In this thesis, we have evaluated a stochastic Lagrangian model for computing particle deposition rates with prospects to use for atmospheric deposition applications.  The model is one-dimensional and models the particle dynamics in the boundary layers near walls and obstacles by simulating the coherent turbulent structures and Brownian motion governing the wall-normal transport. The deposition model is used with a hybrid deterministic/stochastic particle dispersion model governing the dynamics in the turbulent bulk flow. We used a steady-state RANS k-ϵ turbulence model to simulate the turbulent fluid flow in a neutral atmospheric boundary layer (ABL) using the with inflow boundary conditions by Richards & Hoxey (1993). The turbulence model is solved with the SIMPLE algorithm using the OpenFOAM software. The mean-field characteristic of the turbulent flow in the computational domain is exported and used for the particle model. The particle model is a Lagrangian Langevin-type model, consisting of a system of stochastic differential equations. The particle model was solved using a weakly first order a-stable scheme. We evaluated the deposition model by computing the deposition rate for a range of particle sizes and compared our results with collected experimental wind tunnel data. The numerical experiment was done in a computational domain based on the ABL model by Hargreaves & Wright (2007), a rectangular domain with a logarithmic wind profile. We used a particle source near the inflow boundary with an instantaneously release at the initial time. Results showed disagreement with the experimental data and was only valid for medium sized particles. However, time restrictions led to the analysis being cut short and only a single simulation was conducted. A definite conclusion on the suitability of the method could not be made based solely on this single results. Some uncertainties were identified and discussed for further potential work on the evaluation of the method. However, one conclusion was drawn on the performance of the method. The computational cost was concluded to be too high with the first order particle scheme used and higher order schemes is required for any practical use of the method for atmospheric deposition applications.

[pt] Em uma mina a céu aberto, a estabilidade dos taludes rochosos é um dos maiores desafios na engenharia das rochas devido aos processos geodinâmicos que formaram o depósito de minério, fazendo de cada depósito complexo e único. Algumas das complexidades encontradas comumente são: a geologia nos arredores do depósito, a alta variabilidade das propriedades, os complexos defeitos estruturais, o grau de alteração das rochas, a informação geomecânica limitada, etc. Antes de avaliar a estabilidade de taludes devemos caracterizar o maciço rochoso. Para caracterizá-lo se têm construído os modelos geológico, estrutural e do maciço rochoso para formar o modelo geotécnico como recomenda o projeto Large Open Pit (LOP), um projeto de pesquisa internacional relacionado à estabilidade de taludes de rocha nas minas a céu aberto. Uma vez construídos os domínios geotécnicos, a estabilidade de taludes rochosos pode ser avaliada para cada domínio pelos métodos de equilíbrio limite ou numéricos como o método dos elementos finitos ou o método dos elementos discretos. O uso do método depende de diversos fatores, como a influência dos elementos estruturais, a importância da análise, a informação disponível, etc. Os métodos de equilíbrio limite como os tradicionais de Bishop e Janbu podem ser usados na avaliação de estabilidade de grandes taludes de rocha que são susceptíveis a falhas rotacionais do maciço rochoso. Já o método de elementos finitos se tem desenvolvido rapidamente e tem ganhado popularidade para a análise de estabilidade de taludes no caso em que o mecanismo de falha não esteja controlado por estruturas discretas geológicas. Os métodos de elementos finitos estão baseados em modelos constitutivos de tensão – deformação para rochas intactas e têm dificuldades em simular famílias com um número grande de descontinuidades dentro do maciço rochoso. O método dos elementos discretos permite simular um número grande de descontinuidades assim como também permite a simulação de grandes deformações. A presente dissertação usa o modelo SRM (Synthetic Rock Mass) para avaliar a estabilidade de taludes de uma mina a céu aberto no Peru. O SRM é uma nova técnica para simular o comportamento mecânico de maciços rochosos fraturados e permite simular a propagação de fraturas e os efeitos da anisotropia. Está técnica usa o modelo BPM (Bonded Particle Model) para representar a rocha intacta e o SJM (Smooth - Joint Contact Model) para representar as estruturas do maciço rochoso dentro do programa PFC. Para a modelagem estrutural se utilizou o método DFN (Discrete Fracture Network). Para a determinação dos modelos geológicos e estrutural se utilizou o programa Petrel e para a análise de estabilidade de taludes usando o modelo SRM se utilizou o programa PFC 4.0 na versão 2D. / [en] In an open pit mine, stability of rock slope is one of the most challenges in rock mechanics due to geodynamic processes that formed the ore deposit, making each deposit complex and unique. Some of the complexities commonly encountered are: the geology in the vicinity of the deposit, the high variability of properties, the complex structural defects, the rock alteration degree, limited geomechanical data, etc. Before evaluating the slope stability we should characterize the rock mass. To characterize it we have built the geological model, structural model and rock mass model to form the geotechnical model as it recommends the Large Open Pit project (LOP), an international research project related to stability of rock slope in open pit mines. Once constructed geotechnical domains, the stability of rock mass slope can be evaluated for each domain by using some known methods like limit equilibrium, the finite elements and discrete element methods. The use of the method depends of different factors like influence of structural elements (defects), importance of analysis, available information, etc. Limit equilibrium traditional methods like Bishop and Janbu can be used to evaluate the stability of large rock slopes that are susceptible to rotational failure of rock mass. Since the finite element method has developed rapidly and has gained popularity for the slope stability analysis in the case where failure mechanism is not controlled by discrete geological structure. Finite element method is based on constitutive models of stress-strain for intact rocks and has difficulties in simulating sets with a large number of discontinuities within the rock mass. The discrete element method allows to simulate a large number of discontinuities and also allows the simulation of large deformations. This dissertation uses the SRM (Synthetic Rock Mass) model to evaluate the stability of slopes in an open pit mine in Peru. The SRM model is a new technique that allows the simulation of the mechanical behavior of fractured rock mass taking into account propagation of fractures and anisotropic effects. This technique uses two well established techniques like BPM (Bonded Particle Model) for representation of intact rock and the SJM (Smooth-Joint Contact Model) to represent the structural fabric within the PFC program. For structural modeling it was used DFN method (Discrete-Fracture Network). To determine the geological and structural model it was used the Petrel program (Version 2010.1) and for slope stability analysis with the SRM model it was used the version 2D of the PFC 4.0 program.

