One-dimensional Fermi accelerator model with moving wall described by a nonlinear van der Pol oscillator

A modification of the one-dimensional Fermi accelerator model is considered in this work. The dynamics of a classical particle of mass m, confined to bounce elastically between two rigid walls where one is described by a nonlinear van der Pol type oscillator while the other one is fixed, working as a reinjection mechanism of the particle for a next collision, is carefully made by the use of a two-dimensional nonlinear mapping. Two cases are considered: (i) the situation where the particle has mass negligible as compared to the mass of the moving wall and does not affect the motion of it; and (ii) the case where collisions of the particle do affect the movement of the moving wall. For case (i) the phase space is of mixed type leading us to observe a scaling of the average velocity as a function of the parameter (χ) controlling the nonlinearity of the moving wall. For large χ, a diffusion on the velocity is observed leading to the conclusion that Fermi acceleration is taking place. On the other hand, for case (ii), the motion of the moving wall is affected by collisions with the particle. However, due to the properties of the van der Pol oscillator, the moving wall relaxes again to a limit cycle. Such kind of motion absorbs part of the energy of the particle leading to a suppression of the unlimited energy gain as observed in case (i). The phase space shows a set of attractors of different periods whose basin of attraction has a complicated organization. © 2013 American Physical Society.

Saddle points and rare collisions under scaling approach in a Fermi accelerator with two nonlinear terms

Rare collisions of a classical particle bouncing between two walls are studied. The dynamics is described by a two-dimensional, nonlinear and area-preserving mapping in the variables velocity and time at the instant that the particle collides with the moving wall. The phase space is of mixed type preventing diffusion of the particle to high energy. Successive and therefore rare collisions are shown to have a histogram of frequency which is scaling invariant with respect to the control parameters. The saddle fixed points are studied and shown to be scaling invariant with respect to the control parameters too. © 2012 Elsevier B.V. All rights reserved.

Some dynamical properties of a classical dissipative bouncing ball model with two nonlinearities

Some dynamical properties for a bouncing ball model are studied. We show that when dissipation is introduced the structure of the phase space is changed and attractors appear. Increasing the amount of dissipation, the edges of the basins of attraction of an attracting fixed point touch the chaotic attractor. Consequently the chaotic attractor and its basin of attraction are destroyed given place to a transient described by a power law with exponent -2. The parameter-space is also studied and we show that it presents a rich structure with infinite self-similar structures of shrimp-shape. © 2013 Elsevier B.V. All rights reserved.

Propriedades de tranporte, caos e dissipação num sistema dinâmico não linear

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Some comments on the nonlinear dynamics of a portal frame under base excitation

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Uma abordagem geométrica para princípios de localização de integrais funcionais

Pós-graduação em Física - IFT

Uma abordagem de potencial e massa efetiva e a descrição de espaço de fase quântico para tratar sistemas de spins: Caracterizando o tunelamento de spin e propriedades da molécula de Fe8

Pós-graduação em Física - IFT

Canonical group quantization and boundary conditions

In the present thesis, we study quantization of classical systems with non-trivial phase spaces using the group-theoretical quantization technique proposed by Isham. Our main goal is a better understanding of global and topological aspects of quantum theory. In practice, the group-theoretical approach enables direct quantization of systems subject to constraints and boundary conditions in a natural and physically transparent manner -- cases for which the canonical quantization method of Dirac fails. First, we provide a clarification of the quantization formalism. In contrast to prior treatments, we introduce a sharp distinction between the two group structures that are involved and explain their physical meaning. The benefit is a consistent and conceptually much clearer construction of the Canonical Group. In particular, we shed light upon the 'pathological' case for which the Canonical Group must be defined via a central Lie algebra extension and emphasise the role of the central extension in general. In addition, we study direct quantization of a particle restricted to a half-line with 'hard wall' boundary condition. Despite the apparent simplicity of this example, we show that a naive quantization attempt based on the cotangent bundle over the half-line as classical phase space leads to an incomplete quantum theory; the reflection which is a characteristic aspect of the 'hard wall' is not reproduced. Instead, we propose a different phase space that realises the necessary boundary condition as a topological feature and demonstrate that quantization yields a suitable quantum theory for the half-line model. The insights gained in the present special case improve our understanding of the relation between classical and quantum theory and illustrate how contact interactions may be incorporated.

