One-dimensional optical wave turbulence:experiment and theory

We present a review of the latest developments in one-dimensional (1D) optical wave turbulence (OWT). Based on an original experimental setup that allows for the implementation of 1D OWT, we are able to show that an inverse cascade occurs through the spontaneous evolution of the nonlinear field up to the point when modulational instability leads to soliton formation. After solitons are formed, further interaction of the solitons among themselves and with incoherent waves leads to a final condensate state dominated by a single strong soliton. Motivated by the observations, we develop a theoretical description, showing that the inverse cascade develops through six-wave interaction, and that this is the basic mechanism of nonlinear wave coupling for 1D OWT. We describe theory, numerics and experimental observations while trying to incorporate all the different aspects into a consistent context. The experimental system is described by two coupled nonlinear equations, which we explore within two wave limits allowing for the expression of the evolution of the complex amplitude in a single dynamical equation. The long-wave limit corresponds to waves with wave numbers smaller than the electrical coherence length of the liquid crystal, and the opposite limit, when wave numbers are larger. We show that both of these systems are of a dual cascade type, analogous to two-dimensional (2D) turbulence, which can be described by wave turbulence (WT) theory, and conclude that the cascades are induced by a six-wave resonant interaction process. WT theory predicts several stationary solutions (non-equilibrium and thermodynamic) to both the long- and short-wave systems, and we investigate the necessary conditions required for their realization. Interestingly, the long-wave system is close to the integrable 1D nonlinear Schrödinger equation (NLSE) (which contains exact nonlinear soliton solutions), and as a result during the inverse cascade, nonlinearity of the system at low wave numbers becomes strong. Subsequently, due to the focusing nature of the nonlinearity, this leads to modulational instability (MI) of the condensate and the formation of solitons. Finally, with the aid of the probability density function (PDF) description of WT theory, we explain the coexistence and mutual interactions between solitons and the weakly nonlinear random wave background in the form of a wave turbulence life cycle (WTLC).

Essays of strategic alliance portfolio configuration—Its performance properties, strategic antecedents and consequential effects on multinational firms' continuing foreign expansion

This dissertation focused on an increasingly prevalent phenomenon in today's global business environment—strategic alliance portfolio. Building on resource-based view, resource dependency theory and real options theory, this dissertation adopted a multi-dimensional perspective to examine the performance implications, strategic antecedents of alliance portfolio configuration, and its strategic effects on firms' decision-making on their continuing foreign expansion. The dissertation consisted of three interrelated essays, each of which dealt with a specific research question. In the first essay I applied a two-dimensional construct that embraces both alliance relations' and alliance partners' attributes to illustrate alliance portfolio configuration. Based on this framework, a longitudinal study was conducted attempting to explore the performance properties of alliance portfolio configuration. The results revealed that alliance diversity and partner diversity have different relative contributions to firms' economic performance. The relationship between alliance portfolio configuration and firm performance was shaped by degree of multinationality in a curvilinear pattern. The second essay attempted to identify the firm level driving forces of alliance portfolio configuration and how these forces interacting with firms' internationalization influence firms' strategic choices on alliance portfolio configuration. The empirical results indicated that past alliance experience, slack resource and firms' brand images are three critical determinants shaping alliance portfolios, but those shaping relationships are conditioned by firms' multinationality. The third essay primarily employed real options theory to build a conceptual framework, revealing how country-, alliance portfolio-, firm-, and industry level factors and their interactions influence firms' strategic decision-making on post-entry continuing expansion in foreign markets. The two empirical studies were resided in global hospitality and travel industries and use panel data to test the relevant theoretical models. Overall, the dissertation advanced and enriched the theoretical domain of alliance portfolio. It particularly shed valuable insights on three fundamental questions in the domain of alliance portfolio research, namely "if and how alliance portfolios contribute to firms' economic performance"; "what determines the appearance of alliance portfolios”; and "how alliance portfolios affect firms' strategic decision-making". This dissertation also extended the international business and strategic management research on service multinationals' foreign expansion and performance.

