Eulerian quasisymmetric functions were introduced by Shareshian and Wachs in order to obtain a q-analog of Euler's exponential generating function formula for the Eulerian polynomials. They are defined via the symmetric group, and applying the stable and nonstable principal specializations yields formulas for joint distributions of permutation statistics. We consider the wreath product of the cyclic group with the symmetric group, also known as the group of colored permutations. We use this group to introduce colored Eulerian quasisymmetric functions, which are a generalization of Eulerian quasisymmetric functions. We derive a formula for the generating function of these colored Eulerian quasisymmetric functions, which reduces to a formula of Shareshian and Wachs for the Eulerian quasisymmetric functions. We show that applying the stable and nonstable principal specializations yields formulas for joint distributions of colored permutation statistics. The family of colored permutation groups includes the family of symmetric groups and the family of hyperoctahedral groups, also called the type A Coxeter groups and type B Coxeter groups, respectively. By specializing our formulas to these cases, they reduce to the Shareshian-Wachs q-analog of Euler's formula, formulas of Foata and Han, and a new generalization of a formula of Chow and Gessel.

A mathematical model for a consolidation process of a highlyconcentrated, flocculated suspension is developed.Thesuspension is treated as a mixture of a fluid and solidparticles by an Eulerian two-phase fluid model.W e characterizethe suspension by constitutive relations correlating thestresses, interaction forces, and inter-particle forces toconcentration and velocity gradients.This results in threeempirically determined material functions: a hystereticpermeability, a non-Newtonian viscosity and a non-reversibleparticle interaction pressure.P arameters in the models arefitted to experimental data. A simulation program using finite difference methods both intime and space is applied to one and two dimensional testcases.Numer ical experiments are performed to study the effectof different viscosity and permeability models. The effect ofshear on consolidation rate is studied and it is significantwhen the permeability hysteresis model is employed.

The shock compression of Reactive Particle Metal Mixtures (RPMMs) is studied at the microscale by direct numerical simulation. Mixture microstructures are rendered explicitly, providing spatial resolution of the coupled thermal, mechanical, and chemical responses at the particle level during shock compression. A polymer-bonded aluminum-iron oxide thermite system is the focus of this work; however, the computational methods developed here may be extended to other reactive particle systems. Shock waves are propagated through the mixtures in finite element simulations, where Eulerian formulations are used to handle the highly-dynamic nature of particulate shock compression. Thermo-mechano-chemical responses are computed for a set of mixture classes (20% and 50% epoxy content by weight) subjected to a range of dynamic loading conditions (particle velocities ranging from 0.300??00 km/s). Two critical sub-problems are addressed: (i) the calculation of Hugoniot data for variable mixture compositions and (ii) the prediction of sites that experience microscale reaction initiation. Hugoniot calculations are in excellent agreement with experimental data. Microscale reaction initiation sites are predicted in certain load cases for each mixture class, although such predictions cannot currently be validated by experimental methods.

<p>A mathematical model for a consolidation process of a highlyconcentrated, flocculated suspension is developed.Thesuspension is treated as a mixture of a fluid and solidparticles by an Eulerian two-phase fluid model.W e characterizethe suspension by constitutive relations correlating thestresses, interaction forces, and inter-particle forces toconcentration and velocity gradients.This results in threeempirically determined material functions: a hystereticpermeability, a non-Newtonian viscosity and a non-reversibleparticle interaction pressure.P arameters in the models arefitted to experimental data.</p><p>A simulation program using finite difference methods both intime and space is applied to one and two dimensional testcases.Numer ical experiments are performed to study the effectof different viscosity and permeability models. The effect ofshear on consolidation rate is studied and it is significantwhen the permeability hysteresis model is employed.</p>

