MULTI-BAND BOSE HUBBARD MODELS AND EFFECTIVE THREE-BODY INTERACTIONS

Experiments with ultracold atoms in optical lattice have become a versatile testing ground to study diverse quantum many-body Hamiltonians. A single-band Bose-Hubbard (BH) Hamiltonian was first proposed to describe these systems in 1998 and its associated quantum phase-transition was subsequently observed in 2002. Over the years, there has been a rapid progress in experimental realizations of more complex lattice geometries, leading to more exotic BH Hamiltonians with contributions from excited bands, and modified tunneling and interaction energies. There has also been interesting theoretical insights and experimental studies on “un- conventional” Bose-Einstein condensates in optical lattices and predictions of rich orbital physics in higher bands. In this thesis, I present our results on several multi- band BH models and emergent quantum phenomena. In particular, I study optical lattices with two local minima per unit cell and show that the low energy states of a multi-band BH Hamiltonian with only pairwise interactions is equivalent to an effec- tive single-band Hamiltonian with strong three-body interactions. I also propose a second method to create three-body interactions in ultracold gases of bosonic atoms in a optical lattice. In this case, this is achieved by a careful cancellation of two contributions in the pair-wise interaction between the atoms, one proportional to the zero-energy scattering length and a second proportional to the effective range. I subsequently study the physics of Bose-Einstein condensation in the second band of a double-well 2D lattice and show that the collision aided decay rate of the con- densate to the ground band is smaller than the tunneling rate between neighboring unit cells. Finally, I propose a numerical method using the discrete variable repre- sentation for constructing real-valued Wannier functions localized in a unit cell for optical lattices. The developed numerical method is general and can be applied to a wide array of optical lattice geometries in one, two or three dimensions.

Modelling and analysing human behaviour in a department store using discrete event and agent based simulation

Discrete Event Simulation (DES) is a very popular simulation technique in Operational Research. Recently, there has been the emergence of another technique, namely Agent Based Simulation (ABS). Although there is a lot of literature relating to DES and ABS, we have found less that focuses on exploring the capabilities of both in tackling human behaviour issues. In order to understand the gap between these two simulation techniques, therefore, our aim is to understand the distinctions between DES and ABS models with the real world phenomenon in modelling and simulating human behaviour. In achieving the aim, we have carried out a case study at a department store. Both DES and ABS models will be compared using the same problem domain which is concerning on management policy in a fitting room. The behaviour of staffs while working and customers’ satisfaction will be modelled for both models behaviour understanding.

Investigating output accuracy for a discrete event simulation model and an agent based simulation model

In this paper, we investigate output accuracy for a Discrete Event Simulation (DES) model and Agent Based Simulation (ABS) model. The purpose of this investigation is to find out which of these simulation techniques is the best one for modelling human reactive behaviour in the retail sector. In order to study the output accuracy in both models, we have carried out a validation experiment in which we compared the results from our simulation models to the performance of a real system. Our experiment was carried out using a large UK department store as a case study. We had to determine an efficient implementation of management policy in the store’s fitting room using DES and ABS. Overall, we have found that both simulation models were a good representation of the real system when modelling human reactive behaviour.

Some misspecfication problems in long-memory time series models

Doctor of Philosophy in Mathematics

A discrete-time queueing system with feedback and optional service

Queueing systems constitute a central tool in modeling and performance analysis. These types of systems are in our everyday life activities, and the theory of queueing systems was developed to provide models for forecasting behaviors of systems subject to random demand. The practical and useful applications of the discrete-time queues make the researchers to con- tinue making an e ort in analyzing this type of models. Thus the present contribution relates to a discrete-time Geo/G/1 queue in which some messages may need a second service time in addition to the rst essential service. In day-to-day life, there are numerous examples of queueing situations in general, for example, in manufacturing processes, telecommunication, home automation, etc, but in this paper a particular application is the use of video surveil- lance with intrusion recognition where all the arriving messages require the main service and only some may require the subsidiary service provided by the server with di erent types of strategies. We carry out a thorough study of the model, deriving analytical results for the stationary distribution. The generating functions of the number of messages in the queue and in the system are obtained. The generating functions of the busy period as well as the sojourn times of a message in the server, the queue and the system are also provided.