DEP-derived density from two snow trenches from Kohnen Station, Dronning Maud Land, Antarctica from the 2012/13 field season

The density of firn is an important property for monitoring and modeling the ice sheet as well as to model the pore close-off and thus to interpret ice core-based greenhouse gas records. One feature, which is still in debate, is the potential existence of an annual cycle of firn density in low-accumulation regions. Several studies describe or assume seasonally successive density layers, horizontally evenly distributed, as seen in radar data. On the other hand, high-resolution density measurements on firn cores in Antarctica and Greenland showed no clear seasonal cycle in the top few meters. A major caveat of most existing snow-pit and firn-core based studies is that they represent one vertical profile from a laterally heterogeneous density field. To overcome this, we created an extensive dataset of horizontal and vertical density data at Kohnen Station, Dronning Maud Land on the East Antarctic Plateau. We drilled and analyzed three 90 m long firn cores as well as 160 one meter long vertical profiles from two elongated snow trenches to obtain a two dimensional view of the density variations. The analysis of the 45 m wide and 1 m deep density fields reveals a seasonal cycle in density. However, the seasonality is overprinted by strong stratigraphic noise, making it invisible when analyzing single firn cores. Our density dataset extends the view from the local ice-core perspective to a hundred meter scale and thus supports linking spatially integrating methods such as radar and seismic studies to ice and firn cores.

Microscopic Mechanism and Kinetics of Ice Formation at Complex Interfaces: Zooming in on Kaolinite

Most ice in nature forms because of impurities which boost the exceedingly low nucleation rate of pure supercooled water. However, the microscopic details of ice nucleation on these substances remain largely unknown. Here, we have unraveled the molecular mechanism and the kinetics of ice formation on kaolinite, a clay mineral playing a key role in climate science. We find that the formation of ice at strong supercooling in the presence of this clay is about 20 orders of magnitude faster than homogeneous freezing. The critical nucleus is substantially smaller than that found for homogeneous nucleation and, in contrast to the predictions of classical nucleation theory (CNT), it has a strong two-dimensional character. Nonetheless, we show that CNT describes correctly the formation of ice at this complex interface. Kaolinite also promotes the exclusive nucleation of hexagonal ice, as opposed to homogeneous freezing where a mixture of cubic and hexagonal polytypes is observed.

Electric Field Effects on Graphene Materials

Understanding the effect of electric fields on the physical and chemical properties of two-dimensional (2D) nanostructures is instrumental in the design of novel electronic and optoelectronic devices. Several of those properties are characterized in terms of the dielectric constant which play an important role on capacitance, conductivity, screening, dielectric losses and refractive index. Here we review our recent theoretical studies using density functional calculations including van der Waals interactions on two types of layered materials of similar two-dimensional molecular geometry but remarkably different electronic structures, that is, graphene and molybdenum disulphide (MoS2). We focus on such two-dimensional crystals because of they complementary physical and chemical properties, and the appealing interest to incorporate them in the next generation of electronic and optoelectronic devices. We predict that the effective dielectric constant (ε) of few-layer graphene and MoS2 is tunable by external electric fields (E ext). We show that at low fields (E ext < 0.01 V/Å) ε assumes a nearly constant value ∼4 for both materials, but increases at higher fields to values that depend on the layer thickness. The thicker the structure the stronger is the modulation of ε with the electric field. Increasing of the external field perpendicular to the layer surface above a critical value can drive the systems to an unstable state where the layers are weakly coupled and can be easily separated. The observed dependence of ε on the external field is due to charge polarization driven by the bias, which show several similar characteristics despite of the layer considered. All these results provide key information about control and understanding of the screening properties in two-dimensional crystals beyond graphene and MoS2

Desenho do real : análise, representação e consciência crítica

O presente relatório reflete sobre o processo de representação pelo desenho de uma forma tridimensional num suporte bidimensional. A intenção deste relatório é analisar e compreender a relação entre o que é analisado pelo cérebro, o que é representado no papel e a consciência crítica do erro praticado no desenho de observação, bem como conhecer como poderá ser desenvolvida esta triangulação (análise, representação e consciência crítica do erro) de modo a melhorar a qualidade da representação do real. A investigação empírica foi realizada na disciplina de Desenho A, no ano letivo de 2012/2013, com duas turmas do 11º ano do Curso de Design de Produto na Escola Artística Soares dos Reis, no Porto. Os resultados obtidos sugerem que a perspetiva, enquanto estratégia, poderá melhorar significativamente a qualidade da representação do real. Todavia, relativamente ao estímulo da consciência crítica do erro através das estratégias abordadas dentro de sala de aula, não ficou comprovada relevância na qualidade das representações.

