23,735 research outputs found
The Modelling of Primary Alkaline Battery Cathodes: A Simplified Model for porous manganese oxide particle discharge
No full textA simplified model, to that produced previously by the authors, for the galvanostatic discharge of primary alkaline battery cathodes is presented. Laplace transform and perturbation methods are employed to obtain the leading order spatial and temporal behaviour of the porous cathode over two distinct size scales. It is shown that for a wide range of industrially relevant discharge conditions the time taken for KOH electrolyte to diffuse into a porous electrolytic manganese dioxide particle is fast compared with the cathodic discharge time and that ohmic losses within the graphite phase of the cathode can be considered to be negligible. Numerical solution of the simplified model equations is discussed and the results are validated against relevant experimental data
The easy-to-please construction in Middle English
No full textThe aim of this article is to follow the changes that took place in the history of easy-to-please constructions. To fully apprehend that, we will begin by looking at Middle English infinitives and the change which affected them. Our attempt here is to prove that Early Middle English to was at its intermediate stage of development, i.e. it was neither a preposition nor inflection. In Late Middle English, to reached its final stage of a gradual evolution heading TR On account of the analysis of to and infinitives in Middle English, new constructions in which easv-to-please appear will be explained
Tumour dynamics and necrosis: surface tension and stability
No full textA model is developed for the motion of cells within a multicell spherical tumour. The model allows either for the intercellular forces to be in compression and cells to be compacted to a fixed number density, or for the cell number density to fall and cells to become isolated from each other. The model develops necrotic regions naturally due to force balances rather than being directly attributable to a critical oxygen concentration. These necrotic regions may result in a gradual reduction in local cell density rather than jump to a completely dead region.Numerical and analytical analysis of the spherically symmetric model shows that the long time behaviour of the spheroid depends on any surface tension effects created by cells on the outer surface. For small surface tension the spheroid grows linearly in time developing a large necrotic region, while for larger surface tension the growth can be halted. The linear stability to spherically symmetric perturbations of all the possible resulting steady states is revealed
Gas propagation in cracks from cylindrical boreholes during blasting in mines
No full textDuring mine blasts a large number of boreholes are drilled and filled with explosives. The pattern of boreholes and the timing of the explosions is chosen to maximize the fracturing of the rock. To help understand the complex interaction between the explosive and the rock a single borehole is considered. The very high pressure gas created by the explosion propagates out from the cylindrical borehole into pre-stressed rock. Analysis of the rock stresses uses matched asymptotic methods assuming the gas propagates slowly. The resulting equation for the gas movement are derived and various limiting cases considered. The model is a nonlinear integro-differential equation which behaves as a singular parabolic problem in some cases
On the separation of coconuts: a modeling week study
No full textThe modus operandi of "modeling weeks" is explained and illustrated using a classical modeling week problem of subjecting coconuts to an external pressure before splitting them open, in the hope that the coconut meat will then separate easily from the shell. A range of modeling approaches is considered, and a poroelastic model is posed that allows the key problem parameters to be identified and calculated. We conclude that separation by this means is likely to be possible and relatively easy to accomplish
Modelling the cell cycle and cell movement in multicellular tumour spheroids
No full textThis paper analyses a recent mathematical model of avascular tumour spheroid growth which accounts for both cell cycle dynamics and chemotactic driven cell movement. The model considers cells to exist in one of two compartments: proliferating and quiescent, as well as accounting for necrosis and apoptosis. One particular focus of this paper is the behaviour created when proliferating and quiescent cells have different chemotactic responses to an extracellular nutrient supply. Two very different steady-state behaviours are identified corresponding to those cases where proliferating cells move either more quickly or more slowly than quiescent cells in response to a gradient in the extracellular nutrient supply. The case where proliferating cells move more rapidly leads to the commonly accepted spheroid structure of a thin layer of proliferating cells surrounding an inner quiescent core. In the case where proliferating cells move more slowly than quiescent cells the model predicts an interesting structure of a thin layer of quiescent cells surrounding an inner core of proliferating and quiescent cells. The sensitivity of this tumour structure to the cell cycle model parameters is also discussed. In particular variations in the steady-state size of the tumour and the types of transient behaviour are explored. The model reveals interesting transient behaviour with sharply delineated regions of proliferating and quiescent cells
