Continuum, Discrete, and Explicit Solvation Models for Describing the Low-Lying Absorption Spectrum of the Pterin Acid in Aqueous Environment

The absorption spectrum of the acid form of pterin in water was investigated theoretically. Different procedures using continuum, discrete, and explicit models were used to include the solvation effect on the absorption spectrum, characterized by two bands. The discrete and explicit models used Monte Carlo simulation to generate the liquid structure and time-dependent density functional theory (B3LYP/6-31G+(d)) to obtain the excitation energies. The discrete model failed to give the correct qualitative effect on the second absorption band. The continuum model, in turn, has given a correct qualitative picture and a semiquantitative description. The explicit use of 29 solvent molecules, forming a hydration shell of 6 angstrom, embedded in the electrostatic field of the remaining solvent molecules, gives absorption transitions at 3.67 and 4.59 eV in excellent agreement with the S(0)-S(1) and S(0)-S(2) absorption bands at of 3.66 and 4.59 eV, respectively, that characterize the experimental spectrum of pterin in water environment. (C) 2010 Wiley Periodicals, Inc. Int J Quantum Chem 110: 2371-2377, 2010

Comparing a discrete and continuum model of the intestinal crypt

The integration of processes at different scales is a key problem in the modelling of cell populations. Owing to increased computational resources and the accumulation of data at the cellular and subcellular scales, the use of discrete, cell-level models, which are typically solved using numerical simulations, has become prominent. One of the merits of this approach is that important biological factors, such as cell heterogeneity and noise, can be easily incorporated. However, it can be difficult to efficiently draw generalizations from the simulation results, as, often, many simulation runs are required to investigate model behaviour in typically large parameter spaces. In some cases, discrete cell-level models can be coarse-grained, yielding continuum models whose analysis can lead to the development of insight into the underlying simulations. In this paper we apply such an approach to the case of a discrete model of cell dynamics in the intestinal crypt. An analysis of the resulting continuum model demonstrates that there is a limited region of parameter space within which steady-state (and hence biologically realistic) solutions exist. Continuum model predictions show good agreement with corresponding results from the underlying simulations and experimental data taken from murine intestinal crypts.

Switching Between Discrete and Continuous Process Models to Predict Molecular Genetic Activity

Two kinds of process models have been used in programs that reason about change: Discrete and continuous models. We describe the design and implementation of a qualitative simulator, PEPTIDE, which uses both kinds of process models to predict the behavior of molecular energetic systems. The program uses a discrete process model to simulate both situations involving abrupt changes in quantities and the actions of small numbers of molecules. It uses a continuous process model to predict gradual changes in quantities. A novel technique, called aggregation, allows the simulator to switch between theses models through the recognition and summary of cycles. The flexibility of PEPTIDE's aggregator allows the program to detect cycles within cycles and predict the behavior of complex situations.

Nonlinear diffusion and exclusion processes with contact interactions

Exclusion processes on a regular lattice are used to model many biological and physical systems at a discrete level. The average properties of an exclusion process may be described by a continuum model given by a partial differential equation. We combine a general class of contact interactions with an exclusion process. We determine that many different types of contact interactions at the agent-level always give rise to a nonlinear diffusion equation, with a vast variety of diffusion functions D(C). We find that these functions may be dependent on the chosen lattice and the defined neighborhood of the contact interactions. Mild to moderate contact interaction strength generally results in good agreement between discrete and continuum models, while strong interactions often show discrepancies between the two, particularly when D(C) takes on negative values. We present a measure to predict the goodness of fit between the discrete and continuous model, and thus the validity of the continuum description of a motile, contact-interacting population of agents. This work has implications for modeling cell motility and interpreting cell motility assays, giving the ability to incorporate biologically realistic cell-cell interactions and develop global measures of discrete microscopic data.

Discrete (MD) and continuum (DD) simulations of void growth in single crystals.

Void growth in ductile materials is an important problem from the fundamental and technological viewpoint. Most of the models developed to quantify and understand the void growth process did not take into account two important factors: the anisotropic nature of plastic flow in single crystals and the size effects that appear when plastic flow is confined into very small regions.

