Analytical model for active metamaterials with quantum ingredients

We present an analytical model for describing complex dynamics of a hybrid system consisting of resonantly coupled classical resonator and quantum structures. Classical resonators in our model correspond to plasmonic metamaterials of various geometries, as well as other types of nano- and microstructure, the optical responses of which can be described classically. Quantum resonators are represented by atoms or molecules, or their aggregates (for example, quantum dots, carbon nanotubes, dye molecules, polymer or bio-molecules etc), which can be accurately modelled only with the use of the quantum mechanical approach. Our model is based on the set of equations that combines well established density matrix formalism appropriate for quantum systems, coupled with harmonic-oscillator equations ideal for modelling sub-wavelength plasmonic and optical resonators. As a particular example of application of our model, we show that the saturation nonlinearity of carbon nanotubes increases multifold in the resonantly enhanced near field of a metamaterial. In the framework of our model, we discuss the effect of inhomogeneity of the carbon-nanotube layer (bandgap value distribution) on the nonlinearity enhancement. © 2012 IOP Publishing Ltd.

Computer simulation of radio-frequency methane/hydrogen plasmas and their interaction with GaAs Surfaces

The following thesis describes the computer modelling of radio frequency capacitively coupled methane/hydrogen plasmas and the consequences for the reactive ion etching of (100) GaAs surfaces. In addition a range of etching experiments was undertaken over a matrix of pressure, power and methane concentration. The resulting surfaces were investigated using X-ray photoelectron spectroscopy and the results were discussed in terms of physical and chemical models of particle/surface interactions in addition to the predictions for energies, angles and relative fluxes to the substrate of the various plasma species. The model consisted of a Monte Carlo code which followed electrons and ions through the plasma and sheath potentials whilst taking account of collisions with background neutral gas molecules. The ionisation profile output from the electron module was used as input for the ionic module. Momentum scattering interactions of ions with gas molecules were investigated via different models and compared against results given by quantum mechanical code. The interactions were treated as central potential scattering events and the resulting neutral cascades were followed. The resulting predictions for ion energies at the cathode compared well to experimental ion energy distributions and this verified the particular form of the electrical potentials used and their applicability in the particular geometry plasma cell used in the etching experiments. The final code was used to investigate the effect of external plasma parameters on the mass distribution, energy and angles of all species impingent on the electrodes. Comparisons of electron energies in the plasma also agreed favourably with measurements made using a Langmuir electric probe. The surface analysis showed the surfaces all to be depleted in arsenic due to its preferential removal and the resultant Ga:As ratio in the surface was found to be directly linked to the etch rate. The etch rate was determined by the methane flux which was predicted by the code.

Computer simulation of liquid flow patterns on distillation trays

This thesis describes work carried out to improve the fundamental modelling of liquid flows on distillation trays. A mathematical model is presented based on the principles of computerised fluid dynamics. It models the liquid flow in the horizontal directions allowing for the effects of the vapour through the use of an increased liquid turbulence, modelled by an eddy viscosity, and a resistance to liquid flow caused by the vapour being accelerated horizontally by the liquid. The resultant equations are similar to the Navier-Stokes equations with the addition of a resistance term.A mass-transfer model is used to calculate liquid concentration profiles and tray efficiencies. A heat and mass transfer analogy is used to compare theoretical concentration profiles to experimental water-cooling data obtained from a 2.44 metre diameter air-water distillation simulation rig. The ratios of air to water flow rates are varied in order to simulate three pressures: vacuum, atmospheric pressure and moderate pressure.For simulated atmospheric and moderate pressure distillation, the fluid mechanical model constantly over-predicts tray efficiencies with an accuracy of between +1.7% and +11.3%. This compares to -1.8% to -10.9% for the stagnant regions model (Porter et al. 1972) and +12.8% to +34.7% for the plug flow plus back-mixing model (Gerster et al. 1958). The model fails to predict the flow patterns and tray efficiencies for vacuum simulation due to the change in the mechanism of liquid transport, from a liquid continuous layer to a spray as the liquid flow-rate is reduced. This spray is not taken into account in the development of the fluid mechanical model. A sensitivity analysis carried out has shown that the fluid mechanical model is relatively insensitive to the prediction of the average height of clear liquid, and a reduction in the resistance term results in a slight loss of tray efficiency. But these effects are not great. The model is quite sensitive to the prediction of the eddy viscosity term. Variations can produce up to a 15% decrease in tray efficiency. The fluid mechanical model has been incorporated into a column model so that statistical optimisation techniques can be employed to fit a theoretical column concentration profile to experimental data. Through the use of this work mass-transfer data can be obtained.

