Factor models, VARMA processes and parameter instability with applications in macroeconomics

Avec les avancements de la technologie de l'information, les données temporelles économiques et financières sont de plus en plus disponibles. Par contre, si les techniques standard de l'analyse des séries temporelles sont utilisées, une grande quantité d'information est accompagnée du problème de dimensionnalité. Puisque la majorité des séries d'intérêt sont hautement corrélées, leur dimension peut être réduite en utilisant l'analyse factorielle. Cette technique est de plus en plus populaire en sciences économiques depuis les années 90. Étant donnée la disponibilité des données et des avancements computationnels, plusieurs nouvelles questions se posent. Quels sont les effets et la transmission des chocs structurels dans un environnement riche en données? Est-ce que l'information contenue dans un grand ensemble d'indicateurs économiques peut aider à mieux identifier les chocs de politique monétaire, à l'égard des problèmes rencontrés dans les applications utilisant des modèles standards? Peut-on identifier les chocs financiers et mesurer leurs effets sur l'économie réelle? Peut-on améliorer la méthode factorielle existante et y incorporer une autre technique de réduction de dimension comme l'analyse VARMA? Est-ce que cela produit de meilleures prévisions des grands agrégats macroéconomiques et aide au niveau de l'analyse par fonctions de réponse impulsionnelles? Finalement, est-ce qu'on peut appliquer l'analyse factorielle au niveau des paramètres aléatoires? Par exemple, est-ce qu'il existe seulement un petit nombre de sources de l'instabilité temporelle des coefficients dans les modèles macroéconomiques empiriques? Ma thèse, en utilisant l'analyse factorielle structurelle et la modélisation VARMA, répond à ces questions à travers cinq articles. Les deux premiers chapitres étudient les effets des chocs monétaire et financier dans un environnement riche en données. Le troisième article propose une nouvelle méthode en combinant les modèles à facteurs et VARMA. Cette approche est appliquée dans le quatrième article pour mesurer les effets des chocs de crédit au Canada. La contribution du dernier chapitre est d'imposer la structure à facteurs sur les paramètres variant dans le temps et de montrer qu'il existe un petit nombre de sources de cette instabilité. Le premier article analyse la transmission de la politique monétaire au Canada en utilisant le modèle vectoriel autorégressif augmenté par facteurs (FAVAR). Les études antérieures basées sur les modèles VAR ont trouvé plusieurs anomalies empiriques suite à un choc de la politique monétaire. Nous estimons le modèle FAVAR en utilisant un grand nombre de séries macroéconomiques mensuelles et trimestrielles. Nous trouvons que l'information contenue dans les facteurs est importante pour bien identifier la transmission de la politique monétaire et elle aide à corriger les anomalies empiriques standards. Finalement, le cadre d'analyse FAVAR permet d'obtenir les fonctions de réponse impulsionnelles pour tous les indicateurs dans l'ensemble de données, produisant ainsi l'analyse la plus complète à ce jour des effets de la politique monétaire au Canada. Motivée par la dernière crise économique, la recherche sur le rôle du secteur financier a repris de l'importance. Dans le deuxième article nous examinons les effets et la propagation des chocs de crédit sur l'économie réelle en utilisant un grand ensemble d'indicateurs économiques et financiers dans le cadre d'un modèle à facteurs structurel. Nous trouvons qu'un choc de crédit augmente immédiatement les diffusions de crédit (credit spreads), diminue la valeur des bons de Trésor et cause une récession. Ces chocs ont un effet important sur des mesures d'activité réelle, indices de prix, indicateurs avancés et financiers. Contrairement aux autres études, notre procédure d'identification du choc structurel ne requiert pas de restrictions temporelles entre facteurs financiers et macroéconomiques. De plus, elle donne une interprétation des facteurs sans restreindre l'estimation de ceux-ci. Dans le troisième article nous étudions la relation entre les représentations VARMA et factorielle des processus vectoriels stochastiques, et proposons