A mathematical model of crystallization in an emulsion

A mathematical model incorporating many of the important processes at work in the crystallization of emulsions is presented. The model describes nucleation within the discontinuous domain of an emulsion, precipitation in the continuous domain, transport of monomers between the two domains, and formation and subsequent growth of crystals in both domains. The model is formulated as an autonomous system of nonlinear, coupled ordinary differential equations. The description of nucleation and precipitation is based upon the Becker–Döring equations of classical nucleation theory. A particular feature of the model is that the number of particles of all species present is explicitly conserved; this differs from work that employs Arrhenius descriptions of nucleation rate. Since the model includes many physical effects, it is analyzed in stages so that the role of each process may be understood. When precipitation occurs in the continuous domain, the concentration of monomers falls below the equilibrium concentration at the surface of the drops of the discontinuous domain. This leads to a transport of monomers from the drops into the continuous domain that are then incorporated into crystals and nuclei. Since the formation of crystals is irreversible and their subsequent growth inevitable, crystals forming in the continuous domain effectively act as a sink for monomers “sucking” monomers from the drops. In this case, numerical calculations are presented which are consistent with experimental observations. In the case in which critical crystal formation does not occur, the stationary solution is found and a linear stability analysis is performed. Bifurcation diagrams describing the loci of stationary solutions, which may be multiple, are numerically calculated.

Northern hemisphere winter atmospheric climate: modes of natural variability and climate change

Under anthropogenic climate change it is possible that the increased radiative forcing and associated changes in mean climate may affect the “dynamical equilibrium” of the climate system; leading to a change in the relative dominance of different modes of natural variability, the characteristics of their patterns or their behavior in the time domain. Here we use multi-century integrations of version three of the Hadley Centre atmosphere model coupled to a mixed layer ocean to examine potential changes in atmosphere-surface ocean modes of variability. After first evaluating the simulated modes of Northern Hemisphere winter surface temperature and geopotential height against observations, we examine their behavior under an idealized equilibrium doubling of atmospheric CO2. We find no significant changes in the order of dominance, the spatial patterns or the associated time series of the modes. Having established that the dynamic equilibrium is preserved in the model on doubling of CO2, we go on to examine the temperature pattern of mean climate change in terms of the modes of variability; the motivation being that the pattern of change might be explicable in terms of changes in the amount of time the system resides in a particular mode. In addition, if the two are closely related, we might be able to assess the relative credibility of different spatial patterns of climate change from different models (or model versions) by assessing their representation of variability. Significant shifts do appear to occur in the mean position of residence when examining a truncated set of the leading order modes. However, on examining the complete spectrum of modes, it is found that the mean climate change pattern is close to orthogonal to all of the modes and the large shifts are a manifestation of this orthogonality. The results suggest that care should be exercised in using a truncated set of variability EOFs to evaluate climate change signals.

Mathematical modelling of decision making processes in construction projects

Many different individuals, who have their own expertise and criteria for decision making, are involved in making decisions on construction projects. Decision-making processes are thus significantly affected by communication, in which a dynamic performance of human intentions leads to unpredictable outcomes. In order to theorise the decision making processes including communication, it is argued here that the decision making processes resemble evolutionary dynamics in terms of both selection and mutation, which can be expressed by the replicator-mutator equation. To support this argument, a mathematical model of decision making has been made from an analogy with evolutionary dynamics, in which there are three variables: initial support rate, business hierarchy, and power of persuasion. On the other hand, a survey of patterns in decision making in construction projects has also been performed through self-administered mail questionnaire to construction practitioners. Consequently, comparison between the numerical analysis of mathematical model and the statistical analysis of empirical data has shown a significant potential of the replicator-mutator equation as a tool to study dynamic properties of intentions in communication.

A mathematical model of the in vitro keratinocyte response to chromium and nickel exposure

A mathematical model describing the main mechanistic processes involved in keratinocyte response to chromium and nickel has been developed and compared to experimental in vitro data. Accounting for the interactions between the metal ions and the keratinocytes, the law of mass action was used to generate ordinary differential equations which predict the time evolution and ion concentration dependency of keratinocyte viability, the amount of metal associated with the keratinocytes and the release of cytokines by the keratinocytes. Good agreement between model predictions and existing experimental data of these endpoints was observed, supporting the use of this model to explore physiochemical parameters that influence the toxicological response of keratinocytes to these two metals.

Cyclopropylidenes, bicyclopropylidenes, and vinylcarbenes - some modes of formation and preparative applications

The routes of transformation of the simplest bicyclopropylidene into the derivatives of the second and third generations and synthesis of perspirocyclopropanated [3]rotane and linear spiral [4]- and [5]triangulanes are discussed.