Supervisión multidistribuida para el control de procesos de conservación de productos agroalimentarios: optimización de calidad del producto

La presente Tesis está orientada al análisis de la supervisión multidistribuida de tres procesos agroalimentarios: el secado solar, el transporte refrigerado y la fermentación de café, a través de la información obtenida de diferentes dispositivos de adquisición de datos, que incorporan sensores, así como el desarrollo de metodologías de análisis de series temporales, modelos y herramientas de control de procesos para la ayuda a la toma de decisiones en las operaciones de estos entornos. En esta tesis se han utilizado: tarjetas RFID (TemTrip®) con sistema de comunicación por radiofrecuencia y sensor de temperatura; el registrador (i-Button®), con sensor integrado de temperatura y humedad relativa y un tercer prototipo empresarial, módulo de comunicación inalámbrico Nlaza, que integra un sensor de temperatura y humedad relativa Sensirion®. Estos dispositivos se han empleado en la conformación de redes multidistribuidas de sensores para la supervisión de: A) Transportes de producto hortofrutícola realizados en condiciones comerciales reales, que son: dos transportes terrestre de producto de IV gama desde Murcia a Madrid; transporte multimodal (barco-barco) de limones desde Montevideo (Uruguay) a Cartagena (España) y transporte multimodal (barco-camión) desde Montevideo (Uruguay) a Verona (Italia). B) dos fermentaciones de café realizadas en Popayán (Colombia) en un beneficiadero. Estas redes han permitido registrar la dinámica espacio-temporal de temperaturas y humedad relativa de los procesos estudiados. En estos procesos de transporte refrigerado y fermentación la aplicación de herramientas de visualización de datos y análisis de conglomerados, han permitido identificar grupos de sensores que presentan patrones análogos de sus series temporales, caracterizando así zonas con dinámicas similares y significativamente diferentes del resto y permitiendo definir redes de sensores de menor densidad cubriendo las diferentes zonas identificadas. Las metodologías de análisis complejo de las series espacio-temporales (modelos psicrométricos, espacio de fases bidimensional e interpolaciones espaciales) permitieron la cuantificación de la variabilidad del proceso supervisado tanto desde el punto de vista dinámico como espacial así como la identificación de eventos. Constituyendo así herramientas adicionales de ayuda a la toma de decisiones en el control de los procesos. Siendo especialmente novedosa la aplicación de la representación bidimensional de los espacios de fases en el estudio de las series espacio-temporales de variables ambientales en aplicaciones agroalimentarias, aproximación que no se había realizado hasta el momento. En esta tesis también se ha querido mostrar el potencial de un sistema de control basado en el conocimiento experto como es el sistema de lógica difusa. Se han desarrollado en primer lugar, los modelos de estimación del contenido en humedad y las reglas semánticas que dirigen el proceso de control, el mejor modelo se ha seleccionado mediante un ensayo de secado realizado sobre bolas de hidrogel como modelo alimentario y finalmente el modelo se ha validado mediante un ensayo en el que se deshidrataban láminas de zanahoria. Los resultados sugirieron que el sistema de control desarrollado, es capaz de hacer frente a dificultades como las variaciones de temperatura día y noche, consiguiendo un producto con buenas características de calidad comparables a las conseguidas sin aplicar ningún control sobre la operación y disminuyendo así el consumo energético en un 98% con respecto al mismo proceso sin control. La instrumentación y las metodologías de análisis de datos implementadas en esta Tesis se han mostrado suficientemente versátiles y transversales para ser aplicadas a diversos procesos agroalimentarios en los que la temperatura y la humedad relativa sean criterios de control en dichos procesos, teniendo una aplicabilidad directa en el sector industrial ABSTRACT This thesis is focused on the analysis of multi-distributed supervision of three agri-food processes: solar drying, refrigerated transport and coffee fermentation, through the information obtained from different data acquisition devices with incorporated sensors, as well as the development of methodologies for analyzing temporary series, models and tools to control processes in order to help in the decision making in the operations within these environments. For this thesis the following has been used: RFID tags (TemTrip®) with a Radiofrequency ID communication system and a temperature sensor; the recorder (i-Button®), with an integrated temperature and relative humidity and a third corporate prototype, a wireless communication module Nlaza, which has an integrated temperature and relative humidity sensor, Sensirion®. These devices have been used in creating three multi-distributed networks of sensors for monitoring: A) Transport of fruits and vegetables made in real commercial conditions, which are: two land trips of IV range products from Murcia to Madrid; multimodal transport (ship - ship) of lemons from Montevideo (Uruguay) to Cartagena (Spain) and multimodal transport (ship - truck) from Montevideo (Uruguay) to Verona (Italy). B) Two coffee fermentations made in Popayan (Colombia) in a coffee processing plant. These networks have allowed recording the time space dynamics of temperatures and relative humidity of the processed under study. Within these refrigerated transport and fermentation processes, the application of data display and cluster analysis tools have allowed identifying sensor groups showing analogical patterns of their temporary series; thus, featuring areas with similar and significantly different dynamics from the others and enabling the definition of lower density sensor networks covering the different identified areas. The complex analysis methodologies of the time space series (psychrometric models, bi-dimensional phase space and spatial interpolation) allowed quantifying the process variability of the supervised process both from the dynamic and spatial points of view; as well as the identification of events. Thus, building additional tools to aid decision-making on process control brought the innovative application of the bi-dimensional representation of phase spaces in the study of time-space series of environmental variables in agri-food applications, an approach that had not been taken before. This thesis also wanted to show the potential of a control system based on specialized knowledge such as the fuzzy logic system. Firstly, moisture content estimation models and semantic rules directing the control process have been developed, the best model has been selected by an drying assay performed on hydrogel beads as food model; and finally the model has been validated through an assay in which carrot sheets were dehydrated. The results suggested that the control system developed is able to cope with difficulties such as changes in temperature daytime and nighttime, getting a product with good quality features comparable to those features achieved without applying any control over the operation and thus decreasing consumption energy by 98% compared to the same uncontrolled process. Instrumentation and data analysis methodologies implemented in this thesis have proved sufficiently versatile and cross-cutting to apply to several agri-food processes in which the temperature and relative humidity are the control criteria in those processes, having a direct effect on the industry sector.