Simulation by discrete mass modeling of offshore wind turbine system with DC link

This paper presents an integrated model for an offshore wind turbine taking into consideration a contribution for the marine wave and wind speed with perturbations influences on the power quality of current injected into the electric grid. The paper deals with the simulation of one floating offshore wind turbine equipped with a permanent magnet synchronous generator, and a two-level converter connected to an onshore electric grid. The use of discrete mass modeling is accessed in order to reveal by computing the total harmonic distortion on how the perturbations of the captured energy are attenuated at the electric grid injection point. Two torque actions are considered for the three-mass modeling, the aerodynamic on the flexible part and on the rigid part of the blades. Also, a torque due to the influence of marine waves in deep water is considered. Proportional integral fractional-order control supports the control strategy. A comparison between the drive train models is presented.

Offshore Wind Energy System with DC Transmission Discrete Mass: Modeling and Simulation

This paper presents an integrated model for an offshore wind energy system taking into consideration a contribution for the marine wave and wind speed with perturbations influences on the power quality of current injected into the electric grid. The paper deals with the simulation of one floating offshore wind turbine equipped with a PMSG and a two-level converter connected to an onshore electric grid. The use of discrete mass modeling is accessed in order to reveal by computing the THD on how the perturbations of the captured energy are attenuated at the electric grid injection point. Two torque actions are considered for the three-mass modeling, the aerodynamic on the flexible part and on the rigid part of the blades. Also, a torque due to the influence of marine waves in deep water is considered. PI fractional-order control supports the control strategy. A comparison between the drive train models is presented.

Is the maximum velocity of carboxylation (Vcmax) well adjusted for deciduous shrubs in DGVMs: a case study for the Caatinga Biome in Brazil.

Vcmax is the rate of maximum velocity of carboxylation of plants and is considered one of the most critical parameters for changes in vegetation in face of global changes and it has a direct impact on gross primary productivity. Physiological processes are considered the main sources of uncertainties in dynamic global vegetation models (DGVMs). The Caatinga biome, in the semiarid region of northeastern Brazil, is extremely important due to its biodiversity and endemism. In a field work realized in an area of preserved Caatinga forest, measurements of carbon assimilation (in response to light and CO2) were performed on 11 individuals of a native species. These results of Vcmax measurements in Caatinga were compared with parameterization of models, revealing that Vcmax is not well adjusted in several DGVMs. Also, the values obtained in the Caatinga field experiments were very close to empirical values obtained in the Northern hemisphere (Austria). These ecophysiological measurements can contribute in understanding of this biome

Evolution and challenges of dynamic global vegetation models for some aspects of plant physiology and elevated atmospheric CO2.

Dynamic global vegetation models (DGVMs) simulate surface processes such as the transfer of energy, water, CO2, and momentum between the terrestrial surface and the atmosphere, biogeochemical cycles, carbon assimilation by vegetation, phenology, and land use change in scenarios of varying atmospheric CO2 concentrations. DGVMs increase the complexity and the Earth system representation when they are coupled with atmospheric global circulation models (AGCMs) or climate models. However, plant physiological processes are still a major source of uncertainty in DGVMs. The maximum velocity of carboxylation (Vcmax), for example, has a direct impact over productivity in the models. This parameter is often underestimated or imprecisely defined for the various plant functional types (PFTs) and ecosystems. Vcmax is directly related to photosynthesis acclimation (loss of response to elevated CO2), a widely known phenomenon that usually occurs when plants are subjected to elevated atmospheric CO2 and might affect productivity estimation in DGVMs. Despite this, current models have improved substantially, compared to earlier models which had a rudimentary and very simple representation of vegetation?atmosphere interactions. In this paper, we describe this evolution through generations of models and the main events that contributed to their improvements until the current state-of-the-art class of models. Also, we describe some main challenges for further improvements to DGVMs.