une nouvelle classe de modèles VARMA augmentés par facteurs (FAVARMA). Notre point de départ est de constater qu'en général les séries multivariées et facteurs associés ne peuvent simultanément suivre un processus VAR d'ordre fini. Nous montrons que le processus dynamique des facteurs, extraits comme combinaison linéaire des variables observées, est en général un VARMA et non pas un VAR comme c'est supposé ailleurs dans la littérature. Deuxièmement, nous montrons que même si les facteurs suivent un VAR d'ordre fini, cela implique une représentation VARMA pour les séries observées. Alors, nous proposons le cadre d'analyse FAVARMA combinant ces deux méthodes de réduction du nombre de paramètres. Le modèle est appliqué dans deux exercices de prévision en utilisant des données américaines et canadiennes de Boivin, Giannoni et Stevanovic (2010, 2009) respectivement. Les résultats montrent que la partie VARMA aide à mieux prévoir les importants agrégats macroéconomiques relativement aux modèles standards. Finalement, nous estimons les effets de choc monétaire en utilisant les données et le schéma d'identification de Bernanke, Boivin et Eliasz (2005). Notre modèle FAVARMA(2,1) avec six facteurs donne les résultats cohérents et précis des effets et de la transmission monétaire aux États-Unis. Contrairement au modèle FAVAR employé dans l'étude ultérieure où 510 coefficients VAR devaient être estimés, nous produisons les résultats semblables avec seulement 84 paramètres du processus dynamique des facteurs. L'objectif du quatrième article est d'identifier et mesurer les effets des chocs de crédit au Canada dans un environnement riche en données et en utilisant le modèle FAVARMA structurel. Dans le cadre théorique de l'accélérateur financier développé par Bernanke, Gertler et Gilchrist (1999), nous approximons la prime de financement extérieur par les credit spreads. D'un côté, nous trouvons qu'une augmentation non-anticipée de la prime de financement extérieur aux États-Unis génère une récession significative et persistante au Canada, accompagnée d'une hausse immédiate des credit spreads et taux d'intérêt canadiens. La composante commune semble capturer les dimensions importantes des fluctuations cycliques de l'économie canadienne. L'analyse par décomposition de la variance révèle que ce choc de crédit a un effet important sur différents secteurs d'activité réelle, indices de prix, indicateurs avancés et credit spreads. De l'autre côté, une hausse inattendue de la prime canadienne de financement extérieur ne cause pas d'effet significatif au Canada. Nous montrons que les effets des chocs de crédit au Canada sont essentiellement causés par les conditions globales, approximées ici par le marché américain. Finalement, étant donnée la procédure d'identification des chocs structurels, nous trouvons des facteurs interprétables économiquement. Le comportement des agents et de l'environnement économiques peut varier à travers le temps (ex. changements de stratégies de la politique monétaire, volatilité de chocs) induisant de l'instabilité des paramètres dans les modèles en forme réduite. Les modèles à paramètres variant dans le temps (TVP) standards supposent traditionnellement les processus stochastiques indépendants pour tous les TVPs. Dans cet article nous montrons que le nombre de sources de variabilité temporelle des coefficients est probablement très petit, et nous produisons la première évidence empirique connue dans les modèles macroéconomiques empiriques. L'approche Factor-TVP, proposée dans Stevanovic (2010), est appliquée dans le cadre d'un modèle VAR standard avec coefficients aléatoires (TVP-VAR). Nous trouvons qu'un seul facteur explique la majorité de la variabilité des coefficients VAR, tandis que les paramètres de la volatilité des chocs varient d'une façon indépendante. Le facteur commun est positivement corrélé avec le taux de chômage. La même analyse est faite avec les données incluant la récente crise financière. La procédure suggère maintenant deux facteurs et le comportement des coefficients présente un changement important depuis 2007. Finalement, la méthode est appliquée à un modèle TVP-FAVAR. Nous trouvons que seulement 5 facteurs dynamiques gouvernent l'instabilité temporelle dans presque 700 coefficients.

