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1
Stejskal, Jan. "Proudění magnetické kapaliny s aplikací Binghamova modelu." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2013. http://www.nusl.cz/ntk/nusl-230791.
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Main topic of this thesis are magnetic fluids. These are specific type of fluids which can simplistically be considered as Bingham fluids. Main issues regarding the magnetic fluids mentioned in this thesis are: rheological properties of the magnetic fluids, behaviour of the magnetic fluids and the use of the magnetic fluids in industrial applications. Main goal is to apply Binghams model on the the magnetic fluids assuming that this model can be applied with a good accuracy. Equations which describe behaviour of the Bingham fluids are constructed. Some assumptions which have to be respected to use this analytical equations for magnetic fluids are formulated. Flow of bingham fluid is analytically solved in some simplificated cases with consideration of laminar flow. Analytical results are confronted with numerical ones obtained from CFD software Fluent for the purpose of verification.
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Ríos, Bayona Francisco. "Analytical and numerical approaches to estimate peak shear strength of rock joints." Licentiate thesis, KTH, Jord- och bergmekanik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-248019.
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In Sweden, there exists a large number of dams. Many of them are founded on rock masses normally affected by the presence of sub-horizontal rock fractures, which makes sliding along rock joints under the dam foundation one of the most critical failure mechanism. Various attempts have been made to relate the peak shear strength of rock joints to measurable parameters. However, the uncertainty in the determination of the shear strength of rock joints is nonetheless still significant.The main aim of this thesis is to investigate, develop and apply analytical and numerical techniques for estimation of peak shear strength of natural and unfilled rock joints. In a first step, the peak shear strength of several natural and unfilled rock joint was calculated by using surface aperture measurements from high-resolution optical scanning and a modified version of the analytical criterion previously developed by Johansson and Stille in 2014. In a second step, PFC2D was utilised to perform numerical shear tests on two-dimensional profiles selected from high-resolution optical scanning on unweathered and perfectly mated tensile induced rock joints.The results from the analytical approach show that the calculated peak shear strengths of the analysed samples are in good agreement compared with the laboratory investigations. Conversely, the obtained results from the numerical approach show lower peak shear strengths in the analysed two-dimensional profiles compared with the conducted laboratory shear tests.The analytical approach together with the advanced techniques to measure surface roughness available today, may be a possible way forward towards a methodology to determine peak shear strength of large-scale natural rock joints in-situ.Bergsprickors skjuvhållfasthet är en avgörande faktor för att kunna bestämma säkerheten mot gliding för dammar där sub-horisontella utbredda bergsprickor existerar. Samtidigt är parametern svår att bestämma då den påverkas av flera faktorer som sprickytans råhet, vittringsgrad, normalspänning, skala samt passning. Skjuvhållfasthet av bergsprickor kan bestämmas genom att använda empiriska och analytiska brottkriterier samt numeriska metoder. Problemet med de befintliga metodikerna är att de inte beaktar inverkan från sprickans passning. Detta innebär att hållfastheten riskerar att överskattas.Det övergripande syftet med denna licentiatuppsats är att studera, utveckla och tillämpa analytiska och numeriska metoder för uppskattning av skjuvhållfasthet för naturliga och ofyllda bergsprickor. I ett första steg beräknades skjuvhållfastheten för ett antal naturliga och ofyllda bergsprickor. Detta gjordes genom att mäta aperturen baserat på högupplöst skanning och en vidareutvecklad version av det analytiska kriteriet som föreslogs av Johansson och Stille 2014. I ett andra steg användes PFC2D för att genomföra numeriska skjuvtester på två-dimensionella sprickprofiler baserat på högupplöst skanning av perfekt passade och draginducerade bergsprickor.Resultaten från uppskattad skjuvhållfasthet med den analytiska metodiken visar på en bra överensstämmelse i jämförelse med de utförda skjuvförsöken. Resultaten från de utförda analyserna med PFC2D visar på en något lägre skjuvhållfasthet än vad som observeras i verkligheten.Den utvecklade analytiska metodiken, tillsammans med de avancerade tekniker som idag finns för att mäta sprickytornas råhet, bedöms kunna utgöra ett första steg mot att bättre kunna bestämma den storskaliga skjuvhållfastheten för bergsprickor i fält.
QC 20190402
3
Harper, John Stuart. "Analytic cache modelling of numerical programs." Thesis, University of Warwick, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.343887.
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Topcu, Nagihan. "Numerical, Analytical And Experimental Analysis Of Indentation." Master's thesis, METU, 2005. http://etd.lib.metu.edu.tr/upload/12605942/index.pdf.
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Indentation is a practical and easy method, therefore, is a preferred method of material characterization. Main aim of this thesis study is to determine anisotropic properties of metals by indentation tests. The basic property of the indenter used in the finite element analyses and experiments is that it is specific to this process. Thesis includes studies on optimization of the indenter geometry, analyses of effects of friction coefficient, multiple indentations, tilting of the indenter and clamping of the specimen on force-displacements curves during indentation by finite element analyses.
This study also includes finite element analyses of compression tests where these experiments have been necessary to prove anisotropic behavior of the specimen material. In addition to compression, tension tests are done to have a reference for indentation tests. On the other hand, the upper bound method which is an analytical solution is applied on the assumption of plane strain indentation.
5
Hayes, John L. "A numerical analytical investigation of lee cyclogenesis." Thesis, Monterey, California. Naval Postgraduate School, 1985. http://hdl.handle.net/10945/21469.
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Caunt, Stuart Edward. "Analytical and numerical models of accretion disks." Thesis, University of Newcastle Upon Tyne, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.265485.