Exploring new and emerging models for nonlinear performative works

This dissertation seeks to define and classify potential forms of Nonlinear structure and explore the possibilities they afford for the creation of new musical works. It provides the first comprehensive framework for the discussion of Nonlinear structure in musical works and provides a detailed overview of the rise of nonlinearity in music during the 20th century. Nonlinear events are shown to emerge through significant parametrical discontinuity at the boundaries between regions of relatively strong internal cohesion. The dissertation situates Nonlinear structures in relation to linear structures and unstructured sonic phenomena and provides a means of evaluating Nonlinearity in a musical structure through the consideration of the degree to which the structure is integrated, contingent, compressible and determinate as a whole. It is proposed that Nonlinearity can be classified as a three dimensional space described by three continuums: the temporal continuum, encompassing sequential and multilinear forms of organization, the narrative continuum encompassing processual, game structure and developmental narrative forms and the referential continuum encompassing stylistic allusion, adaptation and quotation. The use of spectrograms of recorded musical works is proposed as a means of evaluating Nonlinearity in a musical work through the visual representation of parametrical divergence in pitch, duration, timbre and dynamic over time. Spectral and structural analysis of repertoire works is undertaken as part of an exploration of musical nonlinearity and the compositional and performative features that characterize it. The contribution of cultural, ideological, scientific and technological shifts to the emergence of Nonlinearity in music is discussed and a range of compositional factors that contributed to the emergence of musical Nonlinearity is examined. The evolution of notational innovations from the mobile score to the screen score is plotted and a novel framework for the discussion of these forms of musical transmission is proposed. A computer coordinated performative model is discussed, in which a computer synchronises screening of notational information, provides temporal coordination of the performers through click-tracks or similar methods and synchronises the audio processing and synthesized elements of the work. It is proposed that such a model constitutes a highly effective means of realizing complex Nonlinear structures. A creative folio comprising 29 original works that explore nonlinearity is presented, discussed and categorised utilising the proposed classifications. Spectrograms of these works are employed where appropriate to illustrate the instantiation of parametrically divergent substructures and examples of structural openness through multiple versioning.

Comparison of mechanical behaviour of thin film simulated by discrete dislocation dynamics and continuum crystal plasticity

3D finite element simulations of 9-grain multicrystalline aggregates are performed within the framework of the classical continuum crystal plasticity and discrete dislocation dynamics. The results are processed in a statistical way by ensemble averaging. The comparison is made at three levels: macroscopic stress–strain curves, average stress values per grain, local values of stress and plastic strain. The comparison shows that some similarities are observed in the stress and strain distributions in both simulations approaches. But there are also large discrepancies caused by the discrete nature of plasticity in DDD. The DDD simulations provide higher stress levels in the aggregate due to the small number of dislocation sources and to the stress field induced by individual dislocations.

Continuum models of the mechanical behavior of rolled and die-cast magnesium alloys

