A fresh look at the validity of diffusion equations for modelling phosphorescence imaging of biological tissue

Phosphorescence lifetime imaging has become a widely used technique for tomographic oxygen imaging. The conventional model used to characterize photon transport in phosphorescence imaging is two coupled diffusion equations. On the premise that the total energy of excitation and phosphorescence photon flows must be conserved, we derive the diffusion equations in phosphorescence imaging and show that there must be an additional term to account for the transport of phosphorescent photons. This additional term accounts for the transport of phosphorescence photon energy density due to its gradients. The significance of this term in modelling phosphorescence in biological tissue is assessed.

A fresh look at the validity of the diffusion approximation for modeling fluorescence spectroscopy in biological tissue

Fluorescence has become a widely used technique for applications in noninvasive diagnostic tissue spectroscopy. The standard model used for characterizing fluorescence photon transport in biological tissue is based on the diffusion approximation. On the premise that the total energy of excitation and fluorescent photon flows must be conserved, we derive the widely used diffusion equations in fluorescence spectroscopy and show that there must be an additional term to account for the transport of fluorescent photons. The significance of this additional term in modeling fluorescence spectroscopy in biological tissue is assessed.

Mathematical modelling of deep bed filtration

Numerous mathematical models have been developed to evaluate both initial and transient stage removal efficiency of deep bed filters. Microscopic models either using trajectory analysis or convective-diffusion equations were used to compute the initial removal efficiency. These models predicted the removal efficiency under favorable filtration conditions quantitatively, but failed to predict the removal efficiency under unfavorable conditions. They underestimated the removal efficiency under unfavorable conditions. Thus, semi-empirical formulations were developed to compute initial removal efficiencies under unfavorable conditions. Also, correction for the adhesion of particles onto filter grains improved the results obtained for removal efficiency from the trajectory analysis. Macroscopic models were used to predict the transient stage removal efficiency of deep bed filters. O’Melia and Ali’s model assumed that the particle removal is due to filter grains as well as the particles that are already deposited onto the filter grain. Thus, semi-empirical models were used to predict the ripening of filtration. Several modifications were made to the model developed by O’Melia and Ali to predict the deterioration of particle removal during the transient stages of filtration. Models considering the removal of particles under favorable conditions and the accumulation of charges on the filter grains during the transient stages were also developed. This paper evaluates those models and their applicability under different operating conditions of filtration.

Deep bed filtration : mathematical models and observations

Numerous mathematical models have been developed to evaluate both initial and transient stage removal efficiency of deep bed filters. Microscopic models either using trajectory analysis or convective diffusion equations were used to compute the initial removal efficiency. These models predicted the removal efficiency under favorable filtration conditions quantitatively, but failed to predict the removal efficiency under unfavorable conditions. They underestimated the removal efficiency under unfavorable conditions. Thus, semi-empirical formulations were developed to compute initial removal efficiencies under unfavorable conditions. Also, correction for the adhesion of particles onto filter grains improved the results obtained for removal efficiency from the trajectory analysis. Macroscopic models were used to predict the transient stage removal efficiency of deep bed filters. The O’Melia and Ali1 model assumed that the particle removal is due to filter grains as well as the particles that are already deposited onto the filter grain. Thus, semi-empirical models were used to predict the ripening of filtration. Several modifications were made to the model developed by O’Melia and Ali to predict the deterioration of particle removal during the transient stages of filtration. Models considering the removal of particles under favorable conditions and the accumulation of charges on the filter grains during the transient stages were also developed. This article evaluates those models and their applicability under different operating conditions of filtration.

A new model to imitate the foraging behavior of Physarum polycephalum on a nutrient-poor substrate

Researches on Physarum polycephalum show that methods inspired by the primitive unicellular organism can construct an efficient network and solve some complex problems in graph theory. Current models simulating the intelligent behavior of Physarum are mainly based on Hagen-Poiseuille Law and Kirchhoff Law, reaction-diffusion, Cellular Automaton and multi-agent approach. In this paper, based on an assumption that the plasmodium of Physarum forages for food along the gradient of chemo-attractants on a nutrient-poor substrate, a new model is proposed to imitate its intelligent foraging behavior. The key point of the model is that the growth of Physarum is determined by the simple particle concentration field relating the distance to food source and the shape of food source on a nutrient-poor substrate. To verify this model, numerical experiments are conducted according to Adamatzky[U+05F3]s experiment. Results in spanning tree construction by this model are almost the same as those of Physarum and Oregonator model. The proposed model can also imitate Physarum to avoid repellents. Furthermore, the Euclidean Spanning tree built by this model is similar to its corresponding Minimal Euclidean Spanning tree.

Cr(N,C) diffusion coating formation on pre-nitrocarburised H13 tool steel

The microstructural processes of Cr(N,C) coating formation by thermoreactive deposition and diffusion (TRD) on pre-nitrocarburised H13 tool steel were studied. Both nitrocarburising and TRD were performed in fluidized bed furnaces at 570 °C. During TRD, chromium was transferred from chromium powder in the fluidized bed, to the nitrocarburised substrates by gas-phase reactions initiated by reaction of HCl gas with the chromium. Addition of 30% H2 to the input inert gas was found to increase the rate of coating formation, although hydrogen reduction resulted in rapid loss of nitrogen to the surface. The reason for the increased rate of coating formation could not be established without further investigation, although several possible explanations have been proposed. It was found that porosity and the formation of an iron nitride ‘cover layer’ during nitrocarburising were the biggest influences on the microstructure of the Cr(N,C) coating. Microstructural characterization of the coatings was performed by scanning electron microscopy (SEM), X-ray diffraction (XRD) and glow discharge optical emission spectroscopy (GDOES).