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Pagitz, Markus Emil. "Analytical and numerical studies of superpressure balloons." Thesis, University of Cambridge, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.611958.
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Konečný, Michael. "Porovnání analytického a numerického MKP řešení vzpěrné stability laminátových kompozitních válcových skořepin." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2013. http://www.nusl.cz/ntk/nusl-230525.
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Tato práce zkoumá možností řešení kritické síly vzpěrné stability laminátových kompozitních válcových skořepin jak analytickým tak MKP přístupem. Analytické řešení je prezentováno detailně a je zpracován Matlab program pro jeho výpočet. MKP řešení je prováděno ve dvou řešičích softwaru MSC.Nastran, jsou zjišťována vhodná nastavení těchto řešičů a jejich chování. Všechny způsoby řešení jsou na závěr porovnány a je navrženo několik závěrů.
9
Marcell, Jan. "Přenos tepla v úložném obalovém souboru a jeho vliv na okolí." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2009. http://www.nusl.cz/ntk/nusl-228605.
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The main object of this diploma thesis is solving problems concerning heat transfer in disposal cannister for spent nuclear fuel. In forepart possibilities of conceptual solving according of disposal cannister to particular states are reviwed. On the basis of this a variant of possible protect of a nuclear fuel repository in the Czech republic has been chosen for calculationof a simplified model. Second part is computational solving that was divided into two parts. The first deals with calculation of heat transfer in disposal canister and is done by an analytical method. In the second part is calculation is done by numerical model. In this way region in near surroundings of this model of disposal cannister is analysed. Last part those diploma thesis deals with design of the storage of spacing among disposal canisters as well as optimum placing in underground part of nuclear fuel repository.
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Gish, Lynn Andrew. "Analytic and numerical study of underwater implosion." Thesis, Massachusetts Institute of Technology, 2013. http://hdl.handle.net/1721.1/81699.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2013.Cataloged from PDF version of thesis.
Includes bibliographical references (p. 203-205).
Underwater implosion, the rapid collapse of a structure caused by external pressure, generates a pressure pulse in the surrounding water that is potentially damaging to adjacent structures or personnel. Understanding the mechanics of implosion, specifically the energy transmitted in the pressure pulse, is critical to the safe and efficient design of underwater structures. Hydrostatically-induced implosion of unstiffened metallic cylinders was studied both analytically and numerically. An energy balance approach was used, based on the principle of virtual velocities. Semi-analytic solutions were developed for plastic energy dissipation of a symmetric mode 2 collapse; results agree with numerical simulations within 10%. A novel pseudo-coupled fluid-structure interaction method was developed to predict the energy transmitted in the implosion pulse; results agree with fully-coupled numerical simulations within 6%. The method provides a practical alternative to computationally-expensive simulations when a minimal reduction in accuracy is acceptable. Three design recommendations to reduce the severity of implosion are presented: (1) increase the structure's internal energy dissipation by triggering higher collapse modes, (2) initially pressurize the internals of the structure, and (3) line the cylinder with a flexible or energy absorbing material to cushion the impact between the structure's imploding walls. These recommendations may be used singly or in combination to reduce or completely eliminate the implosion pulse. However, any design efforts to reduce implosion severity must be part of the overall system design, since they may have detrimental effects on other performance areas like strength or survivability.
by Lynn Andrew Gish.
Ph.D.
11
Kaur, Amandeep. "Analytic and numerical aspects of isospectral flows." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/270631.
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In this thesis we address the analytic and numerical aspects of isospectral flows. Such flows occur in mathematical physics and numerical linear algebra. Their main structural feature is to retain the eigenvalues in the solution space. We explore the solution of Isospectral flows and their stochastic counterpart using explicit generalisation of Magnus expansion. \par In the first part of the thesis we expand the solution of Bloch--Iserles equations, the matrix ordinary differential system of the form $ X'=[N,X^{2}],\ \ t\geq0, \ \ X(0)=X_0\in \textrm{Sym}(n),\ N\in \mathfrak{so}(n), $ where $\textrm{Sym}(n)$ denotes the space of real $n\times n$ symmetric matrices and $\mathfrak{so}(n)$ denotes the Lie algebra of real $n\times n$ skew-symmetric matrices. This system is endowed with Poisson structure and is integrable. Various important properties of the flow are discussed. The flow is solved using explicit Magnus expansion and the terms of expansion are represented as binary rooted trees deducing an explicit formalism to construct the trees recursively. Unlike classical numerical methods, e.g.\ Runge--Kutta and multistep methods, Magnus expansion respects the isospectrality of the system, and the shorthand of binary rooted trees reduces the computational cost of the exponentially growing terms. The desired structure of the solution (also with large time steps) has been displayed. \par Having seen the promising results in the first part of the thesis, the technique has been extended to the generalised double bracket flow $ X^{'}=[[N,X]+M,X], \ \ t\geq0, \ \ X(0)=X_0\in \textrm{Sym}(n),$ where $N\in \textrm{diag}(n)$ and $M\in \mathfrak{so}(n)$, which is also a form of an Isospectral flow. In the second part of the thesis we define the generalised double bracket flow and discuss its dynamics. It is noted that $N=0$ reduces it to an integrable flow, while for $M=0$ it results in a gradient flow. We analyse the flow for various non-zero values of $N$ and $M$ by assigning different weights and observe Hopf bifurcation in the system. The discretisation is done using Magnus series and the expansion terms have been portrayed using binary rooted trees. Although this matrix system appears more complex and leads to the tri-colour leaves; it has been possible to formulate the explicit recursive rule. The desired structure of the solution is obtained that leaves the eigenvalues invariant in the solution space.