This thesis presents several ways to understand transports of air and water masses in the atmosphere and ocean, and the transports of energy that they imply. It presents work using various kinds of observations as well as computer simulations of the atmosphere and oceans. One of the main focuses is to identify similarities and differences between models and observations, as well as between different models. The first half of the thesis applies Lagrangian methods to study flows in the atmosphere and oceans. Part of the work focuses on understanding how particles follow the currents in the Baltic Sea and how they disperse. It is suggested that the commonly used regional ocean model for the Baltic Sea, RCO, underestimates the transport and the dispersion of the particles, which can have consequences for studies of e.g. biogeochemistry as well as for operational use. A similar methodology is used to study how particles are transported between the tropics and mid-latitudes by the large-scale atmospheric circulation. It is found that the mass transport associated with northbound and southbound particles can cancel in the zonally averaged circulation, and we propose that the degree of cancellation depends on the method of averaging. The latter half of the thesis focuses on Eulerian stream functions and specifically a thermodynamic stream function that combines the zonal and meridional circulations of the atmosphere into a single circulation. The results are used to study the inter-annual variability of the intensity and thermodynamic properties of the global atmospheric circulation. A significant correlation to ENSO variability is found both in reanalysis and the EC-Earth coupled climate model. It is also shown that a set of models from the CMIP5 project show a slowdown of the atmospheric circulation as a result of global warming and associated changes in near-surface moisture content and upper-level radiative cooling. / Denna avhandling presenterar olika metoder för att studera datormodeller av atmosfä- ren, haven, och klimatsystemet. Metoderna använder såväl Lagrangeska synsätt dvs att betrakta atmosfären eller haven som individuella partiklar i rörelse, som Eulerska synsätt där atmosfären och haven ses som gas eller vätska i rörelse. I artikel 1 sjö- sätts ett antal “surface drifters” i Östersjön som driver fritt med havsströmmarna och vars hastighet mäts av satelliter. Genom att modellera Lagrangeska partiklars rörelser i Östersjön och jämföra med dessa “surface drifters” kan det visas att datormodeller kan underskatta både medelhastigheten av partiklarna samt deras utbredning. I ar- tikel 2 simuleras luftmassornas rörelser mellan tropikerna och mellanbreddgraderna (∼ 45◦N/S). Ett medelvärde över all longituder tenderar att ignorera betydande mass- och energitransporter mellan tropikerna och mellanbredderna, och dessa kvantifieras i detalj i artikel 2. Artiklarna 3 och 4 presenterar en metod för att studera atmosfärens storskaliga rörelser utifrån ett termodynamiskt perspektiv där luftmassornas värme och fukt studeras. Det visas att variationer ytvattentemperatur vid ekvatorn i Stilla havet kan få atmosfären att, i ett globalt medelvärde, bli fuktigare och varmare samtidigt som masstransporter- na saktar ner. På samma sätt visas att en global uppvärmning till följd av ökade utsläpp av växthusgaser kan få atmosfären att bli varmare, fuktigare och att masstransporterna kan sakta ner. / <p>At the time of the doctoral defence the following papers were unpublished and had a status as follows: Paper 3: In press; Paper 4: Manuscript.</p> / BalticWay

