Source localization of reaction-diffusion models for brain tumors

We propose a mathematically well-founded approach for locating the source (initial state) of density functions evolved within a nonlinear reaction-diffusion model. The reconstruction of the initial source is an ill-posed inverse problem since the solution is highly unstable with respect to measurement noise. To address this instability problem, we introduce a regularization procedure based on the nonlinear Landweber method for the stable determination of the source location. This amounts to solving a sequence of well-posed forward reaction-diffusion problems. The developed framework is general, and as a special instance we consider the problem of source localization of brain tumors. We show numerically that the source of the initial densities of tumor cells are reconstructed well on both imaging data consisting of simple and complex geometric structures.

Parametric pattern selection in a reaction-diffusion model

We compare spot patterns generated by Turing mechanisms with those generated by replication cascades, in a model one-dimensional reaction-diffusion system. We determine the stability region of spot solutions in parameter space as a function of a natural control parameter (feed-rate) where degenerate patterns with different numbers of spots coexist for a fixed feed-rate. While it is possible to generate identical patterns via both mechanisms, we show that replication cascades lead to a wider choice of pattern profiles that can be selected through a tuning of the feed-rate, exploiting hysteresis and directionality effects of the different pattern pathways.

Multiscale modelling of heterogeneously catalysed transesterification reaction process:an overview

Biodiesel is fast becoming one of the key transport fuels as the world endeavours to reduce its carbon footprint and find viable alternatives to oil derived fuels. Research in the field is currently focusing on more efficient ways to produce biodiesel, with the most promising avenue of research looking into the use of heterogeneous catalysis. This article presents a framework for kinetic reaction and diffusive transport modelling of the heterogeneously catalysed transesterification of triglycerides into fatty acid methyl esters (FAMEs), unveiled by a model system of tributyrin transesterification in the presence of MgO catalysts. In particular, the paper makes recommendations on multicomponent diffusion calculations such as the diffusion coefficients and molar fluxes from infinite dilution diffusion coefficients using the Wilke and Chang correlation, intrinsic reaction kinetic studies using the Eley-Rideal kinetic mechanism with methanol adsorption as the rate determining steps and multiscale reaction-diffusion process simulation between catalytic porous and bulk reactor scales. © 2013 The Royal Society of Chemistry.

Thermal processing of miscanthus, sugarcane bagasse, sugarcane trash and their acid hydrolysis residues

The research presented in this thesis was developed as part of DIBANET, an EC funded project aiming to develop an energetically self-sustainable process for the production of diesel miscible biofuels (i.e. ethyl levulinate) via acid hydrolysis of selected biomass feedstocks. Three thermal conversion technologies, pyrolysis, gasification and combustion, were evaluated in the present work with the aim of recovering the energy stored in the acid hydrolysis solid residue (AHR). Mainly consisting of lignin and humins, the AHR can contain up to 80% of the energy in the original feedstock. Pyrolysis of AHR proved unsatisfactory, so attention focussed on gasification and combustion with the aim of producing heat and/or power to supply the energy demanded by the ethyl levulinate production process. A thermal processing rig consisting on a Laminar Entrained Flow Reactor (LEFR) equipped with solid and liquid collection and online gas analysis systems was designed and built to explore pyrolysis, gasification and air-blown combustion of AHR. Maximum liquid yield for pyrolysis of AHR was 30wt% with volatile conversion of 80%. Gas yield for AHR gasification was 78wt%, with 8wt% tar yields and conversion of volatiles close to 100%. 90wt% of the AHR was transformed into gas by combustion, with volatile conversions above 90%. 5volO2%-95vol%N2 gasification resulted in a nitrogen diluted, low heating value gas (2MJ/m3). Steam and oxygen-blown gasification of AHR were additionally investigated in a batch gasifier at KTH in Sweden. Steam promoted the formation of hydrogen (25vol%) and methane (14vol%) improving the gas heating value to 10MJ/m3, below the typical for steam gasification due to equipment limitations. Arrhenius kinetic parameters were calculated using data collected with the LEFR to provide reaction rate information for process design and optimisation. Activation energy (EA) and pre-exponential factor (ko in s-1) for pyrolysis (EA=80kJ/mol, lnko=14), gasification (EA=69kJ/mol, lnko=13) and combustion (EA=42kJ/mol, lnko=8) were calculated after linearly fitting the data using the random pore model. Kinetic parameters for pyrolysis and combustion were also determined by dynamic thermogravimetric analysis (TGA), including studies of the original biomass feedstocks for comparison. Results obtained by differential and integral isoconversional methods for activation energy determination were compared. Activation energy calculated by the Vyazovkin method was 103-204kJ/mol for pyrolysis of untreated feedstocks and 185-387kJ/mol for AHRs. Combustion activation energy was 138-163kJ/mol for biomass and 119-158 for AHRs. The non-linear least squares method was used to determine reaction model and pre-exponential factor. Pyrolysis and combustion of biomass were best modelled by a combination of third order reaction and 3 dimensional diffusion models, while AHR decomposed following the third order reaction for pyrolysis and the 3 dimensional diffusion for combustion.