CFD modelling of the fast pyrolysis of an in-flight cellulosic particle subjected to convective heat transfer

The pyrolysis of a freely moving cellulosic particle inside a 41.7mgs -1 source continuously fed fluid bed reactor subjected to convective heat transfer is modelled. The Lagrangian approach is adopted for the particle tracking inside the reactor, while the flow of the inert gas is treated with the standard Eulerian method for gases. The model incorporates the thermal degradation of cellulose to char with simultaneous evolution of gases and vapours from discrete cellulosic particles. The reaction kinetics is represented according to the Broido–Shafizadeh scheme. The convective heat transfer to the surface of the particle is solved by two means, namely the Ranz–Marshall correlation and the limit case of infinitely fast external heat transfer rates. The results from both approaches are compared and discussed. The effect of the different heat transfer rates on the discrete phase trajectory is also considered.

Development of multiphase and multiscale mathematical models for thermal spray process

High velocity oxyfuel (HVOF) thermal spraying is one of the most significant developments in the thermal spray industry since the development of the original plasma spray technique. The first investigation deals with the combustion and discrete particle models within the general purpose commercial CFD code FLUENT to solve the combustion of kerosene and couple the motion of fuel droplets with the gas flow dynamics in a Lagrangian fashion. The effects of liquid fuel droplets on the thermodynamics of the combusting gas flow are examined thoroughly showing that combustion process of kerosene is independent on the initial fuel droplet sizes. The second analysis copes with the full water cooling numerical model, which can assist on thermal performance optimisation or to determine the best method for heat removal without the cost of building physical prototypes. The numerical results indicate that the water flow rate and direction has noticeable influence on the cooling efficiency but no noticeable effect on the gas flow dynamics within the thermal spraying gun. The third investigation deals with the development and implementation of discrete phase particle models. The results indicate that most powder particles are not melted upon hitting the substrate to be coated. The oxidation model confirms that HVOF guns can produce metallic coating with low oxidation within the typical standing-off distance about 30cm. Physical properties such as porosity, microstructure, surface roughness and adhesion strength of coatings produced by droplet deposition in a thermal spray process are determined to a large extent by the dynamics of deformation and solidification of the particles impinging on the substrate. Therefore, is one of the objectives of this study to present a complete numerical model of droplet impact and solidification. The modelling results show that solidification of droplets is significantly affected by the thermal contact resistance/substrate surface roughness.

Gas-liquid-solid flow modelling in a bubble column

An alternative approach to the modelling of solid-liquid and gas-liquid-solid flows for a 5:1 height to width aspect ratio bubble column is presented here. A modified transport equation for the volume fraction of a dispersed phase has been developed for the investigation of turbulent buoyancy driven flows (Chem. Eng. Proc., in press). In this study, a modified transport equation has been employed for discrete phase motion considering both solid-liquid and gas-liquid-solid flows. The modelling of the three-phase flow in a bubble column was achieved in the following case: injecting a slug of solid particles into the column for 10 s at a velocity of 0.1 m s-1 and then the gas phase flow was initiated with a superficial gas velocity of 0.02 cm s-1. © 2003 Elsevier B.V. All rights reserved.

The modelling of buoyancy driven flow in bubble columns

Using the analogy between lateral convection of heat and the two-phase flow in bubble columns, alternative turbulence modelling methods were analysed. The k-ε turbulence and Reynolds stress models were used to predict the buoyant motion of fluids where a density difference arises due to the introduction of heat or a discrete phase. A large height to width aspect ratio cavity was employed in the transport of heat and it was shown that the Reynolds stress model with the use of velocity profiles including the laminar flow solution resulted in turbulent vortices developing. The turbulence models were then applied to the simulation of gas-liquid flow for a 5:1 height to width aspect ratio bubble column. In the case of a gas superficial velocity of 0.02 m s-1 it was determined that employing the Reynolds stress model yielded the most realistic simulation results. © 2003 Elsevier B.V. All rights reserved.

