The Kineticist's Workbench: Combining Symbolic and Numerical Methods in the Simulation of Chemical Reaction Mechanisms

The Kineticist's Workbench is a program that simulates chemical reaction mechanisms by predicting, generating, and interpreting numerical data. Prior to simulation, it analyzes a given mechanism to predict that mechanism's behavior; it then simulates the mechanism numerically; and afterward, it interprets and summarizes the data it has generated. In performing these tasks, the Workbench uses a variety of techniques: graph- theoretic algorithms (for analyzing mechanisms), traditional numerical simulation methods, and algorithms that examine simulation results and reinterpret them in qualitative terms. The Workbench thus serves as a prototype for a new class of scientific computational tools---tools that provide symbiotic collaborations between qualitative and quantitative methods.

Numerical Simulation of Electroosmotic Flow with Step Change in Zeta Potential

Electroosmotic flow is a convenient mechanism for transporting polar fluid in a microfluidic device. The flow is generated through the application of an external electric field that acts on the free charges that exists in a thin Debye layer at the channel walls. The charge on the wall is due to the chemistry of the solid-fluid interface, and it can vary along the channel, e.g. due to modification of the wall. This investigation focuses on the simulation of the electroosmotic flow (EOF) profile in a cylindrical microchannel with step change in zeta potential. The modified Navier-Stoke equation governing the velocity field and a non-linear two-dimensional Poisson-Boltzmann equation governing the electrical double-layer (EDL) field distribution are solved numerically using finite control-volume method. Continuities of flow rate and electric current are enforced resulting in a non-uniform electrical field and pressure gradient distribution along the channel. The resulting parabolic velocity distribution at the junction of the step change in zeta potential, which is more typical of a pressure-driven velocity flow profile, is obtained.

Calculation of Franck-Condon factors including anharmonicity: simulation of the C2 H4+ X̃2B 3u←C2 H4X̃1 Ag band in the photoelectron spectrum of ethylene

Our new simple method for calculating accurate Franck-Condon factors including nondiagonal (i.e., mode-mode) anharmonic coupling is used to simulate the C2H4+X2B 3u←C2H4X̃1 Ag band in the photoelectron spectrum. An improved vibrational basis set truncation algorithm, which permits very efficient computations, is employed. Because the torsional mode is highly anharmonic it is separated from the other modes and treated exactly. All other modes are treated through the second-order perturbation theory. The perturbation-theory corrections are significant and lead to a good agreement with experiment, although the separability assumption for torsion causes the C2 D4 results to be not as good as those for C2 H4. A variational formulation to overcome this circumstance, and deal with large anharmonicities in general, is suggested

Knowledge-based modelling and simulation of operational problems of microbiological origin in wastewater treatment plants

The activated sludge and anaerobic digestion processes have been modelled in widely accepted models. Nevertheless, these models still have limitations when describing operational problems of microbiological origin. The aim of this thesis is to develop a knowledge-based model to simulate risk of plant-wide operational problems of microbiological origin.For the risk model heuristic knowledge from experts and literature was implemented in a rule-based system. Using fuzzy logic, the system can infer a risk index for the main operational problems of microbiological origin (i.e. filamentous bulking, biological foaming, rising sludge and deflocculation). To show the results of the risk model, it was implemented in the Benchmark Simulation Models. This allowed to study the risk model's response in different scenarios and control strategies. The risk model has shown to be really useful providing a third criterion to evaluate control strategies apart from the economical and environmental criteria.

Analysis and Simulation of Transverse Random Fracture of Long Fibre Reinforced Composites

La present tesi proposa una metodología per a la simulació probabilística de la fallada de la matriu en materials compòsits reforçats amb fibres de carboni, basant-se en l'anàlisi de la distribució aleatòria de les fibres. En els primers capítols es revisa l'estat de l'art sobre modelització matemàtica de materials aleatoris, càlcul de propietats efectives i criteris de fallada transversal en materials compòsits. El primer pas en la metodologia proposada és la definició de la determinació del tamany mínim d'un Element de Volum Representatiu Estadístic (SRVE) . Aquesta determinació es du a terme analitzant el volum de fibra, les propietats elàstiques efectives, la condició de Hill, els estadístics de les components de tensió i defromació, la funció de densitat de probabilitat i les funcions estadístiques de distància entre fibres de models d'elements de la microestructura, de diferent tamany. Un cop s'ha determinat aquest tamany mínim, es comparen un model periòdic i un model aleatori, per constatar la magnitud de les diferències que s'hi observen. Es defineix, també, una metodologia per a l'anàlisi estadístic de la distribució de la fibra en el compòsit, a partir d'imatges digitals de la secció transversal. Aquest anàlisi s'aplica a quatre materials diferents. Finalment, es proposa un mètode computacional de dues escales per a simular la fallada transversal de làmines unidireccionals, que permet obtenir funcions de densitat de probabilitat per a les variables mecàniques. Es descriuen algunes aplicacions i possibilitats d'aquest mètode i es comparen els resultats obtinguts de la simulació amb valors experimentals.

