Temperature-and pH-Sensitive Nanohydrogels of Poly(N-Isopropylacrylamide) for Food Packaging Applications: Modelling the Swelling-Collapse Behaviour

Temperature-sensitive poly(N-isopropylacrylamide) (PNIPA) nanohydrogels were synthesized by nanoemulsion polymerization in water-in-oil systems. Several cross-linking degrees and the incorporation of acrylic acid as comonomer at different concentrations were tested to produce nanohydrogels with a wide range of properties. The physicochemical properties of PNIPA nanohydrogels, and their relationship with the swelling-collapse behaviour, were studied to evaluate the suitability of PNIPA nanoparticles as smart delivery systems (for active packaging). The swelling-collapse transition was analyzed by the change in the optical properties of PNIPA nanohydrogels using ultraviolet-visible spectroscopy. The thermodynamic parameters associated with the nanohydrogels collapse were calculated using a mathematical approach based on the van't Hoff analysis, assuming a two-state equilibrium (swollen to collapsed). A mathematical model is proposed to predict both the thermally induced collapse, and the collapse induced by the simultaneous action of two factors (temperature and pH, or temperature and organic solvent concentration). Finally, van't Hoff analysis was compared with differential scanning calorimetry. The results obtained allow us to solve the problem of determining the molecular weight of the structural repeating unit in cross-linked NIPA polymers, which, as we show, can be estimated from the ratio of the molar heat capacity (obtained from the van't Hoff analysis) to the specific heat capacity (obtained from calorimetric measurements).

Wave digital filter model of the entire auditory periphery

A model of the auditory periphery assembled from analog network submodels of all the relevant anatomical structures is described. There is bidirectional coupling between networks representing the outer ear, middle ear and cochlea. A simple voltage source representation of the outer hair cells provides level-dependent basilar membrane curves. The networks are translated into efficient computational modules by means of wave digital filtering. A feedback unit regulates the average firing rate at the output of an inner hair cell module via a simplified modelling of the dynamics of the descending paths to the peripheral ear. This leads to a digital model of the entire auditory periphery with applications to both speech and hearing research.

Beam propagation modelling of tapered waveguide lasers

A dynamic beam propagation model allows design optimization of high power low divergence tapered waveguide lasers. The model is extended to include spatially-resolved temperature profiles and a temperature dependent gain. Using this model, design parameters such as the optimum facet reflectivity, taper angle, and waveguide dimension can be calculated for low far-field divergence and high continuous wave power.

Parameter measurement for heavy-vehicle fuel consumption modelling

A mathematical model is developed to predict the energy consumption of a heavy vehicle. It includes the important factors of heavy-vehicle energy consumption, namely engine and drivetrain performances, losses due to accessories, aerodynamic drag, rolling resistance, road gradients, and driver behaviour. Novel low-cost testing methods were developed to determine engine and drivetrain characteristics. A simple drive cycle was used to validate the model. The model is able to predict the fuel use for a 371 tractor-semitrailer vehicle over a 4 km drive cycle within 1 per cent. This paper demonstrates that accurate and reliable vehicle benchmarking and model parameter measurement can be achieved without expensive equipment overheads, e.g. engine and chassis dynamometers.

Linear quadratic game and non-cooperative predictive methods for potential application to modelling driver-AFS interactive steering control

This paper is concerned with the modelling of strategic interactions between the human driver and the vehicle active front steering (AFS) controller in a path-following task where the two controllers hold different target paths. The work is aimed at extending the use of mathematical models in representing driver steering behaviour in complicated driving situations. Two game theoretic approaches, namely linear quadratic game and non-cooperative model predictive control (non-cooperative MPC), are used for developing the driver-AFS interactive steering control model. For each approach, the open-loop Nash steering control solution is derived; the influences of the path-following weights, preview and control horizons, driver time delay and arm neuromuscular system (NMS) dynamics are investigated, and the CPU time consumed is recorded. It is found that the two approaches give identical time histories as well as control gains, while the non-cooperative MPC method uses much less CPU time. Specifically, it is observed that the introduction of weight on the integral of vehicle lateral displacement error helps to eliminate the steady-state path-following error; the increase in preview horizon and NMS natural frequency and the decline in time delay and NMS damping ratio improve the path-following accuracy. © 2013 Copyright Taylor and Francis Group, LLC.

An example of the use of neural computing techniques in materials science - The modelling of fatigue thresholds in Ni-base superalloys

Two adaptive numerical modelling techniques have been applied to prediction of fatigue thresholds in Ni-base superalloys. A Bayesian neural network and a neurofuzzy network have been compared, both of which have the ability to automatically adjust the network's complexity to the current dataset. In both cases, despite inevitable data restrictions, threshold values have been modelled with some degree of success. However, it is argued in this paper that the neurofuzzy modelling approach offers real benefits over the use of a classical neural network as the mathematical complexity of the relationships can be restricted to allow for the paucity of data, and the linguistic fuzzy rules produced allow assessment of the model without extensive interrogation and examination using a hypothetical dataset. The additive neurofuzzy network structure means that redundant inputs can be excluded from the model and simple sub-networks produced which represent global output trends. Both of these aspects are important for final verification and validation of the information extracted from the numerical data. In some situations neurofuzzy networks may require less data to produce a stable solution, and may be easier to verify in the light of existing physical understanding because of the production of transparent linguistic rules. © 1999 Elsevier Science S.A.