Orientador: Milton Mori / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Quimica / Made available in DSpace on 2018-08-09T09:36:46Z (GMT). No. of bitstreams: 1 Vegini_AtilanoAntonio_D.pdf: 28017713 bytes, checksum: b5c4951104b5d515ebe084a6388a6ea2 (MD5) Previous issue date: 2007 / Resumo: Neste trabalho é apresentado o código computacional CYCLO, programa desenvolvido especificamente para predizer o escoamento multifásico em ciclones. Os ciclones são equipamentos utilizados na indústria, principalmente, para a separação de material particulado de correntes gasosas. Desde o início da industrialização até a atualidade, os ciclones são investigados cientificamente na tentativa de elucidar o real funcionamento deste complexo sistema de escoamento que ocorre no interior destes equipamentos. Com o avanço computacional, as modernas técnicas da fluidodinâmica computacional (CFD), têm se mostrado capaz de auxiliar nas investigações científicas sobre os ciclones. O código CYCLO, é um destes programas baseado nas técnicas da fluidodinâmica computacional (CFD). Consiste de um modelo multifásico num referencial euleriano, e composto de equações diferenciais parciais que são resolvidas numericamente através da aplicação do método dos volumes finitos, com acoplamento pressão-velocidade e malha numérica deslocada. A hipótese de simetria no eixo é assumida, tornando possível a utilização de um modelo 3DSimétrico em coordenadas cilíndricas. O código CYCLO torna possível à utilização de até três fases sólidas, cada uma caracterizada por seu tamanho de partícula, massa específica e fração volumétrica. O escoamento da fase sólida é considerado invíscido e a transferência de quantidade de movimento interfase predito pela adoção de um modelo de força de arraste. Para representar o comportamento anisotrópico dos tensores de Reynolds na fase gasosa, é utilizado um modelo de turbulência híbrido composto por uma combinação do modelo k-e padrão para os componentes radiais e axiais do tensor de Reynolds, e, para os componentes tangenciais por intermédio da teoria do comprimento de mistura de Prandtl. Os objetivos deste trabalho vão desde a verificação e validação do código CYCLO com seu modelo multifásico euleriano-euleriano e todas suas hipóteses simplificadoras, até a apresentação de aplicações práticas do uso das técnicas de CFD. Para a verificação e validação do código, os resultados obtidos numericamente são comparados com valores experimentais para o escoamento monofásico e para o escoamento multifásico. Como exemplo de aplicação prática das técnicas de CFD, é apresentado a utilização do código na análise e projeto de ciclones industriais / Abstract: In this work it is presented the computational code CYCLO, which is a program developed specifically to predict the dynamic behavior of the gas-solid flow in cyclones. The cyclones have been used extensively in many industries for a long time for separating the particles from gaseous streams. Since the beginning of the industrialization until the present time, the cyclones are investigated scientifically in order to elucidate the real functioning of this complex flow behavior inside of these equipments. With the computational advance, the modern techniques of the computational fluid dynamics (CFD), has been capable to assist in the scientific inquiries concerning cyclones. The CYCLO code is one of these programs based on computational fluid dynamics (CFD) techniques. The program consists of a multiphase flow model based on the Eulerian-Eulerian approach and it is composed of several partial differential equations, which are solved using the finite volume method with pressure-velocity coupling and staggered grids. The axial symmetry hypothesis is assumed, which makes possible to apply the 3D symmetric model in cylindrical coordinate. The CYCLO code makes possible the use of up to three solid phases, each one represented by a particle diameter, density and specific volumetric fraction. The solid-phase flow is considered inviscid and drag forces between phases are responsible for the gas-solid interaction. To represent an anisotropic behavior of the Reynolds stress in the gas phase, it is used a hybrid model composed of the combination of the (k-e) standard model for the radial and axial components and Prandt¿s longitudinal mixing model for the tangential components. The purpose of the present study is to verify and validate the model used by the CYCLO code and to show practical applications of the use of CFD techniques. In order to verify and validate the code, numerical results were compared with experimental data for gas and gas-solid flows. As practical examples of application of CFD techniques, the code was used to the analysis and design of industrial cyclones / Doutorado / Desenvolvimento de Processos Químicos / Doutor em Engenharia Química

Orientadores: Celia Picinin de Mello, Anamaria Gomide / Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-26T19:50:54Z (GMT). No. of bitstreams: 1 Vulcani_RenatadeLacerdaMartins_M.pdf: 2431212 bytes, checksum: 702947f1e783d410ef77eb0234852d6a (MD5) Previous issue date: 2015 / Resumo: Neste trabalho apresentamos uma breve introdução à teoria dos grafos, elucidando alguns conceitos básicos e destacando grafos eulerianos. Usamos o conceito de grafos eulerianos para resolver alguns passatempos e jogos conhecidos. Finalizamos apresentando algumas aplicações que envolvem grafos que não são necessariamente eulerianos / Abstract: In this work we present a brief introduction to graph theory, explaining some basic concepts and highlighting eulerians graphs. We use the concept of eulerians graphs to solve some well known puzzles and games. We finalize by presenting some applications involving graphs that are not necessarily eulerians / Mestrado / Matemática em Rede Nacional / Mestra

