<p>The global impact of the converging dual epidemics of tuberculosis (TB) and human immunodeficiency virus (HIV) is one of the major public health challenges of our time, because in many countries, human immunodeficiency virus (HIV) and mycobacterium tuberculosis (TB) are among the leading causes of morbidity and mortality. It is found that infection with HIV increases the risk of reactivating latent TB infection, and HIV-infected individuals who acquire new TB infections have high rates of disease progression. Research has shown that these two diseases are enormous public health burden, and unfortunately, not much has been done in terms of modeling the dynamics of HIV-TB co-infection at a population level. In this thesis, we study these models and design and analyze robust numerical methods to solve them. To proceed in this direction, first we study the sub-models and then the full model. The first sub-model describes the transmission dynamics of HIV that accounts for behavior change. The impact of HIV educational campaigns is also studied. Further, we explore the effects of behavior change and different responses of individuals to educational campaigns in a situation where individuals may not react immediately to these campaigns. This is done by considering a distributed time delay in the HIV sub-model. This leads to Hopf bifurcations around the endemic equilibria of the model. These bifurcations correspond to the existence of periodic solutions that oscillate around the equilibria at given thresholds. Further, we show how the delay can result in more HIV infections causing more increase in the HIV prevalence. Part of this study is then extended to study a co-infection model of HIV-TB. A thorough bifurcation analysis is carried out for this model. Robust numerical methods are then designed and analyzed for these models.&nbsp / Comparative numerical results are also provided for each model.</p>

L'objectif est d'apporter une contribution à la prédiction des phénomènes de striction et de localisation sous forme de bandes par la modélisation des critères d'instabilité plastique, par la comparaison de leurs bases théoriques et par le tracé de Courbes Limites de Formage (CLF) numériques. Une étude bibliographique permet de distinguer quatre approches principales : le principe de force maximum, l'analyse de bifurcation, l'analyse linéaire de stabilité et les méthodes multizones. Afin de permettre une comparaison, les principaux critères sont réécrits dans un cadre commun. Pour la striction diffuse, un rapprochement entre les critères de force maximum et de bifurcation par point limite est proposé. Pour la localisation, les prédictions de CLF obtenues avec le modèle M - K tendent vers celles du critère de Rice lorsque la taille du défaut initial tend vers zéro. Des tracés de CLF illustrent ces résultats et mettent en évidence l'influence du choix de la loi d'écrouissage sur les CLF.

Neuroprosthetics is at the intersection of neuroscience, biomedical engineering, and physics. A biocompatible neuroprosthesis contains artificial neurons exhibiting biophysically plausible dynamics. Hybrid systems analysis could be used to prototype such artificial neurons. Biohybrid systems are composed of artificial and living neurons coupled via real-time computing and dynamic clamp. Model neurons must be thoroughly tested before coupled with a living cell. We use bifurcation theory to identify hazardous regimes of activity that may compromise biocompatibility and to identify control strategies for regimes of activity desirable for functional behavior. We construct real-time artificial neurons for the analysis of hybrid systems and demonstrate a mechanism through which an artificial neuron could maintain duty cycle independent of variations in period.

This work is a first step towards a long-term goal of understanding computations occurring in the brain and using those principles to make more efficient machines. The traditional computing paradigm calls for using digital supercomputers to simulate large scale brain-like neural networks resulting in large power consumption which limits scalability or model detail. For example, IBM's digital simulation of a cat brain with simplistic neurons and synapses consumes power equivalent to that of a thousand houses! Instead of digital methods, this work uses analog processing concepts to develop scalable, low-power silicon models of neurons which have been shown to be around ten thousand times more power efficient. This has been achieved by modeling the dynamical behavior of Hodgkin-Huxley (H-H) or Morris-Lecar type equations instead of modeling the exact equations themselves. In particular, the two silicon neuron designs described exhibit a Hopf and a saddle-node bifurcation. Conditions for the bifurcations allow the identification of correct biasing regimes for the neurons. Also, since the hardware neurons compute in real time, they can be used for dynamic clamp protocols in addition to computational experiments. To empower this analog implementation with the flexibility of a digital simulation, a family of field programmable analog array (FPAA) architectures have been developed in 0.35 um CMOS that provide reconfigurability in the network of neurons as well as tunability of individual neuron parameters. This programmability is obtained using floating-gate (FG) transistors. The neurons are organized in blocks called computational analog blocks (CAB) which are embedded in a programmable switch matrix. An unique feature of the architecture is that the switches, being FG elements, can be used also for computation leading to more than 50,000 analog parameters in 9 sq. mm. Several neural systems including central pattern generators and coincidence detectors are demonstrated. Also, a separate chip that is capable of implementing signal processing algorithms has been designed by modifying the CAB elements to include transconductors, multipliers etc. Several systems including an AM demodulator and a speech processor are presented. An important contribution of this work is developing an architecture for programming the FG elements over a wide dynamic range of currents. An adaptive logarithmic transimpedance amplifier is used for this purpose. This design provides a general solution for wide dynamic range current measurement with a low power dissipation and has been used in imaging chips too. A new generation of integrated circuits have also been designed that are 25 sq. mm in area and contain several new features including adaptive synapses and support for smart sensors. These designs and the previous ones should allow prototyping and rapid development of several neurally inspired systems and pave the path for the design of larger and more complex brain like adaptive neural networks.