Automated computational modelling for solid mechanics

We present some recent developments in automated computational modelling with an emphasis on solid mechanics applications. The automation process permits an abstract mathematical model of a physical problem to be translated into computer code rapidly and trivially, and can lead to computer code which is faster than hand-written and optimised code. Crucial to the approach is ensuring that mathematical abstractions inherent in the mathematical model are inherited by the software library. © Springer Science+Business Media B.V. 2008.

Numerical modelling of chirality-Induced bi-Directional swimming of artificial flagella

Biomimetic micro-swimmers can be used for various medical applications, such as targeted drug delivery and micro-object (e.g. biological cells) manipulation, in lab-on-a-chip devices. Bacteria swim using a bundle of flagella (flexible hair-like structures) that form a rotating cork-screw of chiral shape. To mimic bacterial swimming, we employ a computational approach to design a bacterial (chirality-induced) swimmer whose chiral shape and rotational velocity can be controlled by an external magnetic field. In our model, we numerically solve the coupled governing equations that describe the system dynamics (i.e. solid mechanics, fluid dynamics and magnetostatics). We explore the swimming response as a function of the characteristic dimensionless parameters and put special emphasis on controlling the swimming direction. Our results provide fundamental physical insight on the chirality-induced propulsion, and it provides guidelines for the design of magnetic bi-directional micro-swimmers. © 2013 The Author(s) Published by the Royal Society. All rights reserved.

Kinetic modelling of growth and storage molecule production in microalgae under mixotrophic and autotrophic conditions.

In order to improve algal biofuel production on a commercial-scale, an understanding of algal growth and fuel molecule accumulation is essential. A mathematical model is presented that describes biomass growth and storage molecule (TAG lipid and starch) accumulation in the freshwater microalga Chlorella vulgaris, under mixotrophic and autotrophic conditions. Biomass growth was formulated based on the Droop model, while the storage molecule production was calculated based on the carbon balance within the algal cells incorporating carbon fixation via photosynthesis, organic carbon uptake and functional biomass growth. The model was validated with experimental growth data of C. vulgaris and was found to fit the data well. Sensitivity analysis showed that the model performance was highly sensitive to variations in parameters associated with nutrient factors, photosynthesis and light intensity. The maximum productivity and biomass concentration were achieved under mixotrophic nitrogen sufficient conditions, while the maximum storage content was obtained under mixotrophic nitrogen deficient conditions.

Kinetic modelling of growth and storage molecule production in microalgae under mixotrophic and autotrophic conditions

In order to improve algal biofuel production on a commercial-scale, an understanding of algal growth and fuel molecule accumulation is essential. A mathematical model is presented that describes biomass growth and storage molecule (TAG lipid and starch) accumulation in the freshwater microalga Chlorella vulgaris, under mixotrophic and autotrophic conditions. Biomass growth was formulated based on the Droop model, while the storage molecule production was calculated based on the carbon balance within the algal cells incorporating carbon fixation via photosynthesis, organic carbon uptake and functional biomass growth. The model was validated with experimental growth data of C. vulgaris and was found to fit the data well. Sensitivity analysis showed that the model performance was highly sensitive to variations in parameters associated with nutrient factors, photosynthesis and light intensity. The maximum productivity and biomass concentration were achieved under mixotrophic nitrogen sufficient conditions, while the maximum storage content was obtained under mixotrophic nitrogen deficient conditions. © 2014 Elsevier Ltd.

Intercellular calcium wave propagation in linear and circuit-like bone cell networks

In the present study, the mechanism of intercellular calcium wave propagation in bone cell networks was identified. By using micro-contact printing and self-assembled monolayer technologies, two types of in vitro bone cell networks were constructed: open-ended linear chains and looped hexagonal networks with precisely controlled intercellular distances. Intracellular calcium responses of the cells were recorded and analysed when a single cell in the network was mechanically stimulated by nano-indentation. The looped cell network was shown to be more efficient than the linear pattern in transferring calcium signals from cell to cell. This phenomenon was further examined by pathway-inhibition studies. Intercellular calcium wave propagation was significantly impeded when extracellular adenosine triphosphate (ATP) in the medium was hydrolysed. Chemical uncoupling of gap junctions, however, did not significantly decrease the transferred distance of the calcium wave in the cell networks. Thus, it is extracellular ATP diffusion, rather than molecular transport through gap junctions, that dominantly mediates the transmission of mechanically elicited intercellular calcium waves in bone cells. The inhibition studies also demonstrated that the mechanical stimulation-induced calcium responses required extracellular calcium influx, whereas the ATP-elicited calcium wave relied on calcium release from the calcium store of the endoplasmic reticulum.

Granularity and disaggregation in compositional modelling with applications to ecological systems

J. Keppens and Q. Shen. Granularity and disaggregation in compositional modelling with applications to ecological systems. Applied Intelligence, 25(3):269-292, 2006.