The use of earth observation techniques to improve catchment-scale pollution predictions

Remote sensing can potentially provide information useful in improving pollution transport modelling in agricultural catchments. Realisation of this potential will depend on the availability of the raw data, development of information extraction techniques, and the impact of the assimilation of the derived information into models. High spatial resolution hyperspectral imagery of a farm near Hereford, UK is analysed. A technique is described to automatically identify the soil and vegetation endmembers within a field, enabling vegetation fractional cover estimation. The aerially-acquired laser altimetry is used to produce digital elevation models of the site. At the subfield scale the hypothesis that higher resolution topography will make a substantial difference to contaminant transport is tested using the AGricultural Non-Point Source (AGNPS) model. Slope aspect and direction information are extracted from the topography at different resolutions to study the effects on soil erosion, deposition, runoff and nutrient losses. Field-scale models are often used to model drainage water, nitrate and runoff/sediment loss, but the demanding input data requirements make scaling up to catchment level difficult. By determining the input range of spatial variables gathered from EO data, and comparing the response of models to the range of variation measured, the critical model inputs can be identified. Response surfaces to variation in these inputs constrain uncertainty in model predictions and are presented. Although optical earth observation analysis can provide fractional vegetation cover, cloud cover and semi-random weather patterns can hinder data acquisition in Northern Europe. A Spring and Autumn cloud cover analysis is carried out over seven UK sites close to agricultural districts, using historic satellite image metadata, climate modelling and historic ground weather observations. Results are assessed in terms of probability of acquisition probability and implications for future earth observation missions. (C) 2003 Elsevier Ltd. All rights reserved.

Catchment-scale modelling of flow and nutrient transport in the Chalk unsaturated zone

The unsaturated zone exerts a major control on the delivery of nutrients to Chalk streams, yet flow and transport processes in this complex, dual-porosity medium have remained controversial. A major challenge arises in characterising these processes, both at the detailed mechanistic level and at an appropriate level for inclusion within catchment-scale models for nutrient management. The lowland catchment research (LOCAR) programme in the UK has provided a unique set of comprehensively instrumented groundwater-dominated catchments. Of these, the Pang and Lambourn, tributaries of the Thames near Reading, have been a particular focus for research into subsurface processes and surface water-groundwater interactions. Data from LOCAR and other sources, along with a new dual permeability numerical model of the Chalk, have been used to explore the relative roles of matrix and fracture flow within the unsaturated zone and resolve conflicting hypotheses of response. From the improved understanding gained through these explorations, a parsimonious conceptualisation of the general response of flow and transport within the Chalk unsaturated zone was formulated. This paper summarises the modelling and data findings of these explorations, and describes the integration of the new simplified unsaturated zone representation with a catchment-scale model of nutrients (INCA), resulting in a new model for catchment-scale flow and transport within Chalk systems: INCA-Chalk. This model is applied to the Lambourn, and results, including hindcast and forecast simulations, are presented. These clearly illustrate the decadal time-scales that need to be considered in the context of nutrient management and the EU Water Framework Directive. (C) 2007 Elsevier B.V. All rights reserved.

Different splitting techniques with application to air pollution models

Splitting techniques are commonly used when large-scale models, which appear in different fields of science and engineering, are treated numerically. Four types of splitting procedures are defined and discussed. The problem of the choice of a splitting procedure is investigated. Several numerical tests, by which the influence of the splitting errors on the accuracy of the results is studied, are given. It is shown that the splitting errors decrease linearly when (1) the splitting procedure is of first order and (2) the splitting errors are dominant. Three examples for splitting procedures used in all large-scale air pollution models are presented. Numerical results obtained by a particular air pollution model, Unified Danish Eulerian Model (UNI-DEM), are given and analysed.

A multimodal tablet-based interface for designing and reviewing 3D engineering models

The ability to view and interact with 3D models has been happening for a long time. However, vision-based 3D modeling has only seen limited success in applications, as it faces many technical challenges. Hand-held mobile devices have changed the way we interact with virtual reality environments. Their high mobility and technical features, such as inertial sensors, cameras and fast processors, are especially attractive for advancing the state of the art in virtual reality systems. Also, their ubiquity and fast Internet connection open a path to distributed and collaborative development. However, such path has not been fully explored in many domains. VR systems for real world engineering contexts are still difficult to use, especially when geographically dispersed engineering teams need to collaboratively visualize and review 3D CAD models. Another challenge is the ability to rendering these environments at the required interactive rates and with high fidelity. In this document it is presented a virtual reality system mobile for visualization, navigation and reviewing large scale 3D CAD models, held under the CEDAR (Collaborative Engineering Design and Review) project. It’s focused on interaction using different navigation modes. The system uses the mobile device's inertial sensors and camera to allow users to navigate through large scale models. IT professionals, architects, civil engineers and oil industry experts were involved in a qualitative assessment of the CEDAR system, in the form of direct user interaction with the prototypes and audio-recorded interviews about the prototypes. The lessons learned are valuable and are presented on this document. Subsequently it was prepared a quantitative study on the different navigation modes to analyze the best mode to use it in a given situation.