Shock Train/Boundary-Layer Interaction in Rectangular Scramjet Isolators

Numerous studies of the dual-mode scramjet isolator, a critical component in preventing inlet unstart and/or vehicle loss by containing a collection of flow disturbances called a shock train, have been performed since the dual-mode propulsion cycle was introduced in the 1960s. Low momentum corner flow and other three-dimensional effects inherent to rectangular isolators have, however, been largely ignored in experimental studies of the boundary layer separation driven isolator shock train dynamics. Furthermore, the use of two dimensional diagnostic techniques in past works, be it single-perspective line-of-sight schlieren/shadowgraphy or single axis wall pressure measurements, have been unable to resolve the three-dimensional flow features inside the rectangular isolator. These flow characteristics need to be thoroughly understood if robust dual-mode scramjet designs are to be fielded. The work presented in this thesis is focused on experimentally analyzing shock train/boundary layer interactions from multiple perspectives in aspect ratio 1.0, 3.0, and 6.0 rectangular isolators with inflow Mach numbers ranging from 2.4 to 2.7. Secondary steady-state Computational Fluid Dynamics studies are performed to compare to the experimental results and to provide additional perspectives of the flow field. Specific issues that remain unresolved after decades of isolator shock train studies that are addressed in this work include the three-dimensional formation of the isolator shock train front, the spatial and temporal low momentum corner flow separation scales, the transient behavior of shock train/boundary layer interaction at specific coordinates along the isolator's lateral axis, and effects of the rectangular geometry on semi-empirical relations for shock train length prediction. A novel multiplane shadowgraph technique is developed to resolve the structure of the shock train along both the minor and major duct axis simultaneously. It is shown that the shock train front is of a hybrid oblique/normal nature. Initial low momentum corner flow separation spawns the formation of oblique shock planes which interact and proceed toward the center flow region, becoming more normal in the process. The hybrid structure becomes more two-dimensional as aspect ratio is increased but corner flow separation precedes center flow separation on the order of 1 duct height for all aspect ratios considered. Additional instantaneous oil flow surface visualization shows the symmetry of the three-dimensional shock train front around the lower wall centerline. Quantitative synthetic schlieren visualization shows the density gradient magnitude approximately double between the corner oblique and center flow normal structures. Fast response pressure measurements acquired near the corner region of the duct show preliminary separation in the outer regions preceding centerline separation on the order of 2 seconds. Non-intrusive Focusing Schlieren Deflectometry Velocimeter measurements reveal that both shock train oscillation frequency and velocity component decrease as measurements are taken away from centerline and towards the side-wall region, along with confirming the more two dimensional shock train front approximation for higher aspect ratios. An updated modification to Waltrup \& Billig's original semi-empirical shock train length relation for circular ducts based on centerline pressure measurements is introduced to account for rectangular isolator aspect ratio, upstream corner separation length scale, and major- and minor-axis boundary layer momentum thickness asymmetry. The latter is derived both experimentally and computationally and it is shown that the major-axis (side-wall) boundary layer has lower momentum thickness compared to the minor-axis (nozzle bounded) boundary layer, making it more separable. Furthermore, it is shown that the updated correlation drastically improves shock train length prediction capabilities in higher aspect ratio isolators. This thesis suggests that performance analysis of rectangular confined supersonic flow fields can no longer be based on observations and measurements obtained along a single axis alone. Knowledge gained by the work performed in this study will allow for the development of more robust shock train leading edge detection techniques and isolator designs which can greatly mitigate the risk of inlet unstart and/or vehicle loss in flight.