Flow field analysis of some mixing and conveying screw element regions, within a closely intermeshing, co-rotating twin-screw extruder.

Grafting of antioxidants and other modifiers onto polymers by reactive extrusion, has been performed successfully by the Polymer Processing and Performance Group at Aston University. Traditionally the optimum conditions for the grafting process have been established within a Brabender internal mixer. Transfer of this batch process to a continuous processor, such as an extruder, has, typically, been empirical. To have more confidence in the success of direct transfer of the process requires knowledge of, and comparison between, residence times, mixing intensities, shear rates and flow regimes in the internal mixer and in the continuous processor.The continuous processor chosen for the current work in the closely intermeshing, co-rotating twin-screw extruder (CICo-TSE). CICo-TSEs contain screw elements that convey material with a self-wiping action and are widely used for polymer compounding and blending. Of the different mixing modules contained within the CICo-TSE, the trilobal elements, which impose intensive mixing, and the mixing discs, which impose extensive mixing, are of importance when establishing the intensity of mixing. In this thesis, the flow patterns within the various regions of the single-flighted conveying screw elements and within both the trilobal element and mixing disc zones of a Betol BTS40 CICo-TSE, have been modelled using the computational fluid dynamics package Polyflow. A major obstacle encountered when solving the flow problem within all of these sets of elements, arises from both the complex geometry and the time-dependent flow boundaries as the elements rotate about their fixed axes. Simulation of the time dependent boundaries was overcome by selecting a number of sequential 2D and 3D geometries, used to represent partial mixing cycles. The flow fields were simulated using the ideal rheological properties of polypropylene and characterised in terms of velocity vectors, shear stresses generated and a parameter known as the mixing efficiency. The majority of the large 3D simulations were performed on the Cray J90 supercomputer situated at the Rutherford-Appleton laboratories, with pre- and postprocessing operations achieved via a Silicon Graphics Indy workstation. A mechanical model was constructed consisting of various CICo-TSE elements rotating within a transparent outer barrel. A technique has been developed using coloured viscous clays whereby the flow patterns and mixing characteristics within the CICo-TSE may be visualised. In order to test and verify the simulated predictions, the patterns observed within the mechanical model were compared with the flow patterns predicted by the computational model. The flow patterns within the single-flighted conveying screw elements in particular, showed good agreement between the experimental and simulated results.

Physics and mathematics of dispersion-managed optical solitons

We review the main physical and mathematical properties of dispersion-managed (DM) optical solitons. Theory of DM solitons can be presented at two levels of accuracy: first, simple, but nevertheless, quantitative models based on ordinary differential equations governing evolution of the soliton width and phase parameter (the so-called chirp); and second, a comprehensive path-average theory that is capable of describing in detail both the fine structure of DM soliton form and its evolution along the fiber line. An analogy between DM soliton and a macroscopic nonlinear quantum oscillator model is also discussed. © 2003 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS. All rights reserved.

Effect of microstructure upon elastic behaviour of human tooth enamel

Tooth enamel is the stiffest tissue in the human body with a well-organized microstructure. Developmental diseases, such as enamel hypomineralisation, have been reported to cause marked reduction in the elastic modulus of enamel and consequently impair dental function. We produce evidence, using site-specific transmission electron microscopy (TEM), of difference in microstructure between sound and hypomineralised enamel. Built upon that, we develop a mechanical model to explore the relationship of the elastic modulus of the mineral-protein composite structure of enamel with the thickness of protein layers and the direction of mechanical loading. We conclude that when subject to complex mechanical loading conditions, sound enamel exhibits consistently high stiffness, which is essential for dental function. A marked decrease in stiffness of hypomineralised enamel is caused primarily by an increase in the thickness of protein layers between apatite crystals and to a lesser extent by an increase in the effective crystal orientation angle. © 2009 Elsevier Ltd. All rights reserved.

Niedrigfeld Magnetowiderstand inhomogener Halbleiterschichten

The resistance of semiconductor superlattices under weak magnetic fields is modelled with a classical approach. It is shown, that this is sufficient to explain the experimental features of these systems and that a quantum-mechanical approach will only be needed for significantly smaller lattice structures.

Model of the femtosecond laser inscription by a single pulse

A comprehensive model of processes involved in femtosecond laser inscription and the subsequent structural material modification is developed. Different time scales of the pulse-plasma dynamics and thermo-mechanical relaxation allow for separate numerical treatments of these processes, while linking them by an energy transfer equation. The model is illustrated and analysed on examples of inscription in fused silica and the results are used to explain previous experimental observations. © 2007 Springer Science+Business Media, LLC.