Coordination modes of 3-aminosalicylic and 3-hydroxyanthranilic acids in palladium(II), platinum(II) and rhenium(V) complexes. The crystal structure of cis-[Pt(HsalNH)(PPh3)(2)] (.) 0.25C(2)H(5)OH

New Pd(II), Pt(II) and Re(V) complexes of 3-aminosalicylic acid (H(2)salNH(2)) and 3-hydroxyantranilic acid (HantOH) have been prepared, cis-[Pt (HsalNH)(PPh3)(2)] center dot 0.25C(2)H(5)OH (1), trans-[PdCl(salNH(2))(PPh3)(2)](2), trans-[ReOI2(HsalNH(2))(PPh3)] center dot (CH3)(2)CO (3), cis-[Pt(HantO)(PPh3)(2)] (4), trans-[PdCl(antOH)(PPh3)(2)] center dot 4H(2)O (5), [PdCl(antOH)(bipy)] center dot C2H5OH (6), [PdCl2(HantOH)(2)] (7) and trans-[ReOI(HantO)(PPh3)(2)] center dot (CH3)(2)CO (8). The crystal structure of complex I was determined showing chelation of HsalNH(2-) through the adjacent nitrogen and oxygen atoms of the amino and phenolate groups. Infrared and H-1 NMR spectroscopic data for the complexes are presented. (c) 2005 Elsevier Ltd. All rights reserved.

Pressure-relieving equipment: promoting its correct use amongst nurses via differing modes of educational delivery

Aims and objectives. To examine the impact of written and verbal education on bed-making practices, in an attempt to reduce the prevalence of pressure ulcers. Background. The Department of Health has set targets for a 5% reduction per annum in the incidence of pressure ulcers. Electric profiling beds with a visco-elastic polymer mattress are a new innovation in pressure ulcer prevention; however, mattress efficacy is reduced by tightly tucking sheets around the mattress. Design. A prospective randomized pre/post-test experimental design. Methods. Ward managers at a teaching hospital were approached to participate in the study. Two researchers independently examined the tightness of the sheets around the mattresses. Wards were randomized to one of two groups. Groups A and B received written education. In addition, group B received verbal education on alternate days for one week. Beds were re-examined one month later. One researcher was blinded to the educational delivery received by the wards. Results. Twelve wards agreed to participate in the study and 245 beds were examined. Before education, 113 beds (46%) had sheets tucked correctly around the mattresses. Following education, this increased to 215 beds (87.8%) (chi(2) = 68.03, P < 0.001). There was no significant difference in the number of correctly made beds between the two different education groups: 100 (87.72%) beds correctly made in group A vs. 115 (87.79%) beds in group B (chi(2) = 0, P 0.987). Conclusions. Clear, concise written instruction improved practice but verbal education was not additionally beneficial. Relevance to clinical practice. Nurses are receptive to clear, concise written evidence regarding pressure ulcer prevention and incorporate this into clinical practice.

Mathematical modelling of competitive LDL/VLDL binding and uptake by hepatocytes

Elevated levels of low-density-lipoprotein cholesterol (LDL-C) in the plasma are a well-established risk factor for the development of coronary heart disease. Plasma LDL-C levels are in part determined by the rate at which LDL particles are removed from the bloodstream by hepatic uptake. The uptake of LDL by mammalian liver cells occurs mainly via receptor-mediated endocytosis, a process which entails the binding of these particles to specific receptors in specialised areas of the cell surface, the subsequent internalization of the receptor-lipoprotein complex, and ultimately the degradation and release of the ingested lipoproteins' constituent parts. We formulate a mathematical model to study the binding and internalization (endocytosis) of LDL and VLDL particles by hepatocytes in culture. The system of ordinary differential equations, which includes a cholesterol-dependent pit production term representing feedback regulation of surface receptors in response to intracellular cholesterol levels, is analysed using numerical simulations and steady-state analysis. Our numerical results show good agreement with in vitro experimental data describing LDL uptake by cultured hepatocytes following delivery of a single bolus of lipoprotein. Our model is adapted in order to reflect the in vivo situation, in which lipoproteins are continuously delivered to the hepatocyte. In this case, our model suggests that the competition between the LDL and VLDL particles for binding to the pits on the cell surface affects the intracellular cholesterol concentration. In particular, we predict that when there is continuous delivery of low levels of lipoproteins to the cell surface, more VLDL than LDL occupies the pit, since VLDL are better competitors for receptor binding. VLDL have a cholesterol content comparable to LDL particles; however, due to the larger size of VLDL, one pit-bound VLDL particle blocks binding of several LDLs, and there is a resultant drop in the intracellular cholesterol level. When there is continuous delivery of lipoprotein at high levels to the hepatocytes, VLDL particles still out-compete LDL particles for receptor binding, and consequently more VLDL than LDL particles occupy the pit. Although the maximum intracellular cholesterol level is similar for high and low levels of lipoprotein delivery, the maximum is reached more rapidly when the lipoprotein delivery rates are high. The implications of these results for the design of in vitro experiments is discussed.