Functions: a modelling tool in mathematics and science

It is difficult for the students to transfer concepts, ideas and procedures learned in mathematics to a new and unanticipated situation in science. An alternative to this traditional transfer method stresses the importance of modelling activities in an interdisciplinary context between mathematics and science. In the paper we introduce a modelling approach to the concept of function in upper secondary school is introduced. We discuss pedagogical and didactical issues concerning the interplay between mathematics and science. The discussion is crystallized into a didactical model for interdisciplinary instruction in mathematics and science. The model is considered as an iterative movement with two phases: (1) the horizontal linking of the subjects: Situations from science are embedded in contexts which are mathematized by the students, (2) the vertical structuring in the subjects: The conceptual anchoring of the students' constructs from the horizontal linking in the systematic and framework of mathematics and science respectively.     

Unsymmetrically Substituted Benzonaphthoporphyrazines: A New Class of Cationic Photosensitizers for the Photodynamic Therapy of Cancer*

Abstract— Unsymmetrical zinc(II) complexes of benzonaphthoporphyrazines 5 a-12a bearing between one and eight pyri-dyloxy substituents are synthesized by statistical tetra-merization of 6-(l,l-dimethylethyl)-2,3-naphthalenedi-carbonitrile (1) with 4-(3-pyridyloxy)- or 4,5-bis-(3-pyri-dyloxy)-1,2-benzenedicarbonitrile (2, 3). Methylation of 5a-12a leads to the cationic pyridyloxybenzonaphtho-porphyrazines 5b- 12b having between one to eight positive charges. The Q-band transition in the visible spectra exhibits a bathochromic shift from 680 to 760 nm dependent upon the number of annelated naphthalene rings. The singlet oxygen quantum yields of the benzonaphthoporphyrazines determined by the dye-sensitized photoox-idation of 1,3-diphenylisobenzofurane is surprisingly high (in the range of zinc phthalocyanine). The photoox-idative stabilities of the photosensitizers described quantitatively by first-order kinetics decrease with the number of annelated naphtho groups. A linear correlation between the logarithm of the decomposition rate constant and the position of the highest occupied molecular orbital (HOMO)-level of the photosensitizers is found. Destabi-lization of the HOMO leads to a decrease of the pho-tostability. Due to their adjustable long wavelength absorption, their intramolecular polarity axis and their different hydrophilic/hydrophobic character, these novel compounds may be suitable photosensitizers for the photodynamic therapy of cancer.     

Increased oxygen transfer in a yeast fermentation using a microbubble dispersion

A microbubble dispersion (MBD) was used to supply oxygen for aerobic fermentations in a standard 2 L stirred tank fermenter. The microbubble dispersion was formed using only surfactants produced naturally. Growth rates ofSaccharomyces cerevisiae cultures were found to be equal or greater with MBD sparging than with gas sparging. The oxygen transfer coefficent with MBD sparging was found to be 190/h and independent of impeller speed from 100–580 rpm. The oxygen transfer coefficient with air sparging rose from 55 to 132/h over the same range of impeller speeds. Power requirements for the fermenter systems were estimated.     

Self-assembly of oligomeric porphyrin rings

A cobalt porphyrin equipped with two different but geometrically complementary pyridine ligands self-assembles to form an unusually stable complex with approximately 12 porphyrin monomers arranged in a macrocyclic array.     

Modeling laser-induced incandescence of soot: a summary and comparison of LII models

We have performed a comparison of ten models that predict the temporal behavior of laser-induced incandescence (LII) of soot. In this paper we present a summary of the models and comparisons of calculated temperatures, diameters, signals, and energy-balance terms. The models were run assuming laser heating at 532 nm at fluences of 0.05 and 0.70 J/cm² with a laser temporal profile provided. Calculations were performed for a single primary particle with a diameter of 30 nm at an ambient temperature of 1800 K and a pressure of 1 bar. Preliminary calculations were performed with a fully constrained model. The comparison of unconstrained models demonstrates a wide spread in calculated LII signals. Many of the differences can be attributed to the values of a few important parameters, such as the refractive-index function E(m) and thermal and mass accommodation coefficients. Constraining these parameters brings most of the models into much better agreement with each other, particularly for the low-fluence case. Agreement among models is not as good for the high-fluence case, even when selected parameters are constrained. The reason for greater variability in model results at high fluence appears to be related to solution approaches to mass and heat loss by sublimation. PACS 65.80.+n; 78.20.Nv; 42.62.-b; 44.05.+e     

The isothermal flash problem. Part II. Phase-split calculation

Algorithms for calculation of multiphase equilibrium at given temperature and pressure using a single Equation of State as the thermodynamic model are described. The use of stability analysis to generate initial estimates and of second order convergence methods lead to rapid solution even in the immediate vicinity of critical points.     

Effect of the wavelength dependence of the emissivity on inferred soot temperatures measured by spectrally resolved laser-induced incandescence

Flame-generated soot was heated using a pulsed laser, and temperatures of the irradiated soot were inferred by fitting the Planck function to spectrally resolved laser-induced incandescence with the temperature as an adjustable parameter. The effect of the wavelength dependence of the emissivity on the inferred temperatures of the irradiated soot was studied using selected expressions for the soot emissivity in the fit. Depending upon the choice of the functional form of the emissivity, the maximum temperature reached by the soot during the laser pulse was calculated to span a range of 341 K (3475–3816 K) at a 1064-nm laser fluence of 0.1 J/cm² and 456 K (4115–4571 K) at a 1064-nm laser fluence of 0.4 J/cm² with a 1σ standard deviation about the mean of ∼25 K. Comparison of the present results with temperature measurements from previous studies suggests that the emissivity may depend on flame conditions and that further investigation on the subject is needed. The use of two-color or spectrally resolved LII to infer the soot temperature during or after laser heating requires a careful characterization of the wavelength dependence of the emissivity. The spread in temperature leads to large uncertainties regarding the physico-chemical processes occurring at the surface of the soot during the laser heating.