Scale model research for room acoustics purposes

In the field of Room Acoustics it is common using scale models to study a room. Through this method it is possible to predict its behavior, which may be very useful to detect and correct any problem prior to build it, saving many resources. Nowadays this method has been relegated to a secondary position due to the peak of simulation software, which makes possible studying rooms in a cheap, flexible and simple way, as well as it is potentially less time consuming. Nevertheless, the scale model method is still under study, as it may give some additional information. This project intends to focus in pedagogic possibilities of the scale model method. This method offers the student the opportunity of study and grasp some of the most important phenomena in Room Acoustics, in a more intuitive way than just a software simulation. Furthermore most of the existing software in this field is aimed to the technician working in the lab, as efficiently as possible, not to the student trying to understand and learn something. Here, the facilities and resources of Syddansk Universitet regarding this matter will be studied and evaluated, as well as the procedure for the experiments, paying special attention not only to its reliability and accuracy, but also to its didactic possibilities. Besides, if possible, any improvement that could help to enhance any of the listed aspects will be suggested. En el ámbito de la Acústica Arquitectónica es común el uso de modelos a escala para estudiar un recinto determinado. Mediante esta técnica es posible por ejemplo predecir el comportamiento del recinto y detectar problemas antes de su construcción, con el consecuente ahorro de recursos. Actualmente el uso de modelos a escala está desplazado a un segundo plano por el uso de software simulación, debido a la sencillez y flexibilidad que puede aportar la simulación por ordenador, así como a la economía de tiempo y recursos que supone. Sin embargo sigue siendo objeto de estudio, dado que puede aportar información muy valiosa para el ingeniero. Este proyecto se centra en las posibilidades pedagógicas de dicho método. El uso de modelos a escala brinda la oportunidad a los estudiantes de estudiar y comprender algunos de los fenómenos más importantes en la Acústica Arquitectónica de una forma más directa e intuitiva que una simulación por ordenador. Se pretende estudiar y evaluar los medios al alcance de los estudiantes en la Syddansk Universitet, así como los métodos usados, atendiendo no sólo a su precisión y fiabilidad, si no a su potencial pedagógico. Así mismo, si es posible, se propondrán cambios que puedan suponer una mejora en cualquiera de estos aspectos. Así el proyecto se divide en varias secciones claramente diferenciadas. En el apartado Background and Theoretical Basis se introduce el tema del estudio y simulación de recintos acústicos. Se explica su importancia y utilidad, y se comenta la situación actual de estas técnicas, abordando diferentes métodos usados así como sus bases teóricas y principales ventajas e inconvenientes. Bajo el apartado de Project se analizan diferentes factores relacionados con el problema. Se estudian los recursos a disposición del alumno, desde el software y hardware implicados hasta el equipo de medida y otros recursos necesarios para la realización de las prácticas. Es en esta parte donde se centra la parte más importante del trabajo, consistente en la medición y comprobación de las características más relevantes del equipo implicado. Haciendo posible así confirmar su validez y precisión, tanto desde el punto de vista técnico como pedagógico, así como estableciendo los límites dentro de los que se puede considerar fiable el modelo. Al final de este apartado se aborda la influencia de la absorción del aire en altas frecuencias, y la variación en los coeficientes de absorción y dispersión de los materiales respecto de la frecuencia. Por último se realiza una verificación subjetiva del sistema completo, debido a que por limitaciones técnicas no ha sido posible evaluar el montaje en el rango equivalente a toda la banda audible, y que los métodos estudiados tienen como meta última asegurar una buena percepción por parte del oyente en el recinto dado. Dentro del apartado Conclusions se hace un breve resumen de las conclusiones extraídas anteriormente, y se valora el rendimiento y utilidad general del modelo, que a pesar de algunos problemas de precisión y repetibilidad lógicos debido a los medios usados, es válido para ilustrar los fenómenos físicos que se quieren enseñar al alumno. En la sección de Future Work se proponen diferentes vías de trabajo para futuros proyectos en la Syddansk Universitet que podrían ser útiles confirmar el trabajo realizado en este proyecto, mejorar la precisión y fiabilidad del montaje o enriquecer las posibilidades pedagógicas de las prácticas relacionadas. Por último se encuentra, tras el apartado de referencias, los anexos con tablas y gráficas relativas a las medidas realizadas en diferentes partes del trabajo. También se puede encontrar información y material relacionado con el proyecto en el CD adjunto.