12
Driessen, Brian James. "Analytical and numerical studies in nonholonomic dynamical systems." Thesis, Georgia Institute of Technology, 1993. http://hdl.handle.net/1853/17338.
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Andrianov, Nikolai. "Analytical and numerical investigation of two-phase flows." [S.l. : s.n.], 2003. http://deposit.ddb.de/cgi-bin/dokserv?idn=969695810.
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Nyqvist, Robert. "Algebraic Dynamical Systems, Analytical Results and Numerical Simulations." Doctoral thesis, Växjö : Växjö University Press, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-1142.
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Tomita, Yu. "Numerical and analytical studies of quantum error correction." Diss., Georgia Institute of Technology, 2014. http://hdl.handle.net/1853/53468.
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A reliable large-scale quantum computer, if built, can solve many real-life problems exponentially faster than the existing digital devices. The biggest obstacle to building one is that they are extremely sensitive and error-prone regardless of the selection of physical implementation. Both data storage and data manipulation require careful implementation and precise control due to its quantum mechanical nature. For the development of a practical and scalable computer, it is essential to identify possible quantum errors and reduce them throughout every layer of the hierarchy of quantum computation.
In this dissertation, we present our investigation into new methods to reduce errors in quantum computers from three different directions: quantum memory, quantum control, and quantum error correcting codes. For quantum memory, we pursue the potential of the quantum equivalent of a magnetic hard drive using two-body-interaction structures in fractal dimensions. With regard to quantum control, we show that it is possible to arbitrarily reduce error when manipulating multiple quantum bits using a technique popular in nuclear magnetic resonance. Finally, we introduce an efficient tool to study quantum error correcting codes and present analysis of the codes' performance on model quantum architectures.
16
Yi, Xianjie. "Numerical and analytical modeling of sanding onset prediction." Texas A&M University, 2003. http://hdl.handle.net/1969/369.
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Piret, Cecile. "Analytical and numerical advances in radial basis functions." Connect to online resource, 2008. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3303840.
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Arienti, Marco Hornung H. G. "A numerical and analytical study of detonation diffraction /." Diss., Pasadena, Calif. : California Institute of Technology, 2003. http://resolver.caltech.edu/CaltechETD:etd-02122003-152525.
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Wright, Patrick. "Numerical and analytical solution of optimal multiprocess problems." Thesis, Imperial College London, 1990. http://hdl.handle.net/10044/1/46617.
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Vitucci, Gennaro. "Analytical and numerical modelling of thin functional layers." Thesis, Aberystwyth University, 2018. http://hdl.handle.net/2160/21af2cbb-6c9e-4b1a-8521-0113628e854e.
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The thesis deals with the study of thin layers and their function within larger structures. Different thin intephases appearing in mechanics and biomechanics are considered. The work aims at setting a manageable mathematical framework in mechanical modelling. Analytical methods are provided in order to achieve closed-form solutions and effective numerical procedures. Cartilage, which reveals crucial in transmitting loads without friction along the skeleton, is thoroughly investigated. Governing equations derived within mixture theory are used for a biphasic description of the tissue. Inhomogeneity and anisotropy are introduced and their effect on the global behavior of the tissue is investigated. This is accomplished via integral transforms for relatively small thickness of the layer and short-time asymptotics. The model is extended to study the three-dimensional contact of cartilage surfaces in the joint. The involved integro-differential equations are solved in closed-form. Next, intra-articular pressurization is taken into account via modelling the whole joint capsule. Implications for healthy degenerated and tissues are discussed. Lastly, cylindrical multilayer assemblies of layers are examined in the framework of thermoelasticity. The general solutions for the single components are arranged in a way to conveniently constitute a linear system. Perfect and imperfect contact between the layers are considered. An efficient numerical scheme is developed. Simulations are run with a special eye on ceramics.
21
Guo, Yan, and Yan Guo. "Nonlinear Surface Plasmon Polaritons: Analytical and Numerical Studies." Thesis, University of Oregon, 2012. http://hdl.handle.net/1794/12324.
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This dissertation contains analytical and numerical studies of nonlinear
surface-plasmon polaritons (SPPs). In our studies, we consider SPP propagation
at the interface between a noble metal with a cubic optical nonlinearity and an
optically linear dielectric.
We first consider a sum-frequency generation process during the nonlinear
interaction, where a nonlinear polarization with tripled frequency is generated from
the incident fundamental SPP. Using the non-depletion approximation, the solution
of the nonlinear wave equation shows a third harmonic generation process from the
incident SPP wave. The solution is bound in the dielectric while freely propagating
in the metal. For realistic noble metals with absorption, we use silver for its
transparency window around the plasma frequency. In this window, absorption
losses are reduced and the resultant signal has a good transmittance within the
metal. The energy conversion efficiency from the incident SPP wave to the THG signal is about 0.1% for excitation using a standard continuous wave laser with
visible light intensity I = 103W/cm2. Once generated, the propagation angle of the
signal is fully determined by the optical properties of the dielectric and the metal layers. We next consider a nonlinear polarization with the same frequency as
the incident light. In this process the third order nonlinearity of the metal
is described by a nonlinear optical refractive-index. With the slowly varying
amplitude approximation, the nonlinear wave equation takes the form of a
nonlinear temporal Schr¨odinger (NLS) equation. The solution to the NLS equation
for the nonlinear SPP is a temporal dark soliton (TDS). In addition to analytical
studies, computational methods are also used. With no metal loss, the numerical
solution shows stable propagation of a TDS, when the initial pulse has a tanh
envelope satisfying the threshold peak amplitude. For an arbitrary input pulse,
instabilities such as background-oscillations and multi-peak breakups occur. With
metal loss, the input optical pulse decays while maintaining a single pulse shape
when the initial amplitude satisfies the same tanh envelope condition as in the
lossless case. For an arbitrary pulse, background-oscillations or pulse-breakups
occur after a short time of propagation.