Syftet med denna undersökning är att undersöka hur undervisningen om partikelmodellen bedrivs i årskurserna 4–6 och hur undervisningen utformas. Studien genomfördes med hjälp av kvalitativt inriktade intervjuer med fem olika lärare som undervisar inom No-ämnena i de aktuella årskurserna. Resultatet visar att alla fem lärarna undervisar om fasövergångar och materians byggstenar, men att lärarna fördjupar sig inom olika delar av dessa områden.  Lärarna i undersökningen väljer olika undervisningsmetoder när de undervisar om partikelmodellen: Traditionell undervisning, hypoteser, datoranimeringar, laborationer, dramatiseringar och användning av konkret material. / The purpose with this paper has been to examine how the education about the particle model in grades 4–6 is conducted and how the education is carried out. The study was carried out with the help of qualitatively directed interviews with five teachers that teach in the science subjects in the grades in question. The results show that all five teachers teach about, phase transitions and the building blocks of matter, but choose to immerse in different parts of these subjects. The teachers choose different teaching methods to teach about the particle model: Traditional teaching, hypotheses, computer animations, laboratory, dramatization and use of concrete materials.

Interactions between combinatorics and statistical mechanics have provided many fruitful insights in both fields. A compelling example is Kuperberg’s solution to the alternating sign matrix conjecture, and its following generalisations. In this thesis we investigate two models from statistical mechanics which have received attention in recent years. The first is the fully packed loop model. A conjecture from 2001 by Razumov and Stroganov opened the field for a large ongoing investigation of the O(1) loop model and its connections to a refinement of the fully packed loop model. We apply a combinatorial bijection originally found by de Gier to an older conjecture made by Propp. The second model is the hard particle model. Recent discoveries by Fendley et al. and results by Jonsson suggests that the hard square model with cylindrical boundary conditions possess some beautiful combinatorial properties. We apply both topological and purely combinatorial methods to related independence complexes to try and gain a better understanding of this model.

Jointed rock masses are formed of intact rock and joints. There-fore, proper characterization of rock mass behavior has to consid-er the combined behavior of the intact rock blocks and that of the joints. This thesis presents the theoretical background of the Synthetic Rock Mass (SRM) modeling technique along with example applica-tions. The SRM technique is a new approach for simulating the mechanical behavior of jointed rock masses. The technique uses the Bonded Particle Model (BPM) for rock to represent intact ma-terial and the Smooth-Joint Contact Model (SJM) to represent the in situ joint network. In this manner, the macroscopic behaviour of an SRM sample depends on both the creation of new fractures through intact material, and slip/opening of pre-existing joints. SRM samples containing thousands of non-persistent joints can be submitted to standard laboratory tests (UCS, triaxial loading, and direct tension tests) or tested under a non-trivial stress path repre-sentative of the stresses induced during the engineering activity under study. Output from the SRM methodology includes pre-peak properties (modulus, damage threshold, peak strength) and post-peak proper-ties (brittleness, dilation angle, residual strength, fragmentation). Of particular interest is the ability to obtain predictions of rock mass scale effects, anisotropy and brittleness; properties that can-not be obtained using empirical methods of property estimation. Additionally, the nature of yielding and fracturing can be studied as the rock mass fails. This information can improve our understand-ing of rock mass failure mechanisms. / QC20100720