DIRECT NUMERICAL SIMULATION OF INCOMPRESSIBLE MULTIPHASE FLOW WITH PHASE CHANGE

Phase change problems arise in many practical applications such as air-conditioning and refrigeration, thermal energy storage systems and thermal management of electronic devices. The physical phenomenon in such applications are complex and are often difficult to be studied in detail with the help of only experimental techniques. The efforts to improve computational techniques for analyzing two-phase flow problems with phase change are therefore gaining momentum. The development of numerical methods for multiphase flow has been motivated generally by the need to account more accurately for (a) large topological changes such as phase breakup and merging, (b) sharp representation of the interface and its discontinuous properties and (c) accurate and mass conserving motion of the interface. In addition to these considerations, numerical simulation of multiphase flow with phase change introduces additional challenges related to discontinuities in the velocity and the temperature fields. Moreover, the velocity field is no longer divergence free. For phase change problems, the focus of developmental efforts has thus been on numerically attaining a proper conservation of energy across the interface in addition to the accurate treatment of fluxes of mass and momentum conservation as well as the associated interface advection. Among the initial efforts related to the simulation of bubble growth in film boiling applications the work in \cite{Welch1995} was based on the interface tracking method using a moving unstructured mesh. That study considered moderate interfacial deformations. A similar problem was subsequently studied using moving, boundary fitted grids \cite{Son1997}, again for regimes of relatively small topological changes. A hybrid interface tracking method with a moving interface grid overlapping a static Eulerian grid was developed \cite{Juric1998} for the computation of a range of phase change problems including, three-dimensional film boiling \cite{esmaeeli2004computations}, multimode two-dimensional pool boiling \cite{Esmaeeli2004} and film boiling on horizontal cylinders \cite{Esmaeeli2004a}. The handling of interface merging and pinch off however remains a challenge with methods that explicitly track the interface. As large topological changes are crucial for phase change problems, attention has turned in recent years to front capturing methods utilizing implicit interfaces that are more effective in treating complex interface deformations. The VOF (Volume of Fluid) method was adopted in \cite{Welch2000} to simulate the one-dimensional Stefan problem and the two-dimensional film boiling problem. The approach employed a specific model for mass transfer across the interface involving a mass source term within cells containing the interface. This VOF based approach was further coupled with the level set method in \cite{Son1998}, employing a smeared-out Heaviside function to avoid the numerical instability related to the source term. The coupled level set, volume of fluid method and the diffused interface approach was used for film boiling with water and R134a at the near critical pressure condition \cite{Tomar2005}. The effect of superheat and saturation pressure on the frequency of bubble formation were analyzed with this approach. The work in \cite{Gibou2007} used the ghost fluid and the level set methods for phase change simulations. A similar approach was adopted in \cite{Son2008} to study various boiling problems including three-dimensional film boiling on a horizontal cylinder, nucleate boiling in microcavity \cite{lee2010numerical} and flow boiling in a finned microchannel \cite{lee2012direct}. The work in \cite{tanguy2007level} also used the ghost fluid method and proposed an improved algorithm based on enforcing continuity and divergence-free condition for the extended velocity field. The work in \cite{sato2013sharp} employed a multiphase model based on volume fraction with interface sharpening scheme and derived a phase change model based on local interface area and mass flux. Among the front capturing methods, sharp interface methods have been found to be particularly effective both for implementing sharp jumps and for resolving the interfacial velocity field. However, sharp velocity jumps render the solution susceptible to erroneous oscillations in pressure and also lead to spurious interface velocities. To implement phase change, the work in \cite{Hardt2008} employed point mass source terms derived from a physical basis for the evaporating mass flux. To avoid numerical instability, the authors smeared the mass source by solving a pseudo time-step diffusion equation. This measure however led to mass conservation issues due to non-symmetric integration over the distributed mass source region. The problem of spurious pressure oscillations related to point mass sources was also investigated by \cite{Schlottke2008}. Although their method is based on the VOF, the large pressure peaks associated with sharp mass source was observed to be similar to that for the interface tracking method. Such spurious fluctuation in pressure are essentially undesirable because the effect is globally transmitted in incompressible flow. Hence, the pressure field formation due to phase change need to be implemented with greater accuracy than is reported in current literature. The accuracy of interface advection in the presence of interfacial mass flux (mass flux conservation) has been discussed in \cite{tanguy2007level,tanguy2014benchmarks}. The authors found that the method of extending one phase velocity to entire domain suggested by Nguyen et al. in \cite{nguyen2001boundary} suffers from a lack of mass flux conservation when the density difference is high. To improve the solution, the authors impose a divergence-free condition for the extended velocity field by solving a constant coefficient Poisson equation. The approach has shown good results with enclosed bubble or droplet but is not general for more complex flow and requires additional solution of the linear system of equations. In current thesis, an improved approach that addresses both the numerical oscillation of pressure and the spurious interface velocity field is presented by featuring (i) continuous velocity and density fields within a thin interfacial region and (ii) temporal velocity correction steps to avoid unphysical pressure source term. Also I propose a general (iii) mass flux projection correction for improved mass flux conservation. The pressure and the temperature gradient jump condition are treated sharply. A series of one-dimensional and two-dimensional problems are solved to verify the performance of the new algorithm. Two-dimensional and cylindrical film boiling problems are also demonstrated and show good qualitative agreement with the experimental observations and heat transfer correlations. Finally, a study on Taylor bubble flow with heat transfer and phase change in a small vertical tube in axisymmetric coordinates is carried out using the new multiphase, phase change method.