Simulation of delamination in composites under quasi-static and fatigue loading using cohesive zone models

Es desenvolupa una eina de disseny per l'anàlisi de la tolerància al dany en composites. L'eina pot predir el inici i la propagació de fisures interlaminars. També pot ser utilitzada per avaluar i planificar la necessitat de reparar o reemplaçar components durant la seva vida útil. El model desenvolupat pot ser utilitzat tan per simular càrregues estàtiques com de fatiga. El model proposat és un model de dany termodinàmicament consistent que permet simular la delaminació en composites sota càrregues variables. El model es formula dins el context de la Mecànica del Dany, fent ús dels models de zona cohesiva. Es presenta un metodologia per determinar els paràmetres del model constitutiu que permet utilitzar malles d'elements finits més bastes de les que es poden usar típicament. Finalment, el model és també capaç de simular la delaminació produïda per càrregues de fatiga.

Simulation of interlaminar and intralaminar damage in polymer-based composites for aeronautical applications under impact loading

La aplicación de materiales compuestos de matriz polimérica reforzados mediante fibras largas (FRP, Fiber Reinforced Plastic), está en gradual crecimiento debido a las buenas propiedades específicas y a la flexibilidad en el diseño. Uno de los mayores consumidores es la industria aeroespacial, dado que la aplicación de estos materiales tiene claros beneficios económicos y medioambientales. Cuando los materiales compuestos se aplican en componentes estructurales, se inicia un programa de diseño donde se combinan ensayos reales y técnicas de análisis. El desarrollo de herramientas de análisis fiables que permiten comprender el comportamiento mecánico de la estructura, así como reemplazar muchos, pero no todos, los ensayos reales, es de claro interés. Susceptibilidad al daño debido a cargas de impacto fuera del plano es uno de los aspectos de más importancia que se tienen en cuenta durante el proceso de diseño de estructuras de material compuesto. La falta de conocimiento de los efectos del impacto en estas estructuras es un factor que limita el uso de estos materiales. Por lo tanto, el desarrollo de modelos de ensayo virtual mecánico para analizar la resistencia a impacto de una estructura es de gran interés, pero aún más, la predicción de la resistencia residual después del impacto. En este sentido, el presente trabajo abarca un amplio rango de análisis de eventos de impacto a baja velocidad en placas laminadas de material compuesto, monolíticas, planas, rectangulares, y con secuencias de apilamiento convencionales. Teniendo en cuenta que el principal objetivo del presente trabajo es la predicción de la resistencia residual a compresión, diferentes tareas se llevan a cabo para favorecer el adecuado análisis del problema. Los temas que se desarrollan son: la descripción analítica del impacto, el diseño y la realización de un plan de ensayos experimentales, la formulación e implementación de modelos constitutivos para la descripción del comportamiento del material, y el desarrollo de ensayos virtuales basados en modelos de elementos finitos en los que se usan los modelos constitutivos implementados.

Application of modal interval analysis to the simulation of the behaviour of dynamic systems with uncertain parameters

Els models matemàtics quantitatius són simplificacions de la realitat i per tant el comportament obtingut per simulació d'aquests models difereix dels reals. L'ús de models quantitatius complexes no és una solució perquè en la majoria dels casos hi ha alguna incertesa en el sistema real que no pot ser representada amb aquests models. Una forma de representar aquesta incertesa és mitjançant models qualitatius o semiqualitatius. Un model d'aquest tipus de fet representa un conjunt de models. La simulació del comportament de models quantitatius genera una trajectòria en el temps per a cada variable de sortida. Aquest no pot ser el resultat de la simulació d'un conjunt de models. Una forma de representar el comportament en aquest cas és mitjançant envolupants. L'envolupant exacta és complete, és a dir, inclou tots els possibles comportaments del model, i correcta, és a dir, tots els punts dins de l'envolupant pertanyen a la sortida de, com a mínim, una instància del model. La generació d'una envolupant així normalment és una tasca molt dura que es pot abordar, per exemple, mitjançant algorismes d'optimització global o comprovació de consistència. Per aquesta raó, en molts casos s'obtenen aproximacions a l'envolupant exacta. Una aproximació completa però no correcta a l'envolupant exacta és una envolupant sobredimensionada, mentre que una envolupant correcta però no completa és subdimensionada. Aquestes propietats s'han estudiat per diferents simuladors per a sistemes incerts.

Simulation of monsoon disturbances in the LMD GCM

The monsoon depressions that form over India during the summer are analyzed using simulations from the Laboratoire de Meteorologie Dynamique general circulation model. This type of synoptic system often occurs with a frequency of one to two per month and can produce a strong Indian rainfall. Two kinds of analyses are conducted in this study. The first one is a subjective analysis based on the evolution of the precipitation rate and the pattern of the sea level pressure. The second one is an objective analysis performed using the TRACK program, which identifies and tracks the minima in the sea level pressure anomaly held and computes the statistics for the distribution of systems. The analysis of a 9-yr control run, which simulates strong precipitation rates over the foothills of the Himalayas and over southern India but weak rates over central India, shows that the number of disturbances is coo low and that they almost never occur during August, when break conditions prevail. The generated disturbances more often move north, toward the foothills of the Himalayas. Another analysis is performed to study the effect of the Tibetan Plateau elevation on these disturbances with a 9-yr run carried out with a Tibetan Plateau at 50% of its current height. It is shown that this later integration simulates more frequent monsoon disturbances, which move rather northwestward, in agreement with the current observations. The comparison between the two runs shows that the June-July-August rainfall difference is in large part due to changes in the occurrence of the monsoon disturbances.