<p>Interactions between combinatorics and statistical mechanics have provided many fruitful insights in both fields. A compelling example is Kuperberg’s solution to the alternating sign matrix conjecture, and its following generalisations. In this thesis we investigate two models from statistical mechanics which have received attention in recent years.</p><p>The first is the fully packed loop model. A conjecture from 2001 by Razumov and Stroganov opened the field for a large ongoing investigation of the O(1) loop model and its connections to a refinement of the fully packed loop model. We apply a combinatorial bijection originally found by de Gier to an older conjecture made by Propp.</p><p>The second model is the hard particle model. Recent discoveries by Fendley et al. and results by Jonsson suggests that the hard square model with cylindrical boundary conditions possess some beautiful combinatorial properties. We apply both topological and purely combinatorial methods to related independence complexes to try and gain a better understanding of this model.</p>

A major area of research recently has been the study of nonlinear waves in liquid crystals. The availability of commercial liquid crystals and the formation of solitons at mWpower levels has meant that experimental research and the need to understand how the solitons are formed and interact has been boosted. The first part of the thesis looks at how two laser beams in a nematic liquid crystal interact. Specifically research has centred on the problem of directing a signal beam to a target area by varying the input angle of the control beam. Different approximate models are developed to describe this phenomena, with the results from these models compared to a full numerical analysis. The first model developed is called the particle model and is based on the unmodified modulation equations. The results from this model were acceptable when compared with the results obtained from a full numerical analysis. This comparison is indicative that the underlying assumptions of the model did not capture an essential part of interaction between the two laser beams. The second model used to describe the interaction between the two laser beams was based on the law of conservation of momentum in the laser beams. Here the potential between the laser beams was modified to take into account the profile of the beams. The results from this model were in excellent agreement with results from the full numerical analysis, showing the key role potential between the beams plays in the trajectories of the beams. The interaction between dark solitons was also studied. The model used in this case was based on the modulation equations with a suitable trial function for dark solitons. The results from this model were in excellent agreement with the results from the full numerical analysis. The behaviour of the dark solitons shown by the approximate model and the full numerical analysis showing similar key features. This thesis sets out the equations describing the interaction of laser beams in liquid crystals. These are the equations used to carry out a full numerical analysis. This analysis is valuable in its own right and is the standard to compare the results obtained from other models but to achieve a deeper understanding of how laser beams interact in liquid crystals approximate models are developed so that the important parameters in each model can be identified. The Lagrangian describing the interaction of laser beams in liquid crystals is used in all the approximate models. The approximate models can then be developed through the use of suitable trial functions that adequately describe how the laser beams interact. The derivation of the equations and how these equations are solved is described for each model. The results from each model are compared to a full numerical analysis with a discussion of how the results compare.

Computational Fluid Dynamics Coupled to Discrete Element Method (CFD-DEM) is widely used in simulating a large variety of particulate flow system. This Eulerian-Lagrangian technique tracks all the particles included in the system by the application of point mass models in their equation of motion. CFD-DEM is a more accurate (and more expensive) technique compared to an Eulerian-Eulerian representation. Compared to Particle Resolved Simulations (PRS), CFD-DEM is less expensive since it does not require resolving the flow around each particles and thus can be applied to larger scale systems. Nevertheless, simulating industrial and natural scale systems is a challenge for this numerical technique. This is because the cost of CFD-DEM is proportional to the number of particles in the system under consideration. Thus, massively parallel codes are used to tackle these problems with the help of supercomputers. In this thesis, the CFD-DEM capability in the in-house code Generalized Incompressible Direct and Large Eddy Simulation of Turbulence (GenIDLEST) is used to investigate large scale dense particulate flow systems. Central to the contributions made by this work are developments to reduce the computational cost of CFD-DEM. This includes the development and validation of reduced order history force model for use in large scale systems and validation of the representative particle model, which lumps multiple particles into one, thus reducing the number of particles that need to be tracked in the system. Numerical difficulties in the form of long integration times and instabilities encountered in fully coupling the fluid and particle phases in highly energetic systems are alleviated by proposing a partial coupling scheme which maintains the accuracy of full-coupling to a large extent but at a reduced computational cost. The proposed partial-coupling is found to have a better convergence behavior compared to the full coupling in large systems and can be used in cases where full coupling is not feasible or impractical to use. Alternative modeling approaches for the tangential treatment of the soft-sphere impact model to avoid storing individual impact deformation are proposed and tested. A time advancement technique is developed and proposed for use in dense particulate systems with a hard-sphere impact model. The new advancement technique allows for the use of larger time steps which can speed-up the time to solution by as much as an order of magnitude. / PHD / Computational Fluid Dynamics Coupled to Discrete Element Method (CFD-DEM) is widely used in simulating a large variety of particulate flow system. Nevertheless, simulating industrial and natural scale systems is a challenge for this numerical technique. This is because the cost of CFD-DEM is proportional to the number of particles in the system under consideration. The current work aims to provide alternative efficient models that can reduce the computational requirement of CFD-DEM. This includes reducing the computational time to run the calculation, reducing the memory requirement, or providing an alternative method to get reasonably accurate predictions when the proper implementation fails to converge. Different elements of CFD-DEM were targeted in the current work. The testing and validation work covered different applications and ranged over wide operation conditions. Comparisons with available experimental and numerical work was conducted to evaluate the suggested methods. Good to reasonable agreement was achieved with the suggested models and treatments. Savings in calculation time and resources varies depending on what elements/models are being used. A significant reduction of the calculation time and memory resources was achieved with the use of a reduced order force model. The savings in computational time and memory resources opens the door for using the proposed models in applications with large dense systems of particles where other models become impractical to use.