[EN] The main objective of this work is the modeling of diesel sprays under engine conditions, including the atomization, transport and evaporation processes pivotal in the diesel spray formation and its development. For this purpose, an Eulerian single fluid model, embedded in a RANS environment, is implemented in the CFD platform OpenFOAM. The modeling approach implemented here is based on the &#8512;-Y model. The model is founded on the assumption of flow scales separation. In actual injection systems, it can be assumed that the flow exiting the nozzle is operating at large Reynolds and Weber numbers and thus, it is possible to assume a separation of features such as mass transport (large scales) from the atomization process occurring at smaller scales. The liquid/gas mixture is treated as a pseudo-fluid with variable density and which flows with a single velocity field. Moreover, the mean geometry of the liquid structures can be characterized by modeling the mean surface area of the liquid-gas interphase per unit of volume. Additionally, an evaporation model has been developed around the particular characteristics of the current engine technologies. This means that vaporization process is limited by fuel-air mixing rate and fuel droplets evaporate as long as there is enough air for them to heat up and vaporize. Consequently, the evaporation model is based on the Locally Homogeneous Flow (LHF) approach. Under the assumption of an adiabatic mixing, in the liquid/vapor region, the spray is supposed to have a trend towards adiabatic saturation conditions and to determine this equilibrium between phases Raoult's ideal law is considered. Finally, the spray model is coupled with an advanced combustion model based on approximated diffusion flames (ADF), which reduces the computational effort especially for complex fuels and is a natural step for modeling diesel sprays. First, the model is applied to a basic external flow case under non-vaporizing conditions, extremely convenient due to both the experimental database available and the symmetric layout which allows important simplification of the modeling effort. Good agreement between computational results and experimental data is observed, which encourages its application to a more complex configuration. Secondly, the model is applied to the "Spray A" from the Engine Combustion Network (ECN), under non-vaporizing conditions, in order to reproduce the internal structure of diesel sprays as well as to produce accurate predictions of SMD droplets sizes. Finally, vaporizing "Spray A" studies are conducted together with the baseline reacting condition of this database. The calculated spray penetration, liquid length, spray velocities, ignition delay and lift-off length are compared with experimental data and analysed in detail. / [ES] El objetivo principal de este trabajo es el modelado de chorros diésel en condiciones de motor, incluyendo los fenómenos de atomización, transporte y evaporación fundamentales en la formación y desarrollo del chorro. Para este fin, se implementa un modelo de spray euleriano de tipo monofluido en un entorno RANS en la plataforma CFD OpenFOAM. El enfoque de modelado aplicado aquí sigue la idea de un modelo del tipo &#8512;-Y. El modelo se fundamenta en la hipótesis de separación de escalas del flujo. En los sistemas de inyección actuales, es posible asumir que el flujo que sale de la tobera opera a altos números de Reynolds y Webber y por tanto, es posible considerar la independencia de fenómenos como el transporte de masa (grandes escalas del flujo) de los procesos de atomización que ocurren a escalas menores. La mezcla líquido/gas se trata como un pseudo-fluido con densidad variable y que fluye según un único campo de velocidad. Además, la geometría promedio de las estructuras de líquido se puede caracterizar mediante el modelado de la superficie de la interfase líquido/gas por unidad de volumen. Completando el modelo de chorro, se ha desarrollado un modelo de evaporación alrededor de las características particulares de las tecnologías actuales de los motores. Esto supone que el proceso de evaporación está controlado por mezcla aire-combustible y las gotas de combustible se evaporan siempre que exista suficiente aire para calentarlas y evaporarlas. Debido a esto, el modelo de evaporación implementado está basado en el enfoque de Flujos Localmente Homogéneos (LHF). Considerando una mezcla adiabática, en la región líquido/vapor, se supone que el chorro tiende a las condiciones adiabáticas de saturación y para determinar este equilibrio entre fases, se utiliza la ley ideal de Raoult. Finalmente, el modelo de chorro se acopla con un modelo avanzado de combustión basado en llamas de difusión aproximadas (ADF), que reduce el coste computacional especialmente para combustibles complejos y supone el paso lógico en el desarrollo del modelo para simular chorros diesel. En primer lugar, el modelo se aplica al cálculo de un caso básico de flujo externo no evaporativo, muy adecuado tanto por la extensa base de datos experimentales disponible como por la simetría geométrica que presenta, permitiendo una importante simplificación de la simulación. Los resultados obtenidos presentan un buen acuerdo con los experimentos, lo cual estimula su aplicación en configuraciones más complejas. En segundo lugar, el modelo se aplica al cálculo del "Spray A" del Engine Combustion Network (ECN), no evaporativo, para reproducir la estructura interna del chorro diesel así como predecir tamaños de gota (SMD) de forma precisa. Finalmente, se realizan estudios evaporativos del "Spray A" junto con la condición nominal reactiva de esta base de datos. La penetración de vapor, la longitud líquida, velocidad, el tiempo de retraso y la longitud de despegue de llama calculados se comparan con los datos experimentales y se analizan en detalle. / [CAT] L'objectiu principal d'aquest treball és el modelatge de dolls dièsel en condicions de motor, incloent els fenòmens d'atomització, transport i evaporació fonamentals en la formació i desenvolupament del doll. Amb aquesta finalitat, s'implementa un model de doll eulerià de tipus monofluid en un entorn RANS a la plataforma CFD OpenFOAM. L'enfocament de modelatge aplicat ací segueix la idea d'un model del tipus &#8512;-Y. El model es fonamenta en la hipòtesi de separació d'escales del flux. En els sistemes d'injecció actuals, és possible assumir que el flux que surt de la tovera opera a alts nombres de Reynolds i Webber, i per tant és possible considerar la independència de fenòmens com el transport de massa (grans escales del flux) dels processos d'atomització que ocorren a escales menors. La mescla líquid / gas es tracta com un pseudo-fluid amb densitat variable i que flueix segons un únic camp de velocitat. A més, la geometria mitjana de les estructures de líquid es pot caracteritzar mitjançant el modelatge de la superfície de la interfase líquid / gas per unitat de volum. Completant el model, s'ha desenvolupat un model d'evaporació al voltant de les característiques particulars de les tecnologies actuals dels motors. Això suposa que el procés d'evaporació està controlat per la mescla aire-combustible i les gotes de combustible s'evaporen sempre que hi hagi suficient aire per escalfar i evaporar. A causa d'això, el model d'evaporació implementat està basat en el plantejament de fluxos Localment Homogenis (LHF). Considerant una mescla adiabàtica, a la regió líquid / vapor, se suposa que el doll tendeix a les condicions adiabàtiques de saturació i per determinar aquest equilibri entre fases, s'utilitza la llei ideal de Raoult. Finalment, el model de doll s'acobla amb un model avançat de combustió basat en flamelets de difusió aproximades (ADF), que redueix el cost computacional especialment per a combustibles complexos i suposa el pas lògic en el desenvolupament del model per simular dolls dièsel. En primer lloc, el model s'aplica al càlcul d'un cas bàsic de flux extern no evaporatiu, molt adequat tant per l'extensa base de dades experimentals disponible com per la simetria geomètrica que presenta, permetent una important simplificació de la simulació. Els resultats obtinguts presenten un bon acord amb els experiments, la qual cosa estimula la seva aplicació en configuracions més complexes. En segon lloc, el model s'aplica al càlcul del "Spray A" no evaporatiu de la xarxa Engine Combustion Network (ECN), per reproduir l'estructura interna del doll dièsel així com predir mides de gota (SMD) de forma precisa. Finalment, es realitzen estudis evaporatius del "Spray A" juntament amb la condició nominal reactiva d'aquesta base de dades. La penetració de vapor, la longitud líquida, velocitat, el temps de retard i la longitud d'enlairament de flama calculats es comparen amb les dades experimentals i s'analitzen en detall. / Pandal Blanco, A. (2016). Implementation and Development of an Eulerian Spray Model for CFD simulations of diesel Sprays [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/68490 / TESIS