A multimodal tablet-based interface for designing and reviewing 3D engineering models

The ability to view and interact with 3D models has been happening for a long time. However, vision-based 3D modeling has only seen limited success in applications, as it faces many technical challenges. Hand-held mobile devices have changed the way we interact with virtual reality environments. Their high mobility and technical features, such as inertial sensors, cameras and fast processors, are especially attractive for advancing the state of the art in virtual reality systems. Also, their ubiquity and fast Internet connection open a path to distributed and collaborative development. However, such path has not been fully explored in many domains. VR systems for real world engineering contexts are still difficult to use, especially when geographically dispersed engineering teams need to collaboratively visualize and review 3D CAD models. Another challenge is the ability to rendering these environments at the required interactive rates and with high fidelity. In this document it is presented a virtual reality system mobile for visualization, navigation and reviewing large scale 3D CAD models, held under the CEDAR (Collaborative Engineering Design and Review) project. It’s focused on interaction using different navigation modes. The system uses the mobile device's inertial sensors and camera to allow users to navigate through large scale models. IT professionals, architects, civil engineers and oil industry experts were involved in a qualitative assessment of the CEDAR system, in the form of direct user interaction with the prototypes and audio-recorded interviews about the prototypes. The lessons learned are valuable and are presented on this document. Subsequently it was prepared a quantitative study on the different navigation modes to analyze the best mode to use it in a given situation.

Field-based models for low speed switched reluctance machine designs

Trabalho apresentado na Conferência CPE-POWERENG 2016, 29 junho a 01 de julho 2016, Bydgoszcz, Polónia

Scale model study of low-density concrete impact attenuators. Final report.

Ohio Department of Transportation, Columbus

Development of effective approaches to the large-scale aerodynamic testing of low-rise buildings

Low-rise buildings are often subjected to high wind loads during hurricanes that lead to severe damage and cause water intrusion. It is therefore important to estimate accurate wind pressures for design purposes to reduce losses. Wind loads on low-rise buildings can differ significantly depending upon the laboratory in which they were measured. The differences are due in large part to inadequate simulations of the low-frequency content of atmospheric velocity fluctuations in the laboratory and to the small scale of the models used for the measurements. A new partial turbulence simulation methodology was developed for simulating the effect of low-frequency flow fluctuations on low-rise buildings more effectively from the point of view of testing accuracy and repeatability than is currently the case. The methodology was validated by comparing aerodynamic pressure data for building models obtained in the open-jet 12-Fan Wall of Wind (WOW) facility against their counterparts in a boundary-layer wind tunnel. Field measurements of pressures on Texas Tech University building and Silsoe building were also used for validation purposes. The tests in partial simulation are freed of integral length scale constraints, meaning that model length scales in such testing are only limited by blockage considerations. Thus the partial simulation methodology can be used to produce aerodynamic data for low-rise buildings by using large-scale models in wind tunnels and WOW-like facilities. This is a major advantage, because large-scale models allow for accurate modeling of architectural details, testing at higher Reynolds number, using greater spatial resolution of the pressure taps in high pressure zones, and assessing the performance of aerodynamic devices to reduce wind effects. The technique eliminates a major cause of discrepancies among measurements conducted in different laboratories and can help to standardize flow simulations for testing residential homes as well as significantly improving testing accuracy and repeatability. Partial turbulence simulation was used in the WOW to determine the performance of discontinuous perforated parapets in mitigating roof pressures. The comparisons of pressures with and without parapets showed significant reductions in pressure coefficients in the zones with high suctions. This demonstrated the potential of such aerodynamic add-on devices to reduce uplift forces.

Large-scale neural dynamics: simple and complex

We review the use of neural field models for modelling the brain at the large scales necessary for interpreting EEG, fMRI, MEG and optical imaging data. Albeit a framework that is limited to coarse-grained or mean-field activity, neural field models provide a framework for unifying data from different imaging modalities. Starting with a description of neural mass models we build to spatially extended cortical models of layered two-dimensional sheets with long range axonal connections mediating synaptic interactions. Reformulations of the fundamental non-local mathematical model in terms of more familiar local differential (brain wave) equations are described. Techniques for the analysis of such models, including how to determine the onset of spatio-temporal pattern forming instabilities, are reviewed. Extensions of the basic formalism to treat refractoriness, adaptive feedback and inhomogeneous connectivity are described along with open challenges for the development of multi-scale models that can integrate macroscopic models at large spatial scales with models at the microscopic scale.