Modelling uncertainty in agricultural image analysis

C.M. Onyango, J.A. Marchant and R. Zwiggelaar, 'Modelling uncertainty in agricultural image analysis', Computers and Electronics in Agriculture 17 (3), 295-305 (1997)

Comparison of deterministic, stochastic and fuzzy logic uncertainty modelling for capacity extension projects of DI/WFI pharmaceutical plant utilities with variable/dynamic demand

The last 30 years have seen Fuzzy Logic (FL) emerging as a method either complementing or challenging stochastic methods as the traditional method of modelling uncertainty. But the circumstances under which FL or stochastic methods should be used are shrouded in disagreement, because the areas of application of statistical and FL methods are overlapping with differences in opinion as to when which method should be used. Lacking are practically relevant case studies comparing these two methods. This work compares stochastic and FL methods for the assessment of spare capacity on the example of pharmaceutical high purity water (HPW) utility systems. The goal of this study was to find the most appropriate method modelling uncertainty in industrial scale HPW systems. The results provide evidence which suggests that stochastic methods are superior to the methods of FL in simulating uncertainty in chemical plant utilities including HPW systems in typical cases whereby extreme events, for example peaks in demand, or day-to-day variation rather than average values are of interest. The average production output or other statistical measures may, for instance, be of interest in the assessment of workshops. Furthermore the results indicate that the stochastic model should be used only if found necessary by a deterministic simulation. Consequently, this thesis concludes that either deterministic or stochastic methods should be used to simulate uncertainty in chemical plant utility systems and by extension some process system because extreme events or the modelling of day-to-day variation are important in capacity extension projects. Other reasons supporting the suggestion that stochastic HPW models are preferred to FL HPW models include: 1. The computer code for stochastic models is typically less complex than a FL models, thus reducing code maintenance and validation issues. 2. In many respects FL models are similar to deterministic models. Thus the need for a FL model over a deterministic model is questionable in the case of industrial scale HPW systems as presented here (as well as other similar systems) since the latter requires simpler models. 3. A FL model may be difficult to "sell" to an end-user as its results represent "approximate reasoning" a definition of which is, however, lacking. 4. Stochastic models may be applied with some relatively minor modifications on other systems, whereas FL models may not. For instance, the stochastic HPW system could be used to model municipal drinking water systems, whereas the FL HPW model should or could not be used on such systems. This is because the FL and stochastic model philosophies of a HPW system are fundamentally different. The stochastic model sees schedule and volume uncertainties as random phenomena described by statistical distributions based on either estimated or historical data. The FL model, on the other hand, simulates schedule uncertainties based on estimated operator behaviour e.g. tiredness of the operators and their working schedule. But in a municipal drinking water distribution system the notion of "operator" breaks down. 5. Stochastic methods can account for uncertainties that are difficult to model with FL. The FL HPW system model does not account for dispensed volume uncertainty, as there appears to be no reasonable method to account for it with FL whereas the stochastic model includes volume uncertainty.

Financial modelling with 2-EPT probability density functions

The class of all Exponential-Polynomial-Trigonometric (EPT) functions is classical and equal to the Euler-d’Alembert class of solutions of linear differential equations with constant coefficients. The class of non-negative EPT functions defined on [0;1) was discussed in Hanzon and Holland (2010) of which EPT probability density functions are an important subclass. EPT functions can be represented as ceAxb, where A is a square matrix, b a column vector and c a row vector where the triple (A; b; c) is the minimal realization of the EPT function. The minimal triple is only unique up to a basis transformation. Here the class of 2-EPT probability density functions on R is defined and shown to be closed under a variety of operations. The class is also generalised to include mixtures with the pointmass at zero. This class coincides with the class of probability density functions with rational characteristic functions. It is illustrated that the Variance Gamma density is a 2-EPT density under a parameter restriction. A discrete 2-EPT process is a process which has stochastically independent 2-EPT random variables as increments. It is shown that the distribution of the minimum and maximum of such a process is an EPT density mixed with a pointmass at zero. The Laplace Transform of these distributions correspond to the discrete time Wiener-Hopf factors of the discrete time 2-EPT process. A distribution of daily log-returns, observed over the period 1931-2011 from a prominent US index, is approximated with a 2-EPT density function. Without the non-negativity condition, it is illustrated how this problem is transformed into a discrete time rational approximation problem. The rational approximation software RARL2 is used to carry out this approximation. The non-negativity constraint is then imposed via a convex optimisation procedure after the unconstrained approximation. Sufficient and necessary conditions are derived to characterise infinitely divisible EPT and 2-EPT functions. Infinitely divisible 2-EPT density functions generate 2-EPT Lévy processes. An assets log returns can be modelled as a 2-EPT Lévy process. Closed form pricing formulae are then derived for European Options with specific times to maturity. Formulae for discretely monitored Lookback Options and 2-Period Bermudan Options are also provided. Certain Greeks, including Delta and Gamma, of these options are also computed analytically. MATLAB scripts are provided for calculations involving 2-EPT functions. Numerical option pricing examples illustrate the effectiveness of the 2-EPT approach to financial modelling.