Eulerian graphs have a closed walk traversing each edge exactly once. Finding such a walk is a basic arc routing problem based on a road network. Most of the problems with applications in operational research are NP-hard. We describe a formal model of a road network and vehicle routes and formulate several arc routing problems motivated by winter road maintenance in the Czech Republic. The main part is focused on single vehicle routing problems on trees. We propose a new unfairness minimization problem for finding a vehicle route with properties that lead to a minimal number of resident complaints against unfair maintenance. Residents feel like they are skipped when the vehicle route has multiple trips and passes nearby without providing maintenance to their street. By reduction of the necklace splitting problem to the unfairness minimization problem we prove it is PPA-complete. Further, we define a restricted arc routing problem on trees which formalize condi- tions given by Czech legislation. We proved the existence of a polynomial algorithm for deciding whether a single vehicle route exists when there is a single priority for roads. If multiple priorities are used, we express conditions and conjectures when the problem has polynomial complexity. Finally, a utilization of the model is illustrated by an...

The purpose of this study is to compare two possible methods of computational modeling of straightening long profiles. The study presents fundamentals of the straightening process, basic principles of the finite element method and the principle of fast algorithm based on Eulerian description of motion of continuum. The study investigates how the two methods are computationally demanding and precise. Finally, the acquired results are summarised and the effectiveness of both algorithms is assessed.