Failure Mechanisms in Sand over a Deep Active Trapdoor

An experimental testing program was undertaken to investigate failure mechanisms induced by the active movement of a deep rectangular trapdoor underlying a granular soil. Reduced-scale models were tested under normal gravity as well as under an increased gravitational field using a centrifuge facility. Some models were used to evaluate the performance of both flexible and rigid pipes undergoing a localized loss of support. Failure mechanisms in the longitudinal direction of the models were characterized by a single, well-defined failure surface that developed within the limits of the trapdoor. However, failure mechanisms in the transverse direction of the models were characterized by multiple failure surfaces extending outside the limits of the trapdoor. Significant dilation of the soil located immediately above the trapdoor was identified in the failure of the models. The pattern of the failure mechanisms was found to be affected by the stress level and backfill density. Higher stress levels were found to lead to well-developed failure zones. The influence of backfill density was found to be more relevant in models involving flexible pipes. Pipes embedded within loose backfill were severely damaged after loss of support, while pipes embedded in dense backfill experienced negligible deformations. These results indicate that damage to pipelines caused by ground loss of support can be significantly minimized by controlling the compaction of the fill.

Determination of coalescence kernels for high-shear granulation using DEM simulations

Discrete element method (DEM) modeling is used in parallel with a model for coalescence of deformable surface wet granules. This produces a method capable of predicting both collision rates and coalescence efficiencies for use in derivation of an overall coalescence kernel. These coalescence kernels can then be used in computationally efficient meso-scale models such as population balance equation (PBE) models. A soft-sphere DEM model using periodic boundary conditions and a unique boxing scheme was utilized to simulate particle flow inside a high-shear mixer. Analysis of the simulation results provided collision frequency, aggregation frequency, kinetic energy, coalescence efficiency and compaction rates for the granulation process. This information can be used to bridge the gap in multi-scale modeling of granulation processes between the micro-scale DEM/coalescence modeling approach and a meso-scale PBE modeling approach.

Modelagem da dispersão de odores em ambientes urbanos

O presente trabalho investigou o problema da modelagem da dispersão de compostos odorantes em presença de obstáculos (cúbicos e com forma complexa) sob condição de estabilidade atmosférica neutra. Foi empregada modelagem numérica baseada nas equações de transporte (CFD1) bem como em modelos algébricos baseados na pluma Gausseana (AERMOD2, CALPUFF3 e FPM4). Para a validação dos resultados dos modelos e a avaliação do seu desempenho foram empregados dados de experimentos em túnel de vento e em campo. A fim de incluir os efeitos da turbulência atmosférica na dispersão, dois diferentes modelos de sub-malha associados à Simulação das Grandes Escalas (LES5) foram investigados (Smagorinsky dinâmico e WALE6) e, para a inclusão dos efeitos de obstáculos na dispersão nos modelos Gausseanos, foi empregado o modelo PRIME7. O uso do PRIME também foi proposto para o FPM como uma inovação. De forma geral, os resultados indicam que o uso de CFD/LES é uma ferramenta útil para a investigação da dispersão e o impacto de compostos odorantes em presença de obstáculos e também para desenvolvimento dos modelos Gausseanos. Os resultados também indicam que o modelo FPM proposto, com a inclusão dos efeitos do obstáculo baseado no PRIME também é uma ferramenta muito útil em modelagem da dispersão de odores devido à sua simplicidade e fácil configuração quando comparado a modelos mais complexos como CFD e mesmo os modelos regulatórios AERMOD e CALPUFF. A grande vantagem do FPM é a possibilidade de estimar-se o fator de intermitência e a relação pico-média (P/M), parâmetros úteis para a avaliação do impacto de odores. Os resultados obtidos no presente trabalho indicam que a determinação dos parâmetros de dispersão para os segmentos de pluma, bem como os parâmetros de tempo longo nas proximidades da fonte e do obstáculo no modelo FPM pode ser melhorada e simulações CFD podem ser usadas como uma ferramenta de desenvolvimento para este propósito. Palavras chave: controle de odor, dispersão, fluidodinâmica computacional, modelagem matemática, modelagem gaussiana de pluma flutuante, simulação de grandes vórtices (LES).