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Casalino, Damiano. "Analytical and numerical methods in vortex-body aeroacoustics." Ecully, Ecole centrale de Lyon, 2002. http://bibli.ec-lyon.fr/exl-doc/TH_T1893_dcasalino.pdf.
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The model problem of an airfoil embedded in the fluctuating wake of a rod is investigated in the first part. Such a flow configuration is an effective benchmark for developing and validating numerical methodologies of aeroacoustic prediction. Furthermore, the rod-airfoil configuration is of great academic concern, for it allows to investigate some underlying mechanisms involved in the generation of vortex-airfoil interaction noise. The numerical and theoretical relevance of the rod-airfoil configuration reflects the structure of the first part. An analytical model based on the circulation theory is initially developed. This is used to investigate the influence of the airfoil geometry and the vortex size on the far pressure field, for a given distribution of vortices convected past an airfoil. Particular emphasis is given to the nonlinear effects related to the airfoil thickness and camber, the interaction of the airfoil wake with the incident vortices, and the vortex distortion near the airfoil leading edge. The limits of applicability of the frozen convection hypothesis and other linear approximations are discussed in great detail. Wall pressure and acoustic measurements are carried out with a twofold aim in mind: (i) to obtain data for comparisons with numerical results, (ii) to investigate the three-dimensional character of a nominal two-dimensional flow. Numerical results are obtained by means of a hybrid RANS/Ffowcs-Williams & Hawkings approach. The RANS solver is a finite volume code developed at LMFA, and the FW-H solver is the rotor-noise code Advantia. The latter has been developed in the context of the present study and is based on the so-called advanced time approach, firstly proposed by the author. The intrinsic three-dimensional behaviour of the flow past a bluff body is described for the first time by means of a spanwise statistical model. This allows to perform acoustic analogy predictions by using a two-dimensional aerodynamic field, but accounting, to some extent, for the three-dimensional character of the flow. The hybrid RANS/FW-H approach and the spanwise statistical model are applied to the rod-airfoil system. It is shown that, despite the tonal character of the RANS solution, the spectral broadening around the tonal frequency, as observed in the experiments, is partially recovered. The second part of the work illustrates theories and models in fluid-body aeroacoustics. It is only concerned with sound generation in the absence of acoustic feed-back. Therefore, only external flows are considered, the propagation problem in complex geometries is not addressed, and the aeroacoustic feed-back in resonant configurations is not examined. Unsteady aerodynamic theories are presented in the second part as an ineluctable theoretical basis for devel¬oping aeroacoustic models. Nevertheless, the author's feeling in writing this part was that "aeroacoustic sound is an aerodynamic by-product, bid aeroacoustics are not a by-product of aerodynamics".
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Berryman, John Fagan. "Analytical and Numerical Analysis of Static Coulomb Formations." Thesis, Virginia Tech, 2005. http://hdl.handle.net/10919/36000.
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For close proximity flying on the order of 10-100 meters, Coulomb thrusting presents a
promising alternative to other methods of propulsion. This clean and fuel-efficient propulsion
method is being investigated for use in formation flying and virtual structures. In the latter
application, the individual spacecraft assume fixed positions relative to each other through
the use of Coulomb forces. In the work presented here, an analytical and numerical analysis
is performed on such virtual structures. In the analytical portion, the constant, open-loop
charges necessary to maintain a Hill-frame-static formation are determined for the cases
of linear two- and three-spacecraft formations and for the case of equilateral triangular
formations with spacecraft of equal mass. In addition, analysis is provided for the N-craft
case so that the inter-craft charge products can be determined for any static formation.
In the numerical portion, a genetic algorithm is employed to support the analytical results
by determining formation geometries and charging schemes such that the formation craft
remain static in the Hill frame in the absence of perturbation. The results of the numerical
analysis include examples of static two-craft through nine-craft formations, including several
formations that display a broader range of configurations than considered in previous works.
Issues encountered during the numerical analysis are discussed, as well as the course of
action taken to overcome these issues. Finally, a method is presented by which the genetic
algorithm could be extended to take advantage of cluster computing.Master of Science
24
Ning, Ding. "Analytical and Numerical Models of Multilayered Photonic Devices." University of Akron / OhioLINK, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=akron1207712683.
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Robin, Victor Paul Michel. "Analytical and numerical modelling of artificially structured soils." Thesis, University of Exeter, 2014. http://hdl.handle.net/10871/16565.
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The effects of lime treatment on the mechanical properties of soils are usually not accounted for in the design of geotechnical structures. As a result the potential of lime treatment has not been fully exploited. In this thesis, a comprehensive experimental program has been carried out to identity the key features of the mechanical behaviour of structured materials. The chemical modifications arising from lime treatment were quantified using thermal analysis methods. From these results a non-linear chemo-mechanical coupling was established between the concentration of cementitious compounds and the yield stress. Using these results, a new formulation to model the degradation of the structure at yield has been developed and implemented in a constitutive model for structured materials. This new model, developed in the framework of the Modified Cam Clay model, requires a limited number of additional parameters that all have a physical meaning and can all be determined from a single isotropic compression test. The model has proven to be successful in reproducing the key features of structured materials and for the modelling of the mechanical behaviour of lime treated specimens under various stress paths. Due to similarities in behaviour, it is shown that the formulation is also suitable for naturally structured soils. To account for a structured material in the design of geotechnical structures, a fully functional finite element program for elasto-plastic problems was developed including the pre- and post-processing of the results. A thorough validation has confirmed the good implementation of the finite element method and its suitability for the modelling of complex geometries involving structured materials.