Electrical and optical studies on carbon nanotube arrays

Single-walled carbon nanotubes (SWNTs) have been studied as a prominent class of high performance electronic materials for next generation electronics. Their geometry dependent electronic structure, ballistic transport and low power dissipation due to quasi one dimensional transport, and their capability of carrying high current densities are some of the main reasons for the optimistic expectations on SWNTs. However, device applications of individual SWNTs have been hindered by uncontrolled variations in characteristics and lack of scalable methods to integrate SWNTs into electronic devices. One relatively new direction in SWNT electronics, which avoids these issues, is using arrays of SWNTs, where the ensemble average may provide uniformity from device to device, and this new breed of electronic material can be integrated into electronic devices in a scalable fashion. This dissertation describes (1) methods for characterization of SWNT arrays, (2) how the electrical transport in these two-dimensional arrays depend on length scales and spatial anisotropy, (3) the interaction of aligned SWNTs with the underlying substrate, and (4) methods for scalable integration of SWNT arrays into electronic devices. The electrical characterization of SWNT arrays have been realized by polymer electrolyte-gated SWNT thin film transistors (TFTs). Polymer electrolyte-gating addresses many technical difficulties inherent to electrical characterization by gating through oxide-dielectrics. Having shown polymer electrolyte-gating can be successfully applied on SWNT arrays, we have studied the length scaling dependence of electrical transport in SWNT arrays. Ultrathin films formed by sub-monolayer surface coverage of SWNT arrays are very interesting systems in terms of the physics of two-dimensional electronic transport. We have observed that they behave qualitatively different than the classical conducting films, which obey the Ohm’s law. The resistance of an ultrathin film of SWNT arrays is indeed non-linear with the length of the film, across which the transport occurs. More interestingly, a transition between conducting and insulating states is observed at a critical surface coverage, which is called percolation limit. The surface coverage of conducting SWNTs can be manipulated by turning on and off the semiconductors in the SWNT array, leading to the operation principle of SWNT TFTs. The percolation limit depends also on the length and the spatial orientation of SWNTs. We have also observed that the percolation limit increases abruptly for aligned arrays of SWNTs, which are grown on single crystal quartz substrates. In this dissertation, we also compare our experimental results with a two-dimensional stick network model, which gives a good qualitative picture of the electrical transport in SWNT arrays in terms of surface coverage, length scaling, and spatial orientation, and briefly discuss the validity of this model. However, the electronic properties of SWNT arrays are not only determined by geometrical arguments. The contact resistances at the nanotube-nanotube and nanotube-electrode (bulk metal) interfaces, and interactions with the local chemical groups and the underlying substrates are among other issues related to the electronic transport in SWNT arrays. Different aspects of these factors have been studied in detail by many groups. In fact, I have also included a brief discussion about electron injection onto semiconducting SWNTs by polymer dopants. On the other hand, we have compared the substrate-SWNT interactions for isotropic (in two dimensions) arrays of SWNTs grown on Si/SiO2 substrates and horizontally (on substrate) aligned arrays of SWNTs grown on single crystal quartz substrates. The anisotropic interactions associated with the quartz lattice between quartz and SWNTs that allow near perfect horizontal alignment on substrate along a particular crystallographic direction is examined by Raman spectroscopy, and shown to lead to uniaxial compressive strain in as-grown SWNTs on single crystal quartz. This is the first experimental demonstration of the hard-to-achieve uniaxial compression of SWNTs. Temperature dependence of Raman G-band spectra along the length of individual nanotubes reveals that the compressive strain is non-uniform and can be larger than 1% locally at room temperature. Effects of device fabrication steps on the non-uniform strain are also examined and implications on electrical performance are discussed. Based on our findings, there are discussions about device performances and designs included in this dissertation. The channel length dependences of device mobilities and on/off ratios are included for SWNT TFTs. Time response of polymer-electrolyte gated SWNT TFTs has been measured to be ~300 Hz, and a proof-of-concept logic inverter has been fabricated by using polymer electrolyte gated SWNT TFTs for macroelectronic applications. Finally, I dedicated a chapter on scalable device designs based on aligned arrays of SWNTs, including a design for SWNT memory devices.