Simulation of the diurnal cycle in a climate model and its evaluation using data from Meteosat 7

The representation of the diurnal cycle in the Hadley Centre climate model is evaluated using simulations of the infrared radiances observed by Meteosat 7. In both the window and water vapour channels, the standard version of the model with 19 levels produces a good simulation of the geographical distributions of the mean radiances and of the amplitude of the diurnal cycle. Increasing the vertical resolution to 30 levels leads to further improvements in the mean fields. The timing of the maximum and minimum radiances reveals significant model errors, however, which are sensitive to the frequency with which the radiation scheme is called. In most regions, these errors are consistent with well documented errors in the timing of convective precipitation, which peaks before noon in the model, in contrast to the observed peak in the late afternoon or evening. When the radiation scheme is called every model time step (half an hour), as opposed to every three hours in the standard version, the timing of the minimum radiance is improved for convective regions over central Africa, due to the creation of upper-level layer-cloud by detrainment from the convection scheme, which persists well after the convection itself has dissipated. However, this produces a decoupling between the timing of the diurnal cycles of precipitation and window channel radiance. The possibility is raised that a similar decoupling may occur in reality and the implications of this for the retrieval of the diurnal cycle of precipitation from infrared radiances are discussed.

Numerical simulation of baroclinic waves with a parameterized boundary layer

A dry three-dimensional baroclinic life cycle model is used to investigate the role of turbulent fluxes of heat and momentum within the boundary layer on mid-latitude cyclones. Simulations are performed of life cycles for two basic states, both with and without turbulent fluxes. The different basic states produce cyclones with contrasting frontal and mesoscale-flow structures. The analysis focuses on the generation of potential-vorticity (PV) in the boundary layer and its subsequent transport into the free troposphere. The dynamic mechanism through which friction mitigates a barotropic vortex is that of Ekman pumping. This has often been assumed to be also the dominant mechanism for baroclinic developments. The PV framework highlights an additional, baroclinic mechanism. Positive PV is generated baroclinically due to friction to the north-east of a surface low and is transported out of the boundary layer by a cyclonic conveyor belt flow. The result is an anomaly of increased static stability in the lower troposphere which restricts the growth of the baroclinic wave. The reduced coupling between lower and upper levels can be sufficient to change the character of the upper-level evolution of the mature wave. The basic features of the baroclinic damping mechanism are robust for different frontal structures, with and without turbulent heat fluxes, and for the range of surface roughness found over the oceans.

Improved simulation of water vapour and clear-sky radiation using 24 hour forecasts from ERA40

Monthly mean water vapour and clear-sky radiation extracted from the European Centre for Medium Range Weather Forecasts 40-year reanalysis (ERA40) forecasts are assessed using satellite observations and additional reanalysis data. There is a marked improvement in the interannual variability of column-integrated water vapour (CWV) over the oceans when using the 24-hour forecasts compared with the standard 6-hour forecasts products. The spatial distribution of CWV are well simulated by the 6-hour forecasts; using the 24-hour forecasts does not degrade this simulation substantially and in many cases improves on the quality. There is also an improved simulation of clear-sky radiation from the 24-hour forecasts compared with the 6-hour forecasts based on comparison with satellite observations and empirical estimates. Further work is required to assess the quality of water vapour simulation by reanalyses over land regions. Over the oceans, it is recommended that 24-hour forecasts of CWV and clear-sky radiation are used in preference to the standard 6-hour forecast products from ERA40

Stratosphere-troposphere transport in a numerical simulation of midlatitude convection

The transport of stratospheric air deep into the troposphere via convection is investigated numerically using the UK Met Office Unified Model. A convective system that formed on 27 June 2004 near southeast England, in the vicinity an upper level potential vorticity anomaly and a lowered tropopause, provides the basis for analysis. Transport is diagnosed using a stratospheric tracer that can either be passed through or withheld from the model’s convective parameterization scheme. Three simulations are performed at increasingly finer resolutions, with horizontal grid lengths of 12, 4, and 1 km. In the 12 and 4 km simulations, tracer is transported deeply into the troposphere by the parameterized convection. In the 1 km simulation, for which the convective parameterization is disengaged, deep transport is still accomplished but with a much smaller magnitude. However, the 1 km simulation resolves stirring along the tropopause that does not exist in the coarser simulations. In all three simulations, the concentration of the deeply transported tracer is small, three orders of magnitude less than that of the shallow transport near the tropopause, most likely because of the efficient dilution of parcels in the lower troposphere.