1,720,997 research outputs found
Determination of macro-scale soil properties from pore scale structures - Model derivation
No full textIn this paper we use homogenisation to derive a set of macro-scale poro-elastic equations for soils composed of rigid solid particles, air filled pore-space and aporo-elastic mixed phase. We consider the derivation in the limit of large deformation and show that by solving representative problems on the micro-scale we can parametrise the macro-scale equations. To validate the homogenisation procedure we compare the predictions of the homogenised equations to those of the full equations for a range of different geometriesand material properties. We show that the results differ by . 2% for all cases considered. The success of the homogenisation scheme means that it can be usedto determine the macro-scale poro-elastic properties of soils from the underlying structure. Hence, it will prove a valuable tool in both characterisation andoptimisation
Multiscale modelling of hydraulic conductivity in vuggy porous media
No full textFlow in both saturated and non-saturated vuggy porous media, i.e., soil, is inherently multiscale. The complex microporous structure of the soil aggregates and the wider vugs provides a multitude of flow pathways and has received significant attention from the X-ray CT community with a constant drive to image at higher resolution. Using multiscale homogenization we derive averaged equations to study the effects of the microscale structure on the macroscopic flow. The averaged model captures the underlying geometry through a series of cell problems and is verified through direct comparison to numerical simulations of the full structure. These methods offer significant reductions in computation time and allow us to perform 3D calculations with complex geometries on a desktop PC. The results show that the surface roughness of the aggregate has a significantly greater effect on the flow than the microstructure within the aggregate. Hence, this is the region in which the resolution of X-ray CT for image based modelling has the greatest impact
Light–matter interaction in liquid crystal cells
No full textIn this thesis we study the interactions between light and matter in photorefractive liquid crystalcells. To model the liquid crystal alignment we develop a fast and accurate approximation ofthe normally stiff equations which minimise the Landau-deGennes free energy of a nematicliquid crystal. The resulting equations are suitable for all configurations in which defects arenot present, making them ideal for device simulation. Specifically, they offer an increase incomputational efficiency by a factor of 100 while maintaining an error of order (10?4) whencompared to the full stiff equations. As this approximation is based on aQ–tensor formalism, thesign reversal symmetry of the liquid crystal is respected. We consider both the simplified case,where the director is restricted to a plane, and the full three-dimensional case. An approximationof the error is also given. We use the liquid crystal model to understand two different opticaleffects. The first of these is optical coupling. This effect is observed in liquid crystals in both theBragg and Raman–Nath regimes. To account for this behaviour we develop an extension to thecoupled wave theory which is suitable for all regimes of coupling. The model assumes that therefractive index grating, generated by the liquid crystal, has an arbitrary profile in one directionand is periodic (but not necessarily sinusoidal) in the other. Higher order diffracted terms areconsidered and appropriate mismatch terms dealt with. It is shown that this model is analyticallyequivalent to both the Bragg and Raman–Nath regime coupling models under an appropriate setof assumptions. This model is also verified through comparison to finite element simulations ofMaxwell’s equations. The second effect we model is the coupling of surface plasmon polaritonsat the interface between a metal layer and a photorefractive liquid crystal cell. We implementexisting numerical models to gain a thorough understanding of the system. These models arequalitatively compared with experimental observations. Analytic approximations to describethe coupling of surface plasmon polaritons at the surface of the liquid crystal cell are developed.These expressions provide a great deal of insight into the coupling mechanisms and will be offundamental importance in optimising these systems
Regime independent coupled-wave equations in anisotropic photorefractive media
No full textAn extension to coupled wave theory suitable for all regimes of diffraction is presented. The model assumes that the refractive index grating has an arbitrary profile in one direction and is periodic (but not necessarily sinusoidal) in the other. Higher order diffracted terms are considered and appropriate mismatch terms dealt with. It is shown that this model is analytically equivalent to both the Bragg and Raman–Nath regime coupling models under an appropriate set of assumptions. This model is applied to cases such as optical coupling in liquid crystal cells with photoconductive layers. Its predictions are successfully compared to finite element simulations of the full Maxwell’s equations
Poro-elastic Dataset
No full textDataset 01 for: K.R. Daly, S.D. Keyes, and T. Roose, Determination of macro-scale soil properties from pore scale structures - Image based modelling of poroelastic structures, Proc. Roy. Soc. A. 2018 </span
Mathematical modelling of water and solute movement in ridged versus flat planting systems
No full textWe compared water and solute movement between a ridge and furrow geometry and that of flat soil with a mathematical model. We focused on the effects of two physical processes: root water uptake and pond formation on the soil surface. The mathematical model describes the interaction between solute transport, water movement and surface pond depth. Numerical simulations were used to determine how solutes of varying mobility and rates of degradation penetrated into the two soil geometries over a growing season. Both the ridge and furrow or flat soil geometries could reduce solute leaching, but this depended on several factors. Rain immediately after a solute application was a key factor in determining solute penetration into soil. In cases with delayed rain after a solute application, solutes in ridge and furrow geometries collected adjacent to the root system, resulting in reduced solute penetration compared to the flat soil geometry. In contrast, substantial rain immediately after a solute application resulted in ponding where water infiltration acted as the dominant transport mechanism. This resulted in increased solute penetration in the ridge and furrow geometry compared to the flat soil geometry
Multiscale models of colloidal dispersion of particles in nematic liquid crystals
No full textWe use homogenization theory to develop a multiscale model of colloidal dispersion of particles in nematic liquid crystals under weak-anchoring conditions. We validate the model by comparing it with simulations by using the Landau–de Gennes free energy and show that the agreement is excellent. We then use the multiscale model to study the effect that particle anisotropy has on the liquid crystal: spherically symmetric particles always reduce the effective elastic constant. Asymmetric particles introduce an effective alignment field that can increase the Fredericks threshold and decrease the switch-off time
Mathematical modelling of the phloem: the importance of diffusion on sugar transport at osmotic equilibrium
Full text link3 month old wheat plant cultivar xi19 grown in clay loam soil at a bulk density of 1.1. g cm-3. [Pot 3]
No full textThis consists of 9 scans taken at different heights within the specimen.
From 2017 this dataset can be requested via http://library.soton.ac.uk/datarequest</span
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