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Robin, Victor. "Analytical and numerical modelling of artificially structured soils." Thesis, Université de Lorraine, 2014. http://www.theses.fr/2014LORR0264/document.
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Le traitement des sols à la chaux est une méthode couramment utilisée pour améliorer les propriétés mécaniques de sols aux performances insuffisantes. Cependant, ces améliorations mécaniques ne sont pas prises en compte dans les calculs de dimensionnement. Cette thèse propose une méthodologie pour pallier à ce problème. Un programme expérimental approfondi est réalisé afin de décrire avec précision le comportement mécanique d’un sol traité et les processus associés à la structuration introduite par le traitement. La composition chimique, et notamment la quantité de composés cimentaires hydratés, est déterminée par analyses thermogravimétriques et thermodifférentielles. Un couplage non-linéaire entre la quantité d’hydrates et la limite élastique se basant sur ces résultats expérimentaux est proposé. À partir de ces résultats, une nouvelle formulation a été développée afin de modéliser la dégradation de la structure en plasticité, et a servi au développement d’une nouvelle loi de comportement élasto-plastique basée sur le modèle de Cam Clay Modifié. Cette dernière a montré reproduire correctement les principaux traits de comportement spécifiques aux sols traités. Il est démontré que ce modèle est également adapté aux sols naturellement structurés. Afin de prendre en compte les effets du traitement et la présence de structure dans le dimensionnement, un programme basé sur la méthode des éléments finis, comprenant le pré- et le post-processing de la géométrie et des résultats du problème, a été développé. Une validation rigoureuse a confirmé l'implémentation correcte de la méthode et son potentiel pour l’optimisation du dimensionnement des ouvragesThe effects of lime treatment on the mechanical properties of soils are usually not accounted for in the design of geotechnical structures. As a result the potential of lime treatment has not been fully exploited. In this thesis, a comprehensive experimental program has been carried out to identity the key features of the mechanical behaviour of structured materials. The chemical modifications arising from lime treatment were quantified using thermal analysis methods. From these results a non-linear chemo-mechanical coupling was established between the concentration of cementitious compounds and the yield stress. Using these results, a new formulation to model the degradation of the structure at yield has been developed and implemented in a constitutive model for structured materials. This new model, developed in the framework of the Modified Cam Clay model, requires a limited number of additional parameters that all have a physical meaning and can all be determined from a single isotropic compression test. The model has proven to be successful in reproducing the key features of structured materials and for the modelling of the mechanical behaviour of lime treated specimens under various stress paths. Due to similarities in behaviour, it is shown that the formulation is also suitable for naturally structured soils. To account for a structured material in the design of geotechnical structures, a fully functional finite element program for elasto-plastic problems was developed including the pre- and post-processing of the results. A thorough validation has confirmed the good implementation of the finite element method and its suitability for the modelling of complex geometries involving structured materials
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Weaver, Andrew John. "Numerical and analytical modelling of oceanic/atmospheric processes." Thesis, University of British Columbia, 1987. http://hdl.handle.net/2429/27560.
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Two problems in oceanic/atmospheric modelling are examined in this thesis. In the first problem the release of fresh water from a midlatitude estuary to the continental shelf is modelled numerically as a Rossby adjustment problem using a primitive equation model. As the initial salinity front is relaxed, a first baroclinic mode Kelvin wave propagates into the estuary, while along the continental shelf, the disturbance travels in the direction of coastally trapped waves but with a relatively slow propagation speed. When a submarine canyon extends offshore from the estuary, the joint effect of baroclinicity and bottom relief provides forcing for barotropic flow. The disturbance now propagates along the shelf at the first coastally trapped wave mode phase speed, and the shelf circulation is significantly more energetic and barotropic than in the case without the canyon. For both the experiments with and without a canyon an anticyclonic circulation is formed off the mouth of the estuary, generated by the surface outflow and deeper inflow over changing bottom topography. As the deeper inflow encounters shallower depth, the column of fluid is vertically compressed, thereby spinning up anticyclonically due to the conservation of potential vorticity. This feature is in qualitative agreement with the Tully eddy observed off Juan de Fuca Strait. A study of the reverse estuary (where the estuarine water is denser than the oceanic water) shows that this configuration has more potential energy available for conversion to kinetic energy than the normal estuary. Bass Strait may be considered as a possible reverse estuary source for the generation of coastally trapped waves. Model solutions are compared with field observations in the Bass Strait region and with the results of the Australian Coastal Experiment. The effects of a wider shelf and a wider estuary are examined by two more experiments. For the wider shelf, the resulting baroclinic flow is similar to that of the other runs, although the barotropic flow is weaker. The wide estuary model proves to be the most dynamic of all, with the intensified anticyclonic circulation now extending well into the estuary.
In the second problem the effect of the horizontal structure of midlatitude oceanic heating on the stationary atmospheric response is examined by means of a continuously stratified model and a simple two level model, both in the quasigeostrophic β-plane approximation.
