<p>We review a number of compartmental models in epidemiology which leads to a nonlinear system of ordinary differential equations. We focus an SIR, SEIR and SIS epidemic models with and without vaccination. A threshold parameter R0 is identified which governs the spread of diseases, and this parameter is known as the basic reproductive number. The models have at least two equilibria, an endemic equilibrium and the disease-free equilibrium. We demonstrate that the disease will die out, if the basic reproductive number R0 &lt / 1. This is the case of a disease-free&nbsp / state, with no infection in the population. Otherwise the disease may become endemic if the basic reproductive number R0 is bigger than unity. Furthermore, stability analysis for both endemic&nbsp / and disease-free steady states are investigated and we also give some numerical simulations. The second part of this dissertation deals with optimal vaccination strategy in epidemiology. We&nbsp / use optimal control technique on vaccination to minimize the impact of the disease. Hereby we mean minimizing the spread of the disease in the population, while also minimizing the effort on&nbsp / vaccination roll-out. We do this optimization for the cases of SIR and SEIR models, and show how optimal strategies can be obtained which minimize the damage caused by the infectious&nbsp / disease. Finally, we describe the numerical simulations using the fourth-order Runge-Kutta method.&nbsp / These are the most useful references: [G. Zaman, Y.H Kang, II. H. Jung. BioSystems 93,&nbsp / (2008), 240 &minus / 249], [K. Hattaf, N. Yousfi. The Journal of Advanced Studies in Biology, Vol. 1(8), (2008), 383 &minus / 390.], [Lenhart, J.T. Workman. Optimal Control and Applied to Biological Models.&nbsp / Chapman and Hall/CRC, (2007).], [P. Van den Driessche, J. Watmough. Math. Biosci., 7,&nbsp / (2005)], and [J. Wu, G. R&uml / ost. Mathematical Biosciences and Engineering, Vol 5(2), (2008), 389 &minus / 391].</p>

In spectral methods for numerical PDEs, when the solutions are periodical, the Fourier functions may be used. However, when the solutions are non-periodical, the Legendre and Chebyshev polynomials are recommended, reported in many papers and books. There seems to exist few reports for the study of non-periodical solutions by spectral Fourier methods under the Dirichlet conditions and other boundary conditions. In this paper, we will explore the spectral Fourier methods(SFM) and collocation Fourier methods(CFM) for elliptic and eigenvalue problems. The CFM is simple and easy for computation, thus for saving a great deal of the CPU time. The collocation Fourier methods (CFM) can be regarded as the spectral Fourier methods (SFM) partly with the trapezoidal rule. Furthermore, the error bounds are derived for both the CFM and the SFM. When there exist no errors for the trapezoidal rule, the accuracy of the solutions from the CFM is as accurate as the spectral method using Legendre and Chebyshev polynomials. However, once there exists the truncation errors of the trapezoidal rule, the errors of the elliptic solutions and the leading eigenvalues the CFM are reduced to O(h^2), where h is the mesh length of uniform collocation grids, which are just equivalent to those by the linear elements and the finite difference method (FDM). The O(h^2) and even the superconvergence O(h4) are found numerically. The traditional condition number of the CFM is O(N^2), which is smaller than O(N^3) and O(N^4) of the collocation spectral methods using the Legendre and Chebyshev polynomials. Also the effective condition number is only O(1). Numerical experiments are reported for 1D elliptic and eigenvalue problems, to support the analysis made. The simplicity of algorithms and the promising numerical computation with O(h^4) may grant the CFM to be competent in application in numerical physics, chemistry, engineering, etc., see [7].

Rotordynamic and thermal analyses of compliant flexure pivot tilting pad gas bearings were performed. First, compliant flexure pivot tilting pad gas bearings with pad radial compliance (CFTPBs) were introduced and designed for high-speed oil-free micro turbomachinery. The pad radial compliance was for accommodation of large rotor growth at high speeds. Parametric studies on pivot offset, preload, and tilting stiffness were performed using non-linear orbit simulations and coast-down simulations for an optimum design. Second, coast-down tests for imbalance response and stability of typical rotor-bearing system with a rigid rotor and two CFTPBs designed from the above design studies were conducted over operating speeds up to 55 krpm. Prediction of synchronous rotordynamic responses was made in terms of critical speed for various imbalance modes by using a rotordynamic analysis software (XLTRC), combined with dynamic force coefficients from the perturbation analysis. For stability analyses, a generalized orbit simulation program was developed considering both the translational and angular rotor motions with two different bearings. Linear stability analyses for the conical vibration mode were also performed by using XLTRC and the perturbation analysis based on the Lund method. Predictions of whirl speed showed good agreement to the tests, but the estimated onset speed of instability appeared lower than the measured instability. Finally, a new thermo-hydrodynamic analysis model of a typical rotor-bearing system with CFTPBs was presented, accompanying linear perturbation analyses to investigate thermal effects on the rotordynamic performance. A numerical procedure was established for solving the generalized Reynolds equation, the 3-D energy equation, and the associated boundary conditions at the pad inlet flow and solid walls (rotor and pad) simultaneously. Parametric studies were conducted on nominal clearance and external load. Nominal clearance showed significant influence on temperature fields, and external load had uneven thermal effects among pads. Case studies with heat flux and temperature boundary conditions on the rotor end surface were performed to simulate various working conditions of the bearing. Large rotor thermal growth due to the high rotor temperature showed noticeable influence on rotordynamic performance by increasing direct stiffness and damping coefficients.