En los últimos años ha habido una fuerte tendencia a disminuir las emisiones de CO2 y su negativo impacto medioambiental. En la industria del transporte, reducir el peso de los vehículos aparece como la mejor opción para alcanzar este objetivo. Las aleaciones de Mg constituyen un material con gran potencial para el ahorro de peso. Durante la última década se han realizado muchos esfuerzos encaminados a entender los mecanismos de deformación que gobiernan la plasticidad de estos materiales y así, las aleaciones de Mg de colada inyectadas a alta presión y forjadas son todavía objeto de intensas campañas de investigación. Es ahora necesario desarrollar modelos que contemplen la complejidad inherente de los procesos de deformación de éstos. Esta tesis doctoral constituye un intento de entender mejor la relación entre la microestructura y el comportamiento mecánico de aleaciones de Mg, y dará como resultado modelos de policristales capaces de predecir propiedades macro- y microscópicas. La deformación plástica de las aleaciones de Mg está gobernada por una combinación de mecanismos de deformación característicos de la estructura cristalina hexagonal, que incluye el deslizamiento cristalográfico en planos basales, prismáticos y piramidales, así como el maclado. Las aleaciones de Mg de forja presentan texturas fuertes y por tanto los mecanismos de deformación activos dependen de la orientación de la carga aplicada. En este trabajo se ha desarrollado un modelo de plasticidad cristalina por elementos finitos con el objetivo de entender el comportamiento macro- y micromecánico de la aleación de Mg laminada AZ31 (Mg-3wt.%Al-1wt.%Zn). Este modelo, que incorpora el maclado y tiene en cuenta el endurecimiento por deformación debido a las interacciones dislocación-dislocación, dislocación-macla y macla-macla, predice exitosamente las actividades de los distintos mecanismos de deformación y la evolución de la textura con la deformación. Además, se ha llevado a cabo un estudio que combina difracción de electrones retrodispersados en tres dimensiones y modelización para investigar el efecto de los límites de grano en la propagación del maclado en el mismo material. Ambos, experimentos y simulaciones, confirman que el ángulo de desorientación tiene una influencia decisiva en la propagación del maclado. Se ha observado que los efectos no-Schmid, esto es, eventos de deformación plástica que no cumplen la ley de Schmid con respecto a la carga aplicada, no tienen lugar en la vecindad de los límites de baja desorientación y se hacen más frecuentes a medida que la desorientación aumenta. Esta investigación también prueba que la morfología de las maclas está altamente influenciada por su factor de Schmid. Es conocido que los procesos de colada suelen dar lugar a la formación de microestructuras con una microporosidad elevada, lo cuál afecta negativamente a sus propiedades mecánicas. La aplicación de presión hidrostática después de la colada puede reducir la porosidad y mejorar las propiedades aunque es poco conocido su efecto en el tamaño y morfología de los poros. En este trabajo se ha utilizado un enfoque mixto experimentalcomputacional, basado en tomografía de rayos X, análisis de imagen y análisis por elementos finitos, para la determinación de la distribución tridimensional (3D) de la porosidad y de la evolución de ésta con la presión hidrostática en la aleación de Mg AZ91 (Mg- 9wt.%Al-1wt.%Zn) colada por inyección a alta presión. La distribución real de los poros en 3D obtenida por tomografía se utilizó como input para las simulaciones por elementos finitos. Los resultados revelan que la aplicación de presión tiene una influencia significativa tanto en el cambio de volumen como en el cambio de forma de los poros que han sido cuantificados con precisión. Se ha observado que la reducción del tamaño de éstos está íntimamente ligada con su volumen inicial. En conclusión, el modelo de plasticidad cristalina propuesto en este trabajo describe con éxito los mecanismos intrínsecos de la deformación de las aleaciones de Mg a escalas meso- y microscópica. Más especificamente, es capaz de capturar las activadades del deslizamiento cristalográfico y maclado, sus interacciones, así como los efectos en la porosidad derivados de los procesos de colada. ---ABSTRACT--- The last few years have seen a growing effort to reduce CO2 emissions and their negative environmental impact. In the transport industry more specifically, vehicle weight reduction appears as the most straightforward option to achieve this objective. To this end, Mg alloys constitute a significant weight saving material alternative. Many efforts have been devoted over the last decade to understand the main mechanisms governing the plasticity of these materials and, despite being already widely used, high pressure die-casting and wrought Mg alloys are still the subject of intense research campaigns. Developing models that can contemplate the complexity inherent to the deformation of Mg alloys is now timely. This PhD thesis constitutes an attempt to better understand the relationship between the microstructure and the mechanical behavior of Mg alloys, as it will result in the design of polycrystalline models that successfully predict macro- and microscopic properties. Plastic deformation of Mg alloys is driven by a combination of deformation mechanisms specific to their hexagonal crystal structure, namely, basal, prismatic and pyramidal dislocation slip as well as twinning. Wrought Mg alloys present strong textures and thus specific deformation mechanisms are preferentially activated depending on the orientation of the applied load. In this work a crystal plasticity finite element model has been developed in order to understand the macro- and micromechanical behavior of a rolled Mg AZ31 alloy (Mg-3wt.%Al-1wt.%Zn). The model includes twinning and accounts for slip-slip, slip-twin and twin-twin hardening interactions. Upon calibration and validation against experiments, the model successfully predicts the activity of the various deformation mechanisms and the evolution of the texture at different deformation stages. Furthermore, a combined three-dimensional electron backscatter diffraction and modeling approach has been adopted to investigate the effect of grain boundaries on twin propagation in the same material. Both experiments and simulations confirm that the misorientation angle has a critical influence on twin propagation. Non-Schmid effects, i.e. plastic deformation events that do not comply with the Schmid law with respect to the applied stress, are absent in the vicinity of low misorientation boundaries and become more abundant as misorientation angle increases. This research also proves that twin morphology is highly influenced by the Schmid factor. Finally, casting processes usually lead to the formation of significant amounts of gas and shrinkage microporosity, which adversely affect the mechanical properties. The application of hydrostatic pressure after casting can reduce the porosity and improve the properties but little is known about the effects on the casting’s pores size and morphology. In this work, an experimental-computational approach based on X-ray computed tomography, image analysis and finite element analysis is utilized for the determination of the 3D porosity distribution and its evolution with hydrostatic pressure in a high pressure diecast Mg AZ91 alloy (Mg-9wt.%Al-1wt.%Zn). The real 3D pore distribution obtained by tomography is used as input for the finite element simulations using an isotropic hardening law. The model is calibrated and validated against experimental stress-strain curves. The results reveal that the pressure treatment has a significant influence both on the volume and shape changes of individuals pores, which have been precisely quantified, and which are found to be related to the initial pore volume. In conclusion, the crystal plasticity model proposed in this work successfully describes the intrinsic deformation mechanisms of Mg alloys both at the mesoscale and the microscale. More specifically, it can capture slip and twin activities, their interactions, as well as the potential porosity effects arising from casting processes.

Are in vitro estimates of cell diffusivity and cell proliferation rate sensitive to assay geometry?