Solutions are obtained for three non-periodic zonal heating structures (line source, segmented cosine, and segmented sine). Little difference is observed between the solutions for these two different models (continuously stratified and two level). There are two cases which emerge in obtaining analytic solutions. In case 1, for large meridional wavenumbers, there exists a large local response and a constant downstream response. In case 2, for small meridional wavenumbers, the far field response is now sinusoidal. A critical wavenumber separating these two cases is obtained. The effect of oceanic heating on the atmosphere over the Kuroshio region is examined in an attempt to explain the large correlations observed between winter Kuroshio oceanic heat flux anomalies, and the winter atmospheric surface pressure and 500 & 700 mb geopotential heights, both upstream and downstream of the heating region. In both models, the response is consistent with the observed
correlations. When western North Pacific heating and eastern North Pacific cooling are introduced into the models, a large low pressure response is observed over the central North Pacific. This feature is in excellent agreement with the observed correlations. A time dependent, periodic, two level model (with and without surface friction) is also introduced
in order to study the transient atmospheric response to oceanic heating. The height at which the thermodynamic equation is applied is found to be crucial in determining the response of this model. When the heating is entered into the model near to the surface, unstable modes are prevalent sooner than they would be when the heat forcing is applied at a higher level. As in the steady state models, two cases dependent on the meridional wavenumber ɭ emerge in the analysis. For small scale meridional heating structures (large ɭ), the response consists of an upper level high and a lower level low which propagate eastward with time. For large scale meridional heating structures (small ɭ) the response essentially consists of a wavenumber 3-4 perturbation superimposed on the solution for large ɭ.Science, Faculty of
Mathematics, Department of
Graduate
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Bilodeau, Bernard. "Accuracy of a truncated barotropic spectral model : numerical versus analytical solutions." Thesis, McGill University, 1985. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=66037.
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Kaya, Yasemin. "Analytical And Numerical Solutions To Rotating Orthotropic Disk Problems." Master's thesis, METU, 2007. http://etd.lib.metu.edu.tr/upload/12608868/index.pdf.
Full textAbstract:
Analytical and numerical models are developed to investigate the effect of orthotropy on the stress distribution in variable thickness solid and annular rotating disks. The plastic treatment is based on Hill&rsquos quadratic yield criterion, total deformation theory, and Swift&rsquo
s hardening law. The elastic-plastic stress distributions, residual stresses and radial displacement distributions are obtained after having analysed the cases of rotating solid disk, annular disk with rigid inclusion, annular disk subjected to either internal or external pressure. Thermal loading is also considered for the annular disk with rigid inclusion. Effects of different values of elastic and plastic orthotropy parameters are investigated. It is observed that the elastic orthotropy significantly affects the residual stresses in disks. The most remarkable effect of the plastic orthotropy is observed on the disk with rigid inclusion.
30
Turkakar, Goker. "Numerical Simulation And Analytical Optimization Of Microchannel Heat Sinks." Master's thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/12612377/index.pdf.
Full textAbstract:
This study has two main objectives: The performance evaluation of existing microchannel heat sinks using a CFD model, and the dimensional optimization of various heat sinks by minimizing the total thermal resistance.
For the analyses, the geometric modeling is performed using the software GAMBIT while the thermal analysis is performed with FLUENT. The developed model compares very well with those available in the literature. Eight different metal-polymer microchannel heat sinks are analyzed using the model to find out how much heat could be provided to the systems while keeping the substrate temperatures below 85°C under a constant pumping power requirement. Taking the objective function as the total thermal resistance, the optimum geometries have been obtained for the mentioned metal-polymer heat sinks as well as more conventional silicon ones. The results of the optimization code agreed very well with available ones in the literature. In the optimization study, the Intel Core i7-900 Desktop Processor Extreme Edition Series is considered as a reference processor which is reported to dissipate 130 W of heat and to have chip core dimensions of 1.891 cm ×
1.44 cm. A dimensional optimization study has been performed for various copper and silicon microchannel heat sinks to cool down this processor. To the best of the author&rsquo
s knowledge, this study contributes to the literature in that, as opposed to the available analytical microchannel optimization studies considering constant thermophysical properties at the fluid inlet temperature, the properties are evaluated at the area weighted average of the fluid inlet and iteratively calculated outlet temperatures. Moreover, the effects of the thermal and hydrodynamic entrance regions on heat transfer and flow are also investigated.
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Haller, Emmanuel B. de Haller Emmanuel B. De. "Time resolved breast transillumination : analytical, numerical and experimental study /." [S.l.] : [s.n.], 1993. http://library.epfl.ch/theses/?display=detail&nr=1119.
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au, kaurgurd@willettonshs wa edu, and Gurdeep Kaur. "Electron-helium scattering using analytical and numerical wave functions." Murdoch University, 2002. http://wwwlib.murdoch.edu.au/adt/browse/view/adt-MU20080123.100101.
Full textAbstract:
Theoretical investigations of electron-inert gas scattering are challenging because of the complex target structure. The electron-Helium system has been the most studied both at low and intermediate energies by sophisticated R-matrix and coupled channels methods. For the other inert gases, few calculations have been attempted at the same level sophistication. One problem is that general target-structure codes provide different forms of wave functions that must be interfaced with the scattering equations. The theoretical work presented in this thesis is based on the momentum-space coupled channels equations. For this formalism only one and two-electron atoms have been studied and purpose-built routines, specific to these atoms, have been developed. For the inert gases however such a task is much more formidable and a more practical approach is to use existing structure codes that have taken several man-years to develop.