Combustion systems utilizing bluff bodies to stabilize the combustion processes can experience oscillatory heat release due to the alternate shedding of coherent, von Kármán vortices under certain operating conditions. This phenomenon needs to be understood in greater detail, since unsteady burning due to vortex shedding can lead to combustion instabilities and flame extinction in practical combustion systems. The primary objective of this study was to elucidate the influence of combustion process heat release upon the Bénard-von Kármán (BVK) instability in reacting bluff body wakes. For this purpose, spatial and temporal heat release distributions in bluff body-stabilized combustion of liquid Jet-A fuel with high-temperature, vitiated air were characterized over a wide range of operating conditions. Upon comparing the spatial and temporal heat release distributions, the fuel entrainment and subsequent heat release in the near-wake were found to strongly influence the onset and amplitude of the BVK instability. As the amount of heat release in the near-wake decreased, the BVK instability increased in amplitude. This was attributed to the corresponding decrease in the local density gradient across the reacting shear layers, which resulted in less damping of vorticity due to gas expansion. The experimental results were compared to the results of a parallel, linear stability analysis in order to further understand the influence of the combustion processes in the near-wake upon the wake instability characteristics. The results of this analysis support the postulate that oscillatory heat release due to BVK vortex shedding is the result of local absolute instability in the near-wake, which is eliminated only if the temperature rise across the reacting shear layers is sufficiently high. Furthermore, the results of this thesis demonstrate that non-uniform fuelling of the near-wake reaction zone increases the likelihood of absolutely unstable, BVK flame dynamics due to the possibility of near-unity products-to-reactants density ratios locally, especially when the reactants temperature is high.

No description available.

A general multidisciplinary design problem features coupling and feedback between contributing analyses. This feedback may lead to convergence issues requiring significant iteration in order to obtain a feasible design. This work casts the multidisciplinary design problem as a dynamical system in order to leverage the benefits of dynamical systems theory in a new domain. Three areas from dynamical system theory are chosen for investigation: stability analysis, optimal control, and estimation theory. Stability analysis is used to investigate the existence of a solution to the design problem and how that solution can be found. Optimal control techniques allow consideration of contributing analysis output and design variables constraints at the same level of the optimization hierarchy. Finally, estimation methods are employed to rapidly evaluate the robustness of the multidisciplinary design. These three dynamical system techniques are then combined in a methodology for the rapid robust design of linear multidisciplinary systems. While inherently linear, the developed robust design methodology is shown to be extensible to nonlinear systems. The applicability and performance of the developed technique is demonstrated through linear and nonlinear test problems including the design of a hypersonic aerodynamic surface for a system in which an increase in range or improvement in landed accuracy is sought. In addition, it is shown that the developed robust design methodology scales well compared to other methods.

<p>We review a number of compartmental models in epidemiology which leads to a nonlinear system of ordinary differential equations. We focus an SIR, SEIR and SIS epidemic models with and without vaccination. A threshold parameter R0 is identified which governs the spread of diseases, and this parameter is known as the basic reproductive number. The models have at least two equilibria, an endemic equilibrium and the disease-free equilibrium. We demonstrate that the disease will die out, if the basic reproductive number R0 &lt / 1. This is the case of a disease-free&nbsp / state, with no infection in the population. Otherwise the disease may become endemic if the basic reproductive number R0 is bigger than unity. Furthermore, stability analysis for both endemic&nbsp / and disease-free steady states are investigated and we also give some numerical simulations. The second part of this dissertation deals with optimal vaccination strategy in epidemiology. We&nbsp / use optimal control technique on vaccination to minimize the impact of the disease. Hereby we mean minimizing the spread of the disease in the population, while also minimizing the effort on&nbsp / vaccination roll-out. We do this optimization for the cases of SIR and SEIR models, and show how optimal strategies can be obtained which minimize the damage caused by the infectious&nbsp / disease. Finally, we describe the numerical simulations using the fourth-order Runge-Kutta method.&nbsp / These are the most useful references: [G. Zaman, Y.H Kang, II. H. Jung. BioSystems 93,&nbsp / (2008), 240 &minus / 249], [K. Hattaf, N. Yousfi. The Journal of Advanced Studies in Biology, Vol. 1(8), (2008), 383 &minus / 390.], [Lenhart, J.T. Workman. Optimal Control and Applied to Biological Models.&nbsp / Chapman and Hall/CRC, (2007).], [P. Van den Driessche, J. Watmough. Math. Biosci., 7,&nbsp / (2005)], and [J. Wu, G. R&uml / ost. Mathematical Biosciences and Engineering, Vol 5(2), (2008), 389 &minus / 391].</p>