Cells respond to various biochemical and physical cues during wound–healing and tumour progression. In vitro assays used to study these processes are typically conducted in one particular geometry and it is unclear how the assay geometry affects the capacity of cell populations to spread, or whether the relevant mechanisms, such as cell motility and cell proliferation, are somehow sensitive to the geometry of the assay. In this work we use a circular barrier assay to characterise the spreading of cell populations in two different geometries. Assay 1 describes a tumour–like geometry where a cell population spreads outwards into an open space. Assay 2 describes a wound–like geometry where a cell population spreads inwards to close a void. We use a combination of discrete and continuum mathematical models and automated image processing methods to obtain independent estimates of the effective cell diffusivity, D, and the effective cell proliferation rate, λ. Using our parameterised mathematical model we confirm that our estimates of D and λ accurately predict the time–evolution of the location of the leading edge and the cell density profiles for both assay 1 and assay 2. Our work suggests that the effective cell diffusivity is up to 50% lower for assay 2 compared to assay 1, whereas the effective cell proliferation rate is up to 30% lower for assay 2 compared to assay 1.

Nonlinear oscillations in discrete and continuous systems

The first thesis topic is a perturbation method for resonantly coupled nonlinear oscillators. By successive near-identity transformations of the original equations, one obtains new equations with simple structure that describe the long time evolution of the motion. This technique is related to two-timing in that secular terms are suppressed in the transformation equations. The method has some important advantages. Appropriate time scalings are generated naturally by the method, and don't need to be guessed as in two-timing. Furthermore, by continuing the procedure to higher order, one extends (formally) the time scale of valid approximation. Examples illustrate these claims. Using this method, we investigate resonance in conservative, non-conservative and time dependent problems. Each example is chosen to highlight a certain aspect of the method.

The second thesis topic concerns the coupling of nonlinear chemical oscillators. The first problem is the propagation of chemical waves of an oscillating reaction in a diffusive medium. Using two-timing, we derive a nonlinear equation that determines how spatial variations in the phase of the oscillations evolves in time. This result is the key to understanding the propagation of chemical waves. In particular, we use it to account for certain experimental observations on the Belusov-Zhabotinskii reaction.

Next, we analyse the interaction between a pair of coupled chemical oscillators. This time, we derive an equation for the phase shift, which measures how much the oscillators are out of phase. This result is the key to understanding M. Marek's and I. Stuchl's results on coupled reactor systems. In particular, our model accounts for synchronization and its bifurcation into rhythm splitting.

Finally, we analyse large systems of coupled chemical oscillators. Using a continuum approximation, we demonstrate mechanisms that cause auto-synchronization in such systems.

Assessment of the benefits of Discrete Conditional Survival Models in modelling ambulance response times

Many of the challenges faced in health care delivery can be informed through building models. In particular, Discrete Conditional Survival (DCS) models, recently under development, can provide policymakers with a flexible tool to assess time-to-event data. The DCS model is capable of modelling the survival curve based on various underlying distribution types and is capable of clustering or grouping observations (based on other covariate information) external to the distribution fits. The flexibility of the model comes through the choice of data mining techniques that are available in ascertaining the different subsets and also in the choice of distribution types available in modelling these informed subsets. This paper presents an illustrated example of the Discrete Conditional Survival model being deployed to represent ambulance response-times by a fully parameterised model. This model is contrasted against use of a parametric accelerated failure-time model, illustrating the strength and usefulness of Discrete Conditional Survival models.

Real-time parameter estimation of dynamic temperature and humidity models for greenhouse adaptive climate control

A real-time parameter estimator for the climate discrete-time dynamic models of a greenhouse located at the North of Portugal are presented. The experiments showed that the second order models identified for the air temperature and humidity achieve a close agreement between simulated and experimantal data.

A Representation Theorem for Domains with Discrete and Continuous Variables.

This paper proves a new representation theorem for domains with both discrete and continuous variables. The result generalizes Debreu's well-known representation theorem on connected domains. A strengthening of the standard continuity axiom is used in order to guarantee the existence of a representation. A generalization of the main theorem and an application of the more general result are also presented.

Discrete Time Inventory Models with/without Positive Service Time

In everyday life different flows of customers to avail some service facility or other at some service station are experienced. In some of these situations, congestion of items arriving for service, because an item cannot be serviced Immediately on arrival, is unavoidable. A queuing system can be described as customers arriving for service, waiting for service if it is not immediate, and if having waited for service, leaving the system after being served. Examples Include shoppers waiting in front of checkout stands in a supermarket, Programs waiting to be processed by a digital computer, ships in the harbor Waiting to be unloaded, persons waiting at railway booking office etc. A queuing system is specified completely by the following characteristics: input or arrival pattern, service pattern, number of service channels, System capacity, queue discipline and number of service stages. The ultimate objective of solving queuing models is to determine the characteristics that measure the performance of the system