Theoretical strength of solids is defined as the ultimate strength beyond which plastic deformation, fracture, or decohesion would occur. Understanding the microscopic origin from quantum mechanics and thermoelastic formulation is of great importance to mechanical properties and engineering design of various solids. While quite a few theory models have been made in the past century by several generations of scientists, including Frankel and Born, a general and convincing framework has not been fully established. We study this issue from three respects: (1) Unify various elastic stability criteria for solids that determine an upper bound of theoretical strength; (2) with ab initio method, we test the elastic stability conditions of crystal Au. The phenomenon of bifurcation is observed: under hydrostatic expansion, the rhombohedral modulus reaches zero first of all; while under uniaxial tensile stress, the tetragonal shear modulus first reaches zero; (3) propose a nonlinear theoretical formulation of stability criterion. As an analytic method, this scheme is quite simple, in the mean time, it saves computation resource.

In der vorliegenden Arbeit wird die Fredholm-Methode zur semiklassischen Berechnung einzelner Eigenzustaende von Quantenabbildungen eingesetzt. Es wird gezeigt, wie auch Eigenzustaende zu entarteten Eigenwerten berechnet werden koennen. Die semiklassische Berechnung eines Eigenzustandes erfolgt mittels der Husimifunktion. Es wird gezeigt, wie das Auftreten von Bifurkationen periodischer Bahnen beruecksichtigt werden kann. Dies geschieht auch fuer den Fall von energiegemittelten Eigenzustaenden. Ebenfalls wird die Stoerung einer Quantenabbildung durch einen Punktstreuer und dessen Auswirkungen auf die semiklassische Berechnungen untersucht.

The present project discusses the application of screening techniques in large-scale simulation models with the purpose of determining whether this kind of procedures could be a substitute for or a complement to simulation-based optimization for bottleneck identification and improvement. Based on sensitivity analysis, the screening techniques consist in finding the most important factors in simulation models where there are many factors, in which presumably only a few or some of these factors are important. The screening technique selected to be studied in this project is Sequential Bifurcation. This method consists in grouping the potentially important factors, dividing the groups continuously depending on the response generated from the model of the system under study. The results confirm that the application of the Sequential Bifurcation method can considerably reduce the simulation time because of the number of simulations needed, which decreased compared with the optimization study. Furthermore, by introducing two-factor interactions in the metamodel, the results are more accurate and may even be as accurate as the results from optimization. On the other hand, it has been found that the application of Sequential Bifurcation could become a problem in terms of accuracy when there are many storage buffers in the decision variables list. Due to all of these reasons, the screening techniques cannot be a complete alternative to simulation-based optimization. However, as shown in some initial results, the combination of these two methods could yield a promising roadmap for future research, which is highly recommended by the authors of this project.