Heat transfer performance investigation of nanofluids flow in pipe

Different types of base fluids, such as water, engine oil, kerosene, ethanol, methanol, ethylene glycol etc. are usually used to increase the heat transfer performance in many engineering applications. But these conventional heat transfer fluids have often several limitations. One of those major limitations is that the thermal conductivity of each of these base fluids is very low and this results a lower heat transfer rate in thermal engineering systems. Such limitation also affects the performance of different equipments used in different heat transfer process industries. To overcome such an important drawback, researchers over the years have considered a new generation heat transfer fluid, simply known as nanofluid with higher thermal conductivity. This new generation heat transfer fluid is a mixture of nanometre-size particles and different base fluids. Different researchers suggest that adding spherical or cylindrical shape of uniform/non-uniform nanoparticles into a base fluid can remarkably increase the thermal conductivity of nanofluid. Such augmentation of thermal conductivity could play a more significant role in enhancing the heat transfer rate than that of the base fluid. Nanoparticles diameters used in nanofluid are usually considered to be less than or equal to 100 nm and the nanoparticles concentration usually varies from 5% to 10%. Different researchers mentioned that the smaller nanoparticles concentration with size diameter of 100 nm could enhance the heat transfer rate more significantly compared to that of base fluids. But it is not obvious what effect it will have on the heat transfer performance when nanofluids contain small size nanoparticles of less than 100 nm with different concentrations. Besides, the effect of static and moving nanoparticles on the heat transfer of nanofluid is not known too. The idea of moving nanoparticles brings the effect of Brownian motion of nanoparticles on the heat transfer. The aim of this work is, therefore, to investigate the heat transfer performance of nanofluid using a combination of smaller size of nanoparticles with different concentrations considering the Brownian motion of nanoparticles. A horizontal pipe has been considered as a physical system within which the above mentioned nanofluid performances are investigated under transition to turbulent flow conditions. Three different types of numerical models, such as single phase model, Eulerian-Eulerian multi-phase mixture model and Eulerian-Lagrangian discrete phase model have been used while investigating the performance of nanofluids. The most commonly used model is single phase model which is based on the assumption that nanofluids behave like a conventional fluid. The other two models are used when the interaction between solid and fluid particles is considered. However, two different phases, such as fluid and solid phases is also considered in the Eulerian-Eulerian multi-phase mixture model. Thus, these phases create a fluid-solid mixture. But, two phases in the Eulerian-Lagrangian discrete phase model are independent. One of them is a solid phase and the other one is a fluid phase. In addition, RANS (Reynolds Average Navier Stokes) based Standard κ-ω and SST κ-ω transitional models have been used for the simulation of transitional flow. While the RANS based Standard κ-ϵ, Realizable κ-ϵ and RNG κ-ϵ turbulent models are used for the simulation of turbulent flow. Hydrodynamic as well as temperature behaviour of transition to turbulent flows of nanofluids through the horizontal pipe is studied under a uniform heat flux boundary condition applied to the wall with temperature dependent thermo-physical properties for both water and nanofluids. Numerical results characterising the performances of velocity and temperature fields are presented in terms of velocity and temperature contours, turbulent kinetic energy contours, surface temperature, local and average Nusselt numbers, Darcy friction factor, thermal performance factor and total entropy generation. New correlations are also proposed for the calculation of average Nusselt number for both the single and multi-phase models. Result reveals that the combination of small size of nanoparticles and higher nanoparticles concentrations with the Brownian motion of nanoparticles shows higher heat transfer enhancement and thermal performance factor than those of water. Literature suggests that the use of nanofluids flow in an inclined pipe at transition to turbulent regimes has been ignored despite its significance in real-life applications. Therefore, a particular investigation has been carried out in this thesis with a view to understand the heat transfer behaviour and performance of an inclined pipe under transition flow condition. It is found that the heat transfer rate decreases with the increase of a pipe inclination angle. Also, a higher heat transfer rate is found for a horizontal pipe under forced convection than that of an inclined pipe under mixed convection.

Discrete squeezed states for finite-dimensional spaces

We show how discrete squeezed states in an N-2-dimensional phase space can be properly constructed out of the finite-dimensional context. Such discrete extensions are then applied to the framework of quantum tomography and quantum information theory with the aim of establishing an initial study on the interference effects between discrete variables in a finite phase space. Moreover, the interpretation of the squeezing effects is seen to be direct in the present approach, and has some potential applications in different branches of physics.