Flexible regression models for functional neuroimaging

Current practice for analysing functional neuroimaging data is to average the brain signals recorded at multiple sensors or channels on the scalp over time across hundreds of trials or replicates to eliminate noise and enhance the underlying signal of interest. These studies recording brain signals non-invasively using functional neuroimaging techniques such as electroencephalography (EEG) and magnetoencephalography (MEG) generate complex, high dimensional and noisy data for many subjects at a number of replicates. Single replicate (or single trial) analysis of neuroimaging data have gained focus as they are advantageous to study the features of the signals at each replicate without averaging out important features in the data that the current methods employ. The research here is conducted to systematically develop flexible regression mixed models for single trial analysis of specific brain activities using examples from EEG and MEG to illustrate the models. This thesis follows three specific themes: i) artefact correction to estimate the `brain' signal which is of interest, ii) characterisation of the signals to reduce their dimensions, and iii) model fitting for single trials after accounting for variations between subjects and within subjects (between replicates). The models are developed to establish evidence of two specific neurological phenomena - entrainment of brain signals to an $\alpha$ band of frequencies (8-12Hz) and dipolar brain activation in the same $\alpha$ frequency band in an EEG experiment and a MEG study, respectively.

Dealing with the devil: a critical and creative look at the diabolical pact

This thesis is comprised of three parts: a critical dissertation, a creative work of fiction and a bridge piece that connects the two. The critical work is an examination of the Devil as a satirist in Faustian bargains. Through the usage of the Devil as a literary figure, his character has become a more secular being: a trickster rather than evil incarnate—a facilitator of sin rather than its originator. In the tragicomedy of pacts with the Devil, he acts as a mirror, reflecting mankind’s foibles and vanity, while elevating the reader in the process. The thesis considers the language, tone, purpose and conceits of several versions of the story. While the focus is primarily on American Literature, the influence of English, Scottish, French and German folklore and fiction are recognized as an essential component of the theme’s evolution. In the bridge piece, the pact with the Devil is literalized in a modern context; a corporate business of reaping souls is theorized in which techniques of persuasion are streamlined into an effective formula. Whether immersive or expository in approach, the portrayal of the supernatural depends on the literary principles of science fiction and fantasy in order to manipulate the reader and allow irrational concepts to obey rational laws. Such theories are cited to support how the Devil functions as a believable character. The novel, Could Be Much Worse, relates the story of an egocentric boss and his dependable employee, a scout who disguises himself as a taxi driver and seeks candidates who may succumb to temptation. Passengers’ monologues of desperation and pathos are interspersed throughout the protagonist’s day-to-day narrative. At times, the work is experimental, utilizing irregular storytelling techniques, alternative forms and conceits. Light-hearted, but nonetheless poignant, the story serves as a cautionary tale, illustrating the tedium of a bureaucratic job in a transmundane existence.