Molecular phase space transport in water:non-stationary random walk model

Molecular transport in phase space is crucial for chemical reactions because it defines how pre-reactive molecular configurations are found during the time evolution of the system. Using Molecular Dynamics (MD) simulated atomistic trajectories we test the assumption of the normal diffusion in the phase space for bulk water at ambient conditions by checking the equivalence of the transport to the random walk model. Contrary to common expectations we have found that some statistical features of the transport in the phase space differ from those of the normal diffusion models. This implies a non-random character of the path search process by the reacting complexes in water solutions. Our further numerical experiments show that a significant long period of non-stationarity in the transition probabilities of the segments of molecular trajectories can account for the observed non-uniform filling of the phase space. Surprisingly, the characteristic periods in the model non-stationarity constitute hundreds of nanoseconds, that is much longer time scales compared to typical lifetime of known liquid water molecular structures (several picoseconds).

Noise-induced standing waves in oscillatory systems with time-delayed feedback

In oscillatory reaction-diffusion systems, time-delay feedback can lead to the instability of uniform oscillations with respect to formation of standing waves. Here, we investigate how the presence of additive, Gaussian white noise can induce the appearance of standing waves. Combining analytical solutions of the model with spatio-temporal simulations, we find that noise can promote standing waves in regimes where the deterministic uniform oscillatory modes are stabilized. As the deterministic phase boundary is approached, the spatio-temporal correlations become stronger, such that even small noise can induce standing waves in this parameter regime. With larger noise strengths, standing waves could be induced at finite distances from the (deterministic) phase boundary. The overall dynamics is defined through the interplay of noisy forcing with the inherent reaction-diffusion dynamics.

Dynamics of spatial heterogeneity in a landfill with interacting phase densities:a stochastic analysis

A landfill represents a complex and dynamically evolving structure that can be stochastically perturbed by exogenous factors. Both thermodynamic (equilibrium) and time varying (non-steady state) properties of a landfill are affected by spatially heterogenous and nonlinear subprocesses that combine with constraining initial and boundary conditions arising from the associated surroundings. While multiple approaches have been made to model landfill statistics by incorporating spatially dependent parameters on the one hand (data based approach) and continuum dynamical mass-balance equations on the other (equation based modelling), practically no attempt has been made to amalgamate these two approaches while also incorporating inherent stochastically induced fluctuations affecting the process overall. In this article, we will implement a minimalist scheme of modelling the time evolution of a realistic three dimensional landfill through a reaction-diffusion based approach, focusing on the coupled interactions of four key variables - solid mass density, hydrolysed mass density, acetogenic mass density and methanogenic mass density, that themselves are stochastically affected by fluctuations, coupled with diffusive relaxation of the individual densities, in ambient surroundings. Our results indicate that close to the linearly stable limit, the large time steady state properties, arising out of a series of complex coupled interactions between the stochastically driven variables, are scarcely affected by the biochemical growth-decay statistics. Our results clearly show that an equilibrium landfill structure is primarily determined by the solid and hydrolysed mass densities only rendering the other variables as statistically "irrelevant" in this (large time) asymptotic limit. The other major implication of incorporation of stochasticity in the landfill evolution dynamics is in the hugely reduced production times of the plants that are now approximately 20-30 years instead of the previous deterministic model predictions of 50 years and above. The predictions from this stochastic model are in conformity with available experimental observations.