The materials that exhibit martensite transformation have very important applications in engineering, and the microstructures of the materials play a key role foraffecting their mechanical behavior in macroscope. Therefore many attentions havebeen drawn for studying the related problems. This work focuses on the motion oftwin boundaries. Three questions are being asked: how is a twin boundary is nucleated in a homogenous (untwinned) material? After the twin boundary is nucleated,how is its motion initiated? How fast does it move? This study provides an atomisticunderstanding for these three questions. Linear stability analysis is firstly applied to capture the initiation of motion of atwin boundary. When a twin boundary is about to move, the lowest eigenvalue of thesystem Hessian drops to zero. And the corresponding eigenvector predicts accuratelythe way in which the twin boundary is going to move. The same idea is applied toinvestigate how motion of an irrational twin boundary is initiated. Atomic modelsof irrational twin boundaries are constructed by employment of continuum models,provided that the point group of rotations which relate two variants is extended toany rotations in plane. The zero eigenvectors reveal the complicated behavior ofmotion of irrational twin boundaries. The problem of nonuniqueness of kinetic relations proposed by Schwetlick andZimmer is solved in a thermoelasticity framework. By calculating the net heat fluxcrossing the phase boundary which is carried by the phonons, a unique kinetic relationcan be determined. Finally, a nonlocal criterion for nucleation of twin boundariesis proposed. By checking the stiffness of each unit cell evaluated with respect to asingle variable that represents the displacement along the unit cell diagonal direction,locations and the orientations of nucleated twin boundaries can be predicted.

No description available.

En bergslänts stabilitet styrs av berggrundens egenskaper, så som sprickegenskaper och bergkvalité. För att uppnå önskad stabilitet i en bergslänt behöver de bergmekaniska parametrarna kartläggas och analyseras för att fastställa risker och stabilitetsåtgärder. Syftet med studien är att utvärdera kvalitén på bergteknisk data från digitalfotogrammetriska 3D-modeller genom att jämföra resultatet med manuella mätningar från konventionell kartläggning. Målet är även att utforska potentialen för användning av fotogrammetrisk 3D-modellering vid stabilitetsanalyser i bergslänter genom att utvärdera den bergtekniska analys som kan göras utifrån fotogrammetrisk data. Sprickmätningar framtagna från 3D-modellen visade sig ha samma kvalité som manuella mätningar tagna enligt konventionell metod. Den UAS-baserade fotogrammetrin kan dock inte ersätta den konventionella analysen helt vid stabilitetsanalyser men kan användas som ett kompletterande verktyg i bergtekniska undersökningar. Fotogrammetrin möjliggör datainsamling från ett säkrare avstånd vilket minskar riskmomenten som den konventionella metoden medför vid arbete i fält. Den digitala metoden visade sig även ha fler fördelar såsom möjligheten av kartläggning och analysering framför datorn för mindre tids- och kostnadskrävande moment, digital datalagring samt att slänter med begränsad åtkomst kan karteras. / The stability of a rock slope is controlled by the rock’s mechanical properties, such as rock quality and facets. To achieve the desired stability in a rock slope, the mechanical parameters need to be mapped and analysed to determine possible failures and decide necessary stability measures. The purpose of this study is to evaluate the quality of rock technical data from digital photogrammetry 3D models by comparing the result with manual measurements from conventional mapping. The goal is also to explore the potential uses of photogrammetric 3D models for rock slope stability analyses by evaluate the photogrammetric data. Facets extracted from 3D models were found to have the same quality as manual measurements. However, the UAS-based method cannot completely replace the conventional method but can be useful as a complementary tool. Photogrammetry enables the collection of data from a safer distance, which reduces workplace hazards that the conventional method entails. The digital method also proved to have more advantages, such as the possibility of digital mapping and analysing which is less costly and time-consuming, digital data storage and the possibility to access outcrops that can’t be mapped with manually measurements due to inaccessibility.