What can student-generated diagrams tell us about their understanding of chemical equations?

Chemical equations are representations that use symbols to summarise the net changes occurring in a reaction whereas depictions such as drawings of the submicroscopic level provide representations of the chemical transformations. While the ability to balance and interpret chemical equations is key to understanding many concepts in chemistry, many undergraduate chemistry students struggle to master these skills. The equations contain a great deal of implicit information and novices may not be able to make the connection between the equation and the actual chemical transformations that are occurring. This paper reports on a study which used submicroscopic diagrams to probe students' understanding of chemical equations. Assessment tasks required students to interpret diagrams, construct diagrams and to relate diagrams to symbolic representations. The analysis showed that some students have misconceptions about the molecular nature and chemical formulae and could not distinguish between coefficients and subscripts when representing chemical formulae. While students were generally able to balance a chemical equation presented as a set of diagrams, a significant number could not generate the balanced equation based on a diagram of the progress of a reaction, The study has demonstrated the use of student-generated diagrams to provide insight into students' understandings of chemical equations.

Student-generated submicro diagrams : a useful tool for teaching and learning chemical equations and stoichiometry

This paper reports on a pedagogical approach to the teaching of chemical equations introduced to first year university students with little previous chemical knowledge. During the instruction period students had to interpret and construct diagrams of reactions at the submicro level, and relate them to chemical equations at the symbolic level with the aim of improving their conceptual understanding of chemical equations and stoichiometry. Students received instruction in symbol conventions, practice through graded tutorial tasks, and feedback on their efforts over the semester. Analysis of the student responses to formative test and summative exam items over consecutive years indicates that there was a consistent improvement in the abilities of the various cohorts to answer stoichiometry questions correctly. The responses provide evidence for diagrams of the submicro level being used as tools for reasoning in solving chemical problems, to recognise misconceptions of chemical formulae and to recognise the value of using various multiple representations of chemical reactions connecting the submicro and symbolic levels of representation. The student-generated submicro diagrams serve as a visualisation tool for teaching and learning abstract concepts in solving stoichiometric problems. We argue that the use of diagrams of the submicro level provides a more complete picture of the reaction, rather than a net summary of a chemical equation, leading to a deeper conceptual understanding.

Generalized coupled photon transport equations for handling correlated photon streams with distinct frequencies

A generalized form of coupled photon transport equations that can handle correlated light beams with distinct frequencies is introduced. The derivation is based on the principle of energy conservation. For a single frequency, the current formulation reduces to a standard photon transport equation, and for fluorescence and phosphorescence, the diffusion models derived from the proposed photon transport model match for homogenous media. The generalized photon transport model is extended to handle wideband inputs in the frequency domain. © 2012 Optical Society of America.

The significant effect of the phase composition on the oxygen reduction reaction activity of a layered oxide cathode

Layered oxides of Sr4Fe4Co2O13 (SFC2) which contains alternating perovskite oxide octahedral and polyhedral oxide double layers are attractive for their mixed ionic and electronic conducting and oxygen reduction reaction properties. In this work, we used the EDTA–citrate synthesis technique to prepare SFC2 and vary the calcination temperature between 900 and 1100 _C to obtain SFC2, containing different phase content of perovskite (denoted as SFC-P) and (Fe,Co) layered oxide phases (SFC-L). Rietveld refinements show that the SFC-P phase content increased from _39 wt% to _50 wt% and _61 wt% as the calcination temperature increased from 900 _C (SFC2-900) to 1000 _C (SFC2-1000) and 1050 _C (SFC2-1050). At 1100 _C (SFC2-1100), SFC-P became the dominant phase. The oxygen transport properties (e.g. oxygen chemical diffusion coefficient and oxygen permeability), electrical conductivity and oxygen reduction reaction activity is enhanced in the order of SFC2-1000, SFC2-1100 and SFC2-1050. The trend established here therefore negates the hypothesis that the perovskite phase content correlates with the oxygen transport property enhancement. The results suggest instead that there is an optimum composition value (e.g. 61 wt% of SFC-L for SFC2-1050 in this work) on which synergistic effects take place between the SFC-P and SFC-L phase.

Sulfur-doped porous reduced graphene oxide hollow nanosphere frameworks as metal-free electrocatalysts for oxygen reduction reaction and as supercapacitor electrode materials.

Chemical doping with foreign atoms is an effective approach to significantly enhance the electrochemical performance of the carbon materials. Herein, sulfur-doped three-dimensional (3D) porous reduced graphene oxide (RGO) hollow nanosphere frameworks (S-PGHS) are fabricated by directly annealing graphene oxide (GO)-encapsulated amino-modified SiO2 nanoparticles with dibenzyl disulfide (DBDS), followed by hydrofluoric acid etching. The XPS and Raman spectra confirmed that sulfur atoms were successfully introduced into the PGHS framework via covalent bonds. The as-prepared S-PGHS has been demonstrated to be an efficient metal-free electrocatalyst for oxygen reduction reaction (ORR) with the activity comparable to that of commercial Pt/C (40%) and much better methanol tolerance and durability, and to be a supercapacitor electrode material with a high specific capacitance of 343 F g(-1), good rate capability and excellent cycling stability in aqueous electrolytes. The impressive performance for ORR and supercapacitors is believed to be due to the synergistic effect caused by sulfur-doping enhancing the electrochemical activity and 3D porous hollow nanosphere framework structures facilitating ion diffusion and electronic transfer.