Looking Back in Mathematical Modeling: Classroom Observations and Instructional Strategies

Theorists often characterize modeling as a cyclic problem-solving process. One builds the model, assesses its validity with regard to the underlying problem situation, and revises accordingly. The process halts when, in the opinion of the modeler, the model generates a valid solution to the underlying problem. Recent research suggests that students, like experts, employ cyclic modeling processes. Extensive observations of university and high school students’ modeling efforts, however, suggest the use of linear rather than cyclic modeling strategies. That is, novice modelers often fail to look back or revise their initial models. This paper offers empirical evidence on behalf of the linear modeling theory and identifies five factors that promote the use of linear modeling strategies: students’ conceptions of models and the modeling process, the perceived objectives of the modeling activity, constraints on time and resources, statistical misconceptions, and an overall lack of interest. The paper concludes with several promising instructional strategies (strategies that address students’ difficulties and promote reflective modeling behavior), as well as suggestions for future research.     

Probing the use of small‐angle light scattering for characterizing structure of titanium dioxide/low‐density polyethylene nanocomposites

Small‐angle light scattering (SALS) measurements were used to study the structure of titanium dioxide (TiO₂)/low‐density polyethylene (LDPE) nanocomposites. The results showed that the scattering from LDPE crystalline structures and the scattering from TiO₂ nanoparticles can be resolved and separated. It is shown that the independent effects of crystallization conditions and the presence of nanoparticle aggregates on the spherulitic structure of the LDPE matrix can be determined by analyzing the scattering patterns using the methods proposed. From the SALS results, we conclude that the nanoparticle surface chemistry affects both nucleation of spherulites and their structure particularly under rapid cooling conditions. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1084–1095, 2006     

Synthesis of substituted 5-aminomethyl tetrahydro-isoquinolines and dihydro-isoindoles

The synthesis of ten substituted aminomethylene tetrahydro-isoquinolines is described, proceeding in eight steps from 5-hydroxyisoquinoline via reductive amination of N-Boc tetrahydro-isoquinoline 5-carboxaldehyde. Likewise, reductive amination was used to prepare four substituted dihydro-isoindoles from the corresponding aldehyde. The dihydro-isoindole ring system was conveniently accessed via a 2+2+2 cycloaddition reaction.     

Comparison between biokinetics of inhaled plutonium nitrate and gadolinium oxide in humans and animals

Due to the paucity of human data after inhalation of different chemical forms of radionuclides, the implications for human exposure are often based on animal studies. This paper describes biokinetic studies of plutonium nitrate and gadolinium oxide in human volunteers and rats. The results, together with information from other studies with radionuclides, suggests that animal studies can be used with advantage for assessing the biokinetic behavior in humans, and for providing guidance on the assessment of intake and optimal monitoring regimens.     

Preparation of polymer colloids by chemical reactions in aerosols. I. Poly(p-tertiarybutylstyrene)

A procedure was developed by which polymer colloids can be prepared by polymerizing aerosol droplets of monomers with an initiator in the vapor state. This work describes the formation of poly(p-tertiarybutylstyrene) particles by exposing the corresponding monomer droplets to trifluoromethanesulfonic acid. It was found that the monomer-to-initiator mass ratio is the critical factor in determining the uniformity and morphology of the particles. Under ideal conditions spheres of narrow size distribution are obtained. Otherwise porous particles or soft particles with whiskers may develop. The aerosol was prepared in a falling film generator, but other procedures for producing monomer droplets may be used.     

The Role of Oxygen in the Antiviral Activity of Hypericin and Hypocrellin

The light-induced antiviral activity of hypericin and hypocrellin in the presence and absence of oxygen was examined under experimental conditions where the effect of oxygen depletion could be quantified. There was a significant reduction of light-induced antiviral activity of hypericin and hypocrellin under hypoxic conditions. Interestingly, antiviral activity of hypocrellin was not observed at low oxygen levels at which hypericin retained measurable virucidal activity. This suggests that additional pathways, such as the generation of protons from excited states of hypericin, may enhance the biological activity of activated oxygen species.     

MENTHOR,a database system for the storage and retrieval of three-dimensional molecular structures and associated data searchable by substructural,biologic, physical,or geometric properties

Summary MENTHOR is a database system for the storage and retrieval of three-dimensional coordinate and charge information on molecules as well as of traditional biological and physical properties. Our molecular graphics system retrieves from MENTHOR structural information in individual molecules and receptor map/macromolecular binding site hypotheses. Substructural searches of MENTHOR are used to find starting coordinates for molecular modeling and traditional database searches of MENTHOR identify compounds for which modeling is needed. It also forms the data to be searched with ALLADDIN, our substructure/geometric search program. MENTHOR expedites molecular modeling by organizing previous work and facilitating transmission of information between individuals. Examples from modeling of D-2 receptor agonists are shown.     

2,6-dicyano-1,5-dimethylsemibullvalene as a probe for homoaromatic molecules of the Dewar-Hoffman type

The 2,6-dicyano-1,5-dimethylsemibullvalene (2d) synthesized via the bicyclo[3.3.0]octanedione 7 exists as a classical ground state which is lower in energy by less than 5 kcal/mole than the homoaromatic transition of the Cope rearrangement of 2d.     

Microwave-assisted "libraries from libraries" approach toward the synthesis of allyl- and C-cyclopropylalkylamides

Cascade reactions of internal and terminal alkynes, zirconocene hydrochloride, dimethylzinc, and phosphinoyl imines (prepared in one step from aldehydes and diphenylphosphinoyl amide) lead to allylic phosphinoyl amides after aqueous workup. Microwave acceleration allows the completion of this one-pot reaction sequence in 10 min. These allylic amides can be converted into a variety of derivatives, including carbamates and sulfonamides, or reacted prior to workup with diiodomethane to give novel C-cyclopropylalkylamides. A solution-phase "libraries from libraries" approach was used to generate an intermediate 20-member library which was subsequently expanded to a 100-member library by a series of N-functionalizations. The biological activity was evaluated in an assay for competitive binding to the estrogen receptor (ERalpha), revealing three potent lead compounds of a new structural type.     

The structure and crystallization of thin water films on Pt(111)

When water is adsorbed on Pt(111) above 135 K several different ice structures crystallize, depending on the thickness of the ice layer. At low coverage water forms extended islands of ice with a (square root(37) x square root(37))R25(o) unit cell, which compresses as the monolayer saturates to form a (square root(39) x square root(39))R16(o) structure. The square root(39) low-energy electron diffraction (LEED) pattern becomes more intense as the second layer grows, remaining bright for films up of 10-15 layers and then fading and disappearing for films more than ca. 40 layers thick. The ice multilayer consists of an ordered square root(39) wetting layer, on which ice grows as a crystalline film which progressively loses its registry to the wetting layer. Ice films more than ca. 50 layers thick develop a hexagonal LEED pattern, the entire film and wetting layer reorienting to form an incommensurate bulk ice. These changes are reflected in the vibrational spectra which show changes in line shape and intensity associated with the different ice structures. Thin amorphous solid water films crystallize to form the same phases observed during growth, implying that these structures are thermodynamically stable and not kinetic phases formed during growth. The change from a square root(39) registry to incommensurate bulk ice at ca. 50 layers is associated with a change in crystallization kinetics from nucleation at the Pt(111) interface in thin films to nucleation of incommensurate bulk ice in amorphous solid water films more than 50 layers thick.