The framework of this thesis comprises of two parts. In the first part we discuss the need for, and the way to, modify the existing close-coupling code developed by Berge & Stelbovics in order to interface with other atomic structure packages in the literature. Two mainstream packages, an atomic structure package of Charlotte Froese Fischer and an atomic structure of Alan Hibbert are discussed. Methods to extract the wave functions for Helium and Neon targets using Hibbert's package are given. In the second part, various options and strategies for the calculation of the target structure, including frozen-core and configuration-interaction wave functions, using analytic Slater, Laguerre or numerical orbitals are considered for the Helium target. Hibbert's structure code wave functions are shown to be correctly interfaced into our momentum-space coupled channels code. The pros and cons of the various target structure descriptions are given and applied for lowenergy elastic and inelastic scattering of electron from Helium.
33
Kaur, Gurdeep. "Electron-helium scattering using analytical and numerical wave functions." Kaur, Gurdeep (2002) Electron-helium scattering using analytical and numerical wave functions. PhD thesis, Murdoch University, 2002. http://researchrepository.murdoch.edu.au/472/.
Full textAbstract:
Theoretical investigations of electron-inert gas scattering are challenging because of the complex target structure. The electron-Helium system has been the most studied both at low and intermediate energies by sophisticated R-matrix and coupled channels methods. For the other inert gases, few calculations have been attempted at the same level sophistication. One problem is that general target-structure codes provide different forms of wave functions that must be interfaced with the scattering equations. The theoretical work presented in this thesis is based on the momentum-space coupled channels equations. For this formalism only one and two-electron atoms have been studied and purpose-built routines, specific to these atoms, have been developed. For the inert gases however such a task is much more formidable and a more practical approach is to use existing structure codes that have taken several man-years to develop.
The framework of this thesis comprises of two parts. In the first part we discuss the need for, and the way to, modify the existing close-coupling code developed by Berge & Stelbovics in order to interface with other atomic structure packages in the literature. Two mainstream packages, an atomic structure package of Charlotte Froese Fischer and an atomic structure of Alan Hibbert are discussed. Methods to extract the wave functions for Helium and Neon targets using Hibbert's package are given. In the second part, various options and strategies for the calculation of the target structure, including frozen-core and configuration-interaction wave functions, using analytic Slater, Laguerre or numerical orbitals are considered for the Helium target. Hibbert's structure code wave functions are shown to be correctly interfaced into our momentum-space coupled channels code. The pros and cons of the various target structure descriptions are given and applied for lowenergy elastic and inelastic scattering of electron from Helium.
34
Sondor, Anantha Shayana. "Analytical and numerical investigation of billet augmented hydrostatic extrusion." Ohio : Ohio University, 1989. http://www.ohiolink.edu/etd/view.cgi?ohiou1182520017.
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Filitti, Constantin Alexandru. "Portfolio selection in continuous time : analytical and numerical methods." Online version, 2004. http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&doc_number=012032625&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA.
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Kong, Dali. "Analytical and numerical studies of several fluid mechanical problems." Thesis, University of Exeter, 2012. http://hdl.handle.net/10036/3651.
Full textAbstract:
In this thesis, three parts, each with several chapters, are respectively devoted to hydrostatic, viscous and inertial fluids theories and applications. In the hydrostatics part, the classical Maclaurin spheroids theory is generalized, for the first time, to a more realistic multi-layer model, which enables the studies of some gravity problems and direct numerical simulations of flows in fast rotating spheroidal cavities. As an application of the figure theory, the zonal flow in the deep atmosphere of Jupiter is investigated for a better understanding of the Jovian gravity field. High viscosity flows, for example Stokes flows, occur in a lot of processes involving low-speed motions in fluids. Microorganism swimming is such typical a case. A fully three dimensional analytic solution of incompressible Stokes equation is derived in the exterior domain of an arbitrarily translating and rotating prolate spheroid, which models a large family of microorganisms such as cocci bacteria. The solution is then applied to the magnetotactic bacteria swimming problem and good consistency has been found between theoretical predictions and laboratory observations of the moving patterns of such bacteria under magnetic fields. In the analysis of dynamics of planetary fluid systems, which are featured by fast rotation and very small viscosity effects, three dimensional fully nonlinear numerical simulations of Navier-Stokes equations play important roles. A precession driven flow in a rotating channel is studied by the combination of asymptotic analyses and fully numerical simulations. Various results of laminar and turbulent flows are thereby presented. Computational fluid dynamics requires massive computing capability. To make full use of the power of modern high performance computing facilities, a C++ finite-element analysis code is under development based on PETSc platform. The code and data structures will be elaborated, along with the presentations of some preliminary results.
37
Rossi, Francesco <1987>. "Numerical and Analytical Methods for Laser-Plasma Acceleration Physics." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2015. http://amsdottorato.unibo.it/6771/.
Full textAbstract:
Theories and numerical modeling are fundamental tools for understanding, optimizing and designing present and future laser-plasma accelerators (LPAs).
Laser evolution and plasma wave excitation in a LPA driven by a weakly relativistically intense, short-pulse laser propagating in a preformed parabolic plasma channel, is studied analytically in 3D including the effects of pulse steepening and energy depletion. At higher laser intensities, the process of electron self-injection in the nonlinear bubble wake regime is studied by means of fully self-consistent Particle-in-Cell simulations. Considering a non-evolving laser driver propagating with a prescribed velocity, the geometrical properties of the non-evolving bubble wake are studied. For a range of parameters of interest for laser plasma acceleration, The dependence of the threshold for self-injection in the non-evolving wake on laser intensity and wake velocity is characterized.
