiency of nanoparticles in high-velocity collisions with various target materials

In order to find reliable collector surfaces for the Mesospheric Aerosol – Genesis, Interaction and Composition (MAGIC) sounding rocket experiment, intended to collect atmospheric nanoparticles, the sticking efficiency of nanoparticles was measured on several targets of different materials. The nanoparticles were generated by a molecular beam apparatus in Jena, Germany, by laser ablation (Al₂O₃ particles, diameter 5–50 nm) and by laser pyrolysis (carbon particles, diameter 10–20 nm). In a vacuum environment (>10⁻⁵ mbar) the particles condensed from the gas phase, formed a particle beam, and were accelerated to ∼ ∼1 km/s. The sticking efficiency on the target materials carbon, gold and grease was measured by a microbalance. Results demonstrate moderate to high sticking probabilities. Thus, the capture and retrieval of atmospheric nanoparticles was found to be quantitatively feasible.     

Computation of affinity and selectivity: Binding of 2,4-diaminopteridine and 2,4-diaminoquinazoline inhibitors to dihydrofolate reductases

Binding energy calculations for complexes of mutant and wild-type human dihydrofolate reductases with 2,4-diaminopteridine and 2,4-diaminoquinazoline inhibitors are reported. Quantitative insight into binding energetics of these molecules is obtained from calculations based on force field energy evaluation and thermal sampling by molecular dynamics simulations. The calculated affinity of methotrexate for wild-type and mutant enzymes is reasonably well reproduced. Truncation of the methotrexate glutamate tail results in a loss of affinity by several orders of magnitude. No major difference in binding strength is predicted between the pteridines and the quinazolines, while the N-methyl group present in methotrexate appears to confer significantly stronger binding. The recent improvement, which is used here, of our linear interaction energy method for binding affinity prediction, as well as problems with treating charged and flexible ligands are discussed. This approach should be suitable in a drug discovery context for prediction of binding energies of new inhibitors prior to their synthesis, when some information about the binding mode is available.     

Chaotic particle motion under linear surface waves

We investigate the motion of infinitesimal particles in the flow field inside the fluid under a traveling surface wave. It is shown that, even for two-dimensional waves, a superposition of two or more traveling harmonic waves is enough to generate chaotic particle motion, i.e., Lagrangian chaos. (c) 1996 American Institute of Physics.