Experimental determination of burning velocity in metal dust explosions

The modeling of metal dust explosion phenomenon is important in order to safeguard industries from potential accidents. A key parameter of these models is the burning velocity, which represents the consumption rate of the reactants by the flame front, during the combustion process. This work is focused on the experimental determination of aluminium burning velocity, through an alternative method, called "Direct method". The study of the methods used and the results obtained is preceded by a general analysis on dust explosion phenomenon, flame propagation phenomenon, characteristics of the metals combustion process and standard methods for determining the burning velocity. The “Direct method” requires a flame propagating through a tube recorded by high-speed cameras. Thus, the flame propagation test is carried out inside a vertical prototype made of glass. The study considers two optical technique: the direct visualization of the light emitted by the flame and the Particle Image Velocimetry (PIV) technique. These techniques were used simultaneously and allow the determination of two velocities: the flame propagation velocity and the flow velocity of the unburnt mixture. Since the burning velocity is defined by these two quantities, its direct determination is done by substracting the flow velocity of the fresh mixture from the flame propagation velocity. The results obtained by this direct determination, are approximated by a linear curve and different non-linear curves, which show a fluctuating behaviour of burning velocity. Furthermore, the burning velocity is strongly affected by turbulence. Turbulence intensity can be evaluated from PIV technique data. A comparison between burning velocity and turbulence intensity highlighted that both have a similar trend.

Models and Simulations of Diamond-like Carbon for large-area high voltage power diodes

Silicon-based discrete high-power devices need to be designed with optimal performance up to several thousand volts and amperes to reach power ratings ranging from few kWs to beyond the 1 GW mark. To this purpose, a key element is the improvement of the junction termination (JT) since it allows to drastically reduce surface electric field peaks which may lead to an earlier device failure. This thesis will be mostly focused on the negative bevel termination which from several years constitutes a standard processing step in bipolar production lines. A simple methodology to realize its counterpart, a planar JT with variation of the lateral doping concentration (VLD) will be also described. On the JT a thin layer of a semi insulating material is usually deposited, which acts as passivation layer reducing the interface defects and contributing to increase the device reliability. A thorough understanding of how the passivation layer properties affect the breakdown voltage and the leakage current of a fast-recovery diode is fundamental to preserve the ideal termination effect and provide a stable blocking capability. More recently, amorphous carbon, also called diamond-like carbon (DLC), has been used as a robust surface passivation material. By using a commercial TCAD tool, a detailed physical explanation of DLC electrostatic and transport properties has been provided. The proposed approach is able to predict the breakdown voltage and the leakage current of a negative beveled power diode passivated with DLC as confirmed by the successfully validation against the available experiments. In addition, the VLD JT proposed to overcome the limitation of the negative bevel architecture has been simulated showing a breakdown voltage very close to the ideal one with a much smaller area consumption. Finally, the effect of a low junction depth on the formation of current filaments has been analyzed by performing reverse-recovery simulations.

Analytic models of self-gravitating rotating gaseous tori with central black hole

In this thesis project, I present stationary models of rotating fluids with toroidal distributions that can be used to represent the active galactic nuclei (AGN) central obscurers, i.e. molecular tori (Combes et al., 2019), as well as geometrically thick accretion discs, like ADAF discs (Narayan and Yi, 1995) or Polish doughnuts (Abramowicz, 2005). In particular, I study stationary rotating systems with a more general baroclinic distribution (with a vertical gradient of the angular velocity), which are often more realistic and less studied, due to their complexity, than the barotropic ones (with cylindrical rotation), which are easier to construct. In the thesis, I compute analytically the main intrinsic and projected properties of the power-law tori based on the potential-density pairs of Ciotti and Bertin (2005). I study the density distribution and the resulting gravitational potential for different values of α, in the range 2 < α < 5. For the same models, I compute the surface density of the systems when seen face-on and edge-on. I then apply the stationary Euler equations to obtain rotational velocity and temperature distributions of the self-gravitating models in the absence of an external gravitational potential. In the thesis I also consider the power-law tori with the presence of a central black hole in addition to the gas self-gravity, and solving analytically the stationary Euler equations, I compute how the properties of the system are modified by the black hole and how they vary as a function of the black hole mass. Finally, applying the Solberg-Høiland criterion, I show that these baroclinic stationary models are linearly stable in the absence of the black hole. In the presence of the black hole I derive the analytical condition for stability, which depends on α and on the black hole mass. I also study the stability of the tori in the hypothesis that they are weakly magnetized, finding that they are always unstable to this instability.