Asymptotic analysis of the growth of cake layers in filters
No full textThe problem of fluid flow in a two-dimensional pleated filter is considered. Of particular interest is the change in the flow due to cake build-up on the surface of the filter material. The flow is taken to be Darcy flow in the cake and the filter material, with Stokes' flow outside the cake. The particles in the flow are taken to be transported with the flow and to stick to the cake without slippage or resuspension, and the cake is taken to be incompressible. The flow is considered in various geometries, particularly long thin filters and corners. The main parameter in the problem is the ratio of the filter-material resistance to the cake resistance, and limiting cases are considered. Travelling waves of cake build-up are found for arbitrary time-dependent variations in the inflow conditions. The time taken for the filter to become clogged by the cake is also considered
Residual stress generation and necrosis formation in multi-cell tumour spheroids
No full textWe consider how cell proliferation and death generate residual stresses within a multi-cell tumour spheroid (MCTS). Previous work by Jones and co-workers [8] has shown that isotropic growth in a purely elastic MCTS produces growth induced stresses which eventually become unbounded, and hence are physically unrealistic. Since viscoelastic materials show stress relaxation under a fixed deformation we consider the effect of the addition of a small amount of viscosity to the elastic system by examining formation of equilibrium stress profiles within a Maxwell type viscoelastic MCTS. A model of necrosis formation based upon that proposed by Please and co-workers (see [16] [17] [18]) is then presented in which necrosis forms under conditions of adverse mechanical stress rather than in regions of extreme chemical stress as is usually assumed. The influence of rheology on necrosis formation is then investigated, and it is shown that the excessive stress generated in the purely elastic tumour can be relieved either by the addition of some viscosity to the system or by accounting for an inner necrotic interface with an appropriate stress boundary condition
A mathematical model of dynamic glioma-host interactions: receptor-mediated invasion and local proteolysis
No full textWe present a mathematical model of glioma spread based on cellular movement by receptor-mediated haptotaxis, local proteolysis of healthy tissue components by glioma-derived proteinases, malignant proliferative enhancement and host up-regulation of specific key extracellular matrix (ECM) components in response to the invading glioma. We subsequently consider the nature of glioma–host interactions as predicted by our model in order to test the hypothesis given in (Knott et al. (1998) that production of adhesive ECM components by the brain in response to the invading glioma may have the counter-intuitive effect of enhancing glioma invasion by assisting haptotactic migration. We suggest that host production of certain adhesive ECM chemicals can have a profound effect on both glioma invasion speed and the character of the glioma–host interface. In particular, we conclude that up-regulation of host ECM production in the vicinity of the glioma may produce a less diffuse glioma, providing clearer demarcation between glioma and healthy tissue, and thus improving the possibility of surgical resection within reasonable bounds
Asymptotic analysis of the flow of shear-thinning foodstuffs in annular scraped heat exchangers
No full textThe problem of isothermal flow of a shear-thinning (pseudoplastic) fluid in the gap between two concentric cylinders is considered. A pump provides an axial pressure gradient which causes flow down the device. The outer cylinder is fixed and has scrapers attached to it to cause flow mixing, whilst the inner cylinder rotates about its axis to provide shear and thus thin the fluid. The goal is to determine the optimal distribution of power between rotation and pumping. Although ostensibly the flow is nonlinear and three-dimensional we show that judicious use of fairly straightforward asymptotic methods can yield a great deal of information about the device, including cross-sectional flow predictions and throughput results. Furthermore, these results are derived for a variety of different flow conditions. Some numerical calculations are carried out using a commercial CFD code. These show good agreement with the asymptotic analysis
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