Grouting is performed in order to decrease the permeability and increase the stiffness of the material, especially soil and rock. For tunnelling and underground constructions, permeation grouting is done where cement based materials are pumped inside drilled boreholes under a constant pressure, higher than the ground water pressure. The aim of permeation grouting is to reduce the water flow into tunnels and caverns and to limit the lowering of the surrounding groundwater table. Cement based materials are commonly used as grout due to their availability and lower costs. To obtain a proper water sealing and reduce the lowering of the ground water table, a desired spread of grout must be achieved and the rheology of the cement grout is the governing factor for estimating the required spread. Rheological properties of cement grout such as viscosity and yield stress are commonly measured off-line using laboratory instruments, and some simple tools are available to make field measurements. Although the rheological properties of the grout that is used play a fundamental role in design and execution, no method has yet been developed to measure these properties in-line in field work. In addition to the real time measurement, there is no standard method for determining the yield stress for grouting applications. Despite the common usage of Bingham model fitting to determine the yield stress, the range of shear rate is often not specified or is neglected.   In this work, an in-line rheometry method combining the Ultrasound Velocity Profiling (UVP) technique with Pressure Difference (PD) measurements, known as “UVP+PD”, was successfully tested for continuous in-line measurements of concentrated micro cement based grouts. A major obstacle of using the ultrasound based methodology was the transducers, which would be capable of emitting sufficient acoustic energy and can be used in field conditions. The transducer technology was developed in a parallel project and the Flow-Viz industrial rheometer was found to be capable of detail measurement of the velocity profiles of cement grout. The shape of the velocity profiles was visualized, and the change in the shape of the profiles with concentration and time was observed. The viscosity and yield stress of the grout were determined using rheological models, e.g. Bingham and Herschel-Bulkley. In addition, rheological properties were determined using the non-model approach (gradient method) and the tube viscometry concept and were compared with results obtained using the rheological models. The UVP+PD method was found to be capable of determining the rheological behavior of cement grout regardless of the rheological model. The yield stress of cement grout was investigated using off-line rheometry techniques and UVP+PD in-line measurements. Tests were performed applying different shear histories and it was found that two ranges of yield stress indeed exist. Therefore, the design value of yield stress should be chosen with respect to the prevailing shear rate at the grout front for the required spread of grout. In addition, an appropriate shear rate range should be used when a Bingham fitting is done to determine the yield stress. In order to estimate the shear rate, plug thickness and velocity for one dimensional and two dimensional geometry, a non- dimensional nomogram was developed. The advantage of using the nomogram is that it does not depend on the applied pressure and the rheological properties of the grout and can therefore, be used as a simple design tool. Analytical approaches were used for the estimation and good agreements were found with numerical calculations and experimental results. In conclusion, in this work, it was found that it is possible to continuously measure the velocity profiles and determine the change of the rheological properties of cement grout using the ultrasound based UVP+PD method under field conditions. The yield stress was also investigated and it was found that two range of yield stress exist depending on the prevailing shear rate of the grout, which should be used for designing the grouting time at different conditions. In order to decide the design value of yield stress for grouting applications, a non-dimensional nomogram was developed that can be used to estimate the plug thickness, shear rate and velocity of the grout. / <p>Funding for the project was provided by the Swedish Rock Engineering Research Foundation (BeFo), The Swedish Research Council (FORMAS) and The Development Fund of the Swedish Construction Industry (SBUF), who are gratefully acknowledged. QC 20151112</p>

Στην παρούσα εργασία εξετάζεται η δυναμική συμπεριφορά αμιγούς και απλού συναγωνισμού δύο μικροβιακών πληθυσμών που αναπτύσσονται σε δύο συζευγμένους χημοστάτες. Χρησιμοποιώντας το μοντέλο Andrews για τους ειδικούς ρυθμούς ανάπτυξης και συνθήκες βαθμίδας συγκέντρωσης στην τροφοδοσία, η μελέτη του συστήματος γίνεται με εφαρμογή μεθόδων της θεωρίας διακλαδώσεων. Εξετάζοντας δύο περιπτώσεις τροφοδοσίας, παρουσία μικροοργανισμών και απουσία, κατασκευάστηκαν δύο λειτουργικά διαγράμματα ως προς το βαθμό σύζευξης r και το λόγο των όγκων λ των δύο αντιδραστήρων και βρέθηκε το είδος ευστάθειας των υπαρχουσών καταστάσεων ισορροπίας. Παρουσία μικροοργανισμών στην τροφοδοσία παρατηρήθηκαν περιοχές συνύπαρξης των δύο πληθυσμών σε μόνιμη, περιοδική και οιονεί περιοδική κατάσταση, ενώ υπάρχουν ενδείξεις και για χαοτική συμπεριφορά. Υπό στείρα τροφοδοσία βρέθηκε ότι συνύπαρξη μπορεί να επιτευχθεί μόνο σε μόνιμη και περιοδική κατάσταση σε μία ευρεία περιοχή των παραμέτρων λειτουργίας λ και r. / The dynamic behavior of pure and simple competition of two microbial populations growing in two interconnected bioreactors is investigated. Using Andrews inhibitory model and gradient in feed concentration, the use of bifurcation theory allows an in-depth analysis of the stability change mechanisms occurring in the system, when the operating parameters of the degree of coupling and the volume ratio change. Regions of species coexistence in all steady, periodic and quasi-periodic states are observed, while there is substantial indication of chaotic behavior. Under clean feed conditions coexistence is only possible in steady and periodic states.

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