Locus of Control revisited: development of a new bi-dimensional measure

Locus of control (LOC) has a long tradition in Psychology, and various instruments have been designed for its measurement. However, the dimensionality of the construct is unclear, and still gives rise to considerable controversy. The aim of the present work is to present new evidence of validity in relation to the dimensionality of LOC. To this end, we developed a new measurement instrument with 23 items. The sample was made up of 697 Spanish participants, of whom 57.5% were women (M=22.43; SD= 9.19). The results support the bi-dimensionality of LOC: internal (α=.87) and external (α=.85). Furthermore, both subscales have shown adequate validity evidence in relation to self-efficacy, achievement motivation and optimism (r xy> .21). Statistically significant differences were found by sex (p < .05): men scored higher in external LOC and women in internal LOC. The validity evidence supports a two-dimensional structure for the LOC, and the measurement instrument developed showed adequate psychometric properties.

Fully Anisotropic Solution of the Three Dimensional Boltzmann Transport Equation

The development of accurate modeling techniques for nanoscale thermal transport is an active area of research. Modern day nanoscale devices have length scales of tens of nanometers and are prone to overheating, which reduces device performance and lifetime. Therefore, accurate temperature profiles are needed to predict the reliability of nanoscale devices. The majority of models that appear in the literature obtain temperature profiles through the solution of the Boltzmann transport equation (BTE). These models often make simplifying assumptions about the nature of the quantized energy carriers (phonons). Additionally, most previous work has focused on simulation of planar two dimensional structures. This thesis presents a method which captures the full anisotropy of the Brillouin zone within a three dimensional solution to the BTE. The anisotropy of the Brillouin zone is captured by solving the BTE for all vibrational modes allowed by the Born Von-Karman boundary conditions.

Efficient split eld FDTD analysis of third-order nonlinear materials in two-dimensionally periodic media

In this work the split-field finite-difference time-domain method (SF-FDTD) has been extended for the analysis of two-dimensionally periodic structures with third-order nonlinear media. The accuracy of the method is verified by comparisons with the nonlinear Fourier Modal Method (FMM). Once the formalism has been validated, examples of one- and two-dimensional nonlinear gratings are analysed. Regarding the 2D case, the shifting in resonant waveguides is corroborated. Here, not only the scalar Kerr effect is considered, the tensorial nature of the third-order nonlinear susceptibility is also included. The consideration of nonlinear materials in this kind of devices permits to design tunable devices such as variable band filters. However, the third-order nonlinear susceptibility is usually small and high intensities are needed in order to trigger the nonlinear effect. Here, a one-dimensional CBG is analysed in both linear and nonlinear regime and the shifting of the resonance peaks in both TE and TM are achieved numerically. The application of a numerical method based on the finite- difference time-domain method permits to analyse this issue from the time domain, thus bistability curves are also computed by means of the numerical method. These curves show how the nonlinear effect modifies the properties of the structure as a function of variable input pump field. When taking the nonlinear behaviour into account, the estimation of the electric field components becomes more challenging. In this paper, we present a set of acceleration strategies based on parallel software and hardware solutions.

A two-fluid model for tissue growth within a dynamic flow environment

We study the growth of a tissue construct in a perfusion bioreactor, focussing on its response to the mechanical environment. The bioreactor system is modelled as a two-dimensional channel containing a tissue construct through which a flow of culture medium is driven. We employ a multiphase formulation of the type presented by G. Lemon, J. King, H. Byrne, O. Jensen and K. Shakesheff in their study (Multiphase modelling of tissue growth using the theory of mixtures. J. Math. Biol. 52(2), 2006, 571–594) restricted to two interacting fluid phases, representing a cell population (and attendant extracellular matrix) and a culture medium, and employ the simplifying limit of large interphase viscous drag after S. Franks in her study (Mathematical Modelling of Tumour Growth and Stability. Ph.D. Thesis, University of Nottingham, UK, 2002) and S. Franks and J. King in their study Interactions between a uniformly proliferating tumour and its surrounding: Uniform material properties. Math. Med. Biol. 20, 2003, 47–89). The novel aspects of this study are: (i) the investigation of the effect of an imposed flow on the growth of the tissue construct, and (ii) the inclusion of a chanotransduction mechanism regulating the response of the cells to the local mechanical environment. Specifically, we consider the response of the cells to their local density and the culture medium pressure. As such, this study forms the first step towards a general multiphase formulation that incorporates the effect of mechanotransduction on the growth and morphology of a tissue construct. The model is analysed using analytic and numerical techniques, the results of which illustrate the potential use of the model to predict the dominant regulatory stimuli in a cell population.