On models for magnetic field line diffusion

In this contribution, certain aspects of the nonlinear dynamics of magnetic field lines are reviewed. First, the basic facts (known from literature) concerning the Hamiltonian structure are briefly summarized. The paper then concentrates on the following subjects: (i) Transition from the continuous description to discrete maps; (ii) Characteristics of incomplete chaos; (iii) Control of chaos. The presentation is concluded by some remarks on the motion of particles in stochastic magnetic fields.

Stock price reaction following large one-day price changes: UK evidence

We examine the short-term price reaction of 424 UK stocks to large one-day price changes. Using the GJR-GARCH(1,1), we find no statistical difference amongst the cumulative abnormal returns (CARs) of the Single Index, the Fama–French and the Carhart–Fama–French models. Shocks bigger or equal to 5% are followed by a significant one-day CAR of 1% for all the models. Whilst shocks smaller or equal to -5% are followed by a significant one-day CAR of -0.43% for the Single Index, the CARs are around -0.34% for the other two models. Positive shocks of all sizes and negative shocks maller or equal to -5% are followed by return continuations, whilst the market is efficient following larger negative shocks. The price reaction to shocks is unaffected when we estimate the CARs using the conditional covariances of the pricing variables.

On the adoption decision and the intensity of use of complementary innovations: The intra firm diffusion of management practices across UK establishments

This paper contributes to the literature on the intra-firm diffusion of innovations by investigating the factors that affect the firm’s decision to adopt and use sets of complementary innovations. We define complementary innovations those innovations whose joint use generates super additive gains, i.e. the gain from the joint adoption is higher than the sum of the gains derived from the adoption of each innovation in isolation. From a theoretical perspective, we present a simple decision model, whereby the firm decides ‘whether’ and ‘how much’ to invest in each of the innovations under investigation based upon the expected profit gain from each possible combination of adoption and use. The model shows how the extent of complementarity among the innovations can affect the firm’s profit gains and therefore the likelihood that the firm will adopt these innovations jointly, rather than individually. From an empirical perspective, we focus on four sets of management practices, namely operating (OMP), monitoring (MMP), targets (TMP) and incentives (IMP) management practices. We show that these sets of practices, although to a different extent, are complementary to each other. Then, we construct a synthetic indicator of the depth of their use. The resulting intra-firm index is built to reflect not only the number of practices adopted but also the depth of their individual use and the extent of their complementarity. The empirical testing of the decision model is carried out using the evidence from the adoption behaviour of a sample of 1,238 UK establishments present in the 2004 Workplace Employment Relations Survey (WERS). Our empirical results show that the intra-firm profitability based model is a good model in that it can explain more of the variability of joint adoption than models based upon the variability of adoption and use of individual practices. We also investigate whether a number of firm specific and market characteristics by affecting the size of the gains (which the joint adoption of innovations can generate) may drive the intensity of use of the four innovations. We find that establishment size, whether foreign owned, whether exposed to an international market and the degree of homogeneity of the final product are important determinants of the intensity of the joint adoption of the four innovations. Most importantly, our results point out that the factors that the economics of innovation literature has been showing to affect the intensity of use of a technological innovation do also affect the intensity of use of sets of innovative management practices. However, they can explain only a small part of the diversity of their joint adoption use by the firms in the sample.