Electronic energy transfer has been investigated in pure donor systems by means of computer simulations. Calculated properties were the probability that the initially excited donor is excited at a time t after the excitation, Gs(t), the mean square displacement of the excitation and different fluorescence observables. For three dimensional systems the results obtained by Monte Carlo simulations were compared to the so-called GAF-theory {Gouchanour,C. R., Andersen, H. C. and Fayer, M. D., J. Chem. Phys. 81, 4380 (1984)}, and the agreement was found to be good. Anisotropic systems, i.e. mono-, bi- and multilayer systems, were compared to the two-particle model {Baumann,J. and Fayer, M. D., J. Chem. Phys. 85, 4087 (1986)}. The agreement between the Gs(t) calculated from the tp- model and the Monte Carlo simulations were good for all systems investigated. However, the agreement between the fluorescence observables obtained by MC and the tp-model were in general poor. A much better agreement was found when a phenomenological approach was used for calculating the fluorescence depolarization ratios. Three dimensional systems where the donors are rotating on the same time scale as the energy transfer takes place have also been studied and compared to analytical theories. The Molecular Dynamics simulations of decapeptide H142 shows that simulations in a continuum with a relative permeability do not provide a reliable alternative to simulations with explicit solvent molecules. / <p>Diss. (sammanfattning) Umeå : Umeå universitet, 1991, härtill 5 uppsatser</p> / digitalisering@umu

This thesis investigates novel algorithms for enabling the use of first-principle electrochemical models for battery monitoring and control in advanced battery management systems (BMSs). Specifically, the fast solution and state estimation of a high-fidelity spatially resolved thermal-electrochemical lithium-ion battery model commonly referred to as the pseudo two-dimensional (P2D) model are investigated. The partial-differential algebraic equations (PDAEs) constituting the model are spatially discretised using Chebyshev orthogonal collocation enabling fast and accurate simulations up to high C-rates. This implementation of the P2D model is then used in combination with an extended Kalman filter (EKF) algorithm modified for differential-algebraic equations (DAEs) to estimate the states of the model, e.g. lithium concentrations, overpotential. The state estimation algorithm is able to rapidly recover the model states from current, voltage and temperature measurements. Results show that the error on the state estimate falls below 1% in less than 200s despite a 30% error on battery initial state-of-charge (SoC) and additive measurement noise with 10mV and 0.5&deg;C standard deviations. The parameter accuracy of such first-principle models is of utmost importance for the trustworthy estimation of internal battery electrochemical states. Therefore, the identifiability of the simpler single particle (SP) electrochemical model is investigated both in principle and in practice. Grouping parameters and partially non-dimensionalising the SP model equations in order to understand the maximum expected degrees of freedom in the problem reveals that there are only six unique parameters in the SP model. The structural identifiability is then examined by asking whether the transfer function of the linearised SP model is unique. It is found that the model is unique provided that the electrode open circuit voltage curves have a non-zero gradient, the parameters are ordered, and that the behaviour of the kinetics of each electrode is lumped together into a single parameter which is the charge transfer resistance. The practical estimation of the SP model parameters from frequency-domain experimental data obtained by electrochemical impedance spectroscopy (EIS) is then investigated and shows that estimation at a single SoC is insufficient to obtain satisfactory results and EIS data at multiple SoCs must be combined.