Local and nonlocal integro-differential reaction-diffusion models for protein dynamics in Alzheimer's disease

In this work, integro-differential reaction-diffusion models are presented for the description of the temporal and spatial evolution of the concentrations of Abeta and tau proteins involved in Alzheimer's disease. Initially, a local model is analysed: this is obtained by coupling with an interaction term two heterodimer models, modified by adding diffusion and Holling functional terms of the second type. We then move on to the presentation of three nonlocal models, which differ according to the type of the growth (exponential, logistic or Gompertzian) considered for healthy proteins. In these models integral terms are introduced to consider the interaction between proteins that are located at different spatial points possibly far apart. For each of the models introduced, the determination of equilibrium points with their stability and a study of the clearance inequalities are carried out. In addition, since the integrals introduced imply a spatial nonlocality in the models exhibited, some general features of nonlocal models are presented. Afterwards, with the aim of developing simulations, it is decided to transfer the nonlocal models to a brain graph called connectome. Therefore, after setting out the construction of such a graph, we move on to the description of Laplacian and convolution operations on a graph. Taking advantage of all these elements, we finally move on to the translation of the continuous models described above into discrete models on the connectome. To conclude, the results of some simulations concerning the discrete models just derived are presented.

Characterization Of Microsatellite Markers Developed From Prosopis Rubriflora And Prosopis Ruscifolia (leguminosae - Mimosoideae), Legume Species That Are Used As Models For Genetic Diversity Studies In Chaquenian Areas Under Anthropization In South America.

Prosopis rubriflora and Prosopis ruscifolia are important species in the Chaquenian regions of Brazil. Because of the restriction and frequency of their physiognomy, they are excellent models for conservation genetics studies. The use of microsatellite markers (Simple Sequence Repeats, SSRs) has become increasingly important in recent years and has proven to be a powerful tool for both ecological and molecular studies. In this study, we present the development and characterization of 10 new markers for P. rubriflora and 13 new markers for P. ruscifolia. The genotyping was performed using 40 P. rubriflora samples and 48 P. ruscifolia samples from the Chaquenian remnants in Brazil. The polymorphism information content (PIC) of the P. rubriflora markers ranged from 0.073 to 0.791, and no null alleles or deviation from Hardy-Weinberg equilibrium (HW) were detected. The PIC values for the P. ruscifolia markers ranged from 0.289 to 0.883, but a departure from HW and null alleles were detected for certain loci; however, this departure may have resulted from anthropic activities, such as the presence of livestock, which is very common in the remnant areas. In this study, we describe novel SSR polymorphic markers that may be helpful in future genetic studies of P. rubriflora and P. ruscifolia.

Mastication Movements And Sleep Quality Of Patients With Myofascial Pain: Occlusal Device Therapy Improvements.

Patients with myofascial pain experience impaired mastication, which might also interfere with their sleep quality. The purpose of this study was to evaluate the jaw motion and sleep quality of patients with myofascial pain and the impact of a stabilization device therapy on both parameters. Fifty women diagnosed with myofascial pain by the Research Diagnostic Criteria were enrolled. Pain levels (visual analog scale), jaw movements (kinesiography), and sleep quality (Epworth Sleepiness Scale; Pittsburgh Sleep Quality Index) were evaluated before (control) and after stabilization device use. Range of motion (maximum opening, right and left excursions, and protrusion) and masticatory movements during Optosil mastication (opening, closing, and total cycle time; opening and closing angles; and maximum velocity) also were evaluated. Repeated-measures analysis of variance in a generalized linear mixed models procedure was used for statistical analysis (α=.05). At baseline, participants with myofascial pain showed a reduced range of jaw motion and poorer sleep quality. Treatment with a stabilization device reduced pain (P<.001) and increased both mouth opening (P<.001) and anteroposterior movement (P=.01). Also, after treatment, the maximum opening (P<.001) and closing (P=.04) velocities during mastication increased, and improvements in sleep scores for the Pittsburgh Sleep Quality Index (P<.001) and Epworth Sleepiness Scale (P=.04) were found. Myofascial pain impairs jaw motion and quality of sleep; the reduction of pain after the use of a stabilization device improves the range of motion and sleep parameters.