Numerical Comparison of the Drag Models of Granular Flows Applied to the Fast Pyrolysis of Biomass

The paper presents a comparison between the different drag models for granular flows developed in the literature and the effect of each one of them on the fast pyrolysis of wood. The process takes place on an 100 g/h lab scale bubbling fluidized bed reactor located at Aston University. FLUENT 6.3 is used as the modeling framework of the fluidized bed hydrodynamics, while the fast pyrolysis of the discrete wood particles is incorporated as an external user defined function (UDF) hooked to FLUENT’s main code structure. Three different drag models for granular flows are compared, namely the Gidaspow, Syamlal O’Brien, and Wen-Yu, already incorporated in FLUENT’s main code, and their impact on particle trajectory, heat transfer, degradation rate, product yields, and char residence time is quantified. The Eulerian approach is used to model the bubbling behavior of the sand, which is treated as a continuum. Biomass reaction kinetics is modeled according to the literature using a two-stage, semiglobal model that takes into account secondary reactions.

A longitudinal study of the diffusion of the ISO/IEC information resource dictionary system standard (IRDS.)

The IRDS standard is an international standard produced by the International Organisation for Standardisation (ISO). In this work the process for producing standards in formal standards organisations, for example the ISO, and in more informal bodies, for example the Object Management Group (OMG), is examined. This thesis examines previous models and classifications of standards. The previous models and classifications are then combined to produce a new classification. The IRDS standard is then placed in a class in the new model as a reference anticipatory standard. Anticipatory standards are standards which are developed ahead of the technology in order to attempt to guide the market. The diffusion of the IRDS is traced over a period of eleven years. The economic conditions which affect the diffusion of standards are examined, particularly the economic conditions which prevail in compatibility markets such as the IT and ICT markets. Additionally the consequences of the introduction of gateway or converter devices into a market where a standard has not yet been established is examined. The IRDS standard did not have an installed base and this hindered its diffusion. The thesis concludes that the IRDS standard was overtaken by new developments such as object oriented technologies and middleware. This was partly because of the slow development process of developing standards in traditional organisations which operate on a consensus basis and partly because the IRDS standard did not have an installed base. Also the rise and proliferation of middleware products resulted in exchange mechanisms becoming dominant rather than repository solutions. The research method used in this work is a longitudinal study of the development and diffusion of the ISO/EEC IRDS standard. The research is regarded as a single case study and follows the interpretative epistemological point of view.

Modeling competitive reaction effects

In this study I critically review models that specify competitive reaction effects. I discuss different model structures and summarize my findings on competitive reaction effects and factors that explain competitive reactions. I discuss the many models of competitive market response that have been developed and classify them into twelve sets of models that are related to each other in a logical manner through the evolutionary model-building concept.

Travelling waves in a complex Ginzburg-Landau equation with time-delay feedback

One of the simplest ways to create nonlinear oscillations is the Hopf bifurcation. The spatiotemporal dynamics observed in an extended medium with diffusion (e.g., a chemical reaction) undergoing this bifurcation is governed by the complex Ginzburg-Landau equation, one of the best-studied generic models for pattern formation, where besides uniform oscillations, spiral waves, coherent structures and turbulence are found. The presence of time delay terms in this equation changes the pattern formation scenario, and different kind of travelling waves have been reported. In particular, we study the complex Ginzburg-Landau equation that contains local and global time-delay feedback terms. We focus our attention on plane wave solutions in this model. The first novel result is the derivation of the plane wave solution in the presence of time-delay feedback with global and local contributions. The second and more important result of this study consists of a linear stability analysis of plane waves in that model. Evaluation of the eigenvalue equation does not show stabilisation of plane waves for the parameters studied. We discuss these results and compare to results of other models.

An examination of NPD models in the context of business models

Most prior new product diffusion (NPD) models do not specifically consider the role of the business model in the process. However, the context of NPD in today's market has been changed dramatically by the introduction of new business models. Through reinterpretation and extension, this paper empirically examines the feasibility of applying Bass-type NPD models to products that are commercialized by different business models. More specifically, the results and analysis of this study consider the subscription business model for service products, the freemium business model for digital products, and a pre-paid and post-paid business model that is widely used by mobile network providers. The paper offers new insights derived from implementing the models in real-life cases. It also highlights three themes for future research.