Due to the nonlinear and complex nature of the Physics involved, computationally challenging numerical simulations are required to model laser-plasma accelerators operating at relativistic laser intensities. The numerical and computational optimizations, that combined in the codes INF&RNO and INF&RNO/quasi-static give the possibility to accurately model multi-GeV laser wakefield acceleration stages with present supercomputing architectures, are discussed. The PIC code jasmine, capable of efficiently running laser-plasma simulations on Graphics Processing Units (GPUs) clusters, is presented. GPUs deliver exceptional performance to PIC codes, but the core algorithms had to be redesigned for satisfying the constraints imposed by the intrinsic parallelism of the architecture. The simulation campaigns, run with the code jasmine for modeling the recent LPA experiments with the INFN-FLAME and CNR-ILIL laser systems, are also presented.
38
Wessels, Gert Jermia Cornelus. "A numerical and analytical investigation into non-Hermitian Hamiltonians." Thesis, Stellenbosch : University of Stellenbosch, 2009. http://hdl.handle.net/10019.1/2894.
Full textAbstract:
Thesis (MSc (Physical and Mathematical Analysis))--University of Stellenbosch, 2009.In this thesis we aim to show that the Schr odinger equation, which is a boundary eigenvalue problem, can have a discrete and real energy spectrum (eigenvalues) even when the Hamiltonian is non-Hermitian. After a brief introduction into non-Hermiticity, we will focus on solving the Schr odinger equation with a special class of non-Hermitian Hamiltonians, namely PT - symmetric Hamiltonians. PT -symmetric Hamiltonians have been discussed by various authors [1, 2, 3, 4, 5] with some of them focusing speci cally on obtaining the real and discrete energy spectrum. Various methods for solving this problematic Schr odinger equation will be considered. After starting with perturbation theory, we will move on to numerical methods. Three di erent categories of methods will be discussed. First there is the shooting method based on a Runge-Kutta solver. Next, we investigate various implementations of the spectral method. Finally, we will look at the Riccati-Pad e method, which is a numerical implemented analytical method. PT -symmetric potentials need to be solved along a contour in the complex plane. We will propose modi cations to the numerical methods to handle this. After solving the widely documented PT -symmetric Hamiltonian H = p2 (ix)N with these methods, we give a discussion and comparison of the obtained results. Finally, we solve another PT -symmetric potential, illustrating the use of paths in the complex plane to obtain a real and discrete spectrum and their in uence on the results.
39
Chen, Guanlu. "Calculation of well productivity by analytical and numerical simulators." Thesis, Heriot-Watt University, 1995. http://hdl.handle.net/10399/1313.
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Selsil, Alana. "Analytical and numerical modelling of a compact catalytic reformer." Thesis, University of Liverpool, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.415761.
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Corney, Ransome Kyle Tyrone. "Numerical, analytical & experimental modelling of channelised gravity currents." Thesis, University of Leeds, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.426853.
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Kelly, Gavin. "An analytical and numerical investigation of liquid crystal defects." Thesis, University of Strathclyde, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.431822.
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Hong, Lan Tuyet. "A numerical and analytical study of the Prandtl equations /." For electronic version search Digital dissertations database. Restricted to UC campuses. Access is free to UC campus dissertations, 2002. http://uclibs.org/PID/11984.
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ESCOBAR, RENATO GUTIÉRREZ. "INVESTIGATION OF HYDRAULIC FRACTURING THROUGH ANALYTICAL AND NUMERICAL MODELS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2016. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=28072@1.
Full textAbstract:
PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIROCOORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
PROGRAMA DE EXCELENCIA ACADEMICA
O processo de fraturamento hidráulico tem sido amplamente usado para aumentar o volume de petróleo e gás extraído na indústria petroleira. Durante a injeção de fluido, uma região determinada do reservatório é fraturada com a finalidade de aumentar a permeabilidade do meio poroso, de tal forma que o fluxo do fluido desde o reservatório para o poço seja favorecido notoriamente. Porém, este processo pode ocasionar danos ambientais tais como contaminação de aguas subterrâneas, vazamentos de gás, fraturas indesejadas nas camadas capeadoras pela injeção de agua e atividade sísmica fazendo primordial um estudo rigoroso do fraturamento hidráulico com a finalidade de reduzir os riscos potenciais associados a esta operação. Umas das metodologias usadas para projetar o fraturamento hidráulico é a simulação computacional. É possível determinar o volume injetado e a potência da bomba de injeção necessária para obter a geometria de fratura (comprimento, abertura e altura) desejada. A modelagem numérica através de elementos coesivos acoplados do processo de fraturamento hidráulico pode ser efetuada considerando o processo transiente ou permanente, tendo geometrias da fratura e curvas de injeção diferentes. Neste trabalho foi simulado numericamente o modelo KGD nos regimes de fluxo transiente e permanente para dois casos de estudo, (1) injeção numa única camada e (2) injeção em três camadas com contraste de tensões e poropressões entre elas. O estudo numérico foi desenvolvido usando o método dos elementos finitos com modelo de zona coesiva no software Abaqus o qual foi comparado com as soluções analíticas do KGD no regime dominado pela rigidez (Vértice-K) para uma camada e de Simonson e Fung para três camadas.
The hydraulic fracturing process has been widely used to improve oil and gas recovery in the petroleum industry. During the fluid injection, the desired section of rock formation is fractured in order to increase the permeability of the medium that can facilitate the flow of oil to a producing well. However, this process can lead to potential environmental risks such as seismic activity, unwanted fractures in cap layers by water injection, water contamination and gas leakage making primordial to develop a rigorous study in order to reduce this environmental risks associated to hydraulic fracturing. One of the studies developed to design the hydraulic fracturing is computational simulation to determine the fluid volume and hydraulic horsepower required in order to produce the wanted fracture geometry (length, opening and height). The numerical modelling of fracturing process by using fully coupled cohesive element hydraulic can be carried out considering either a steady state or a transient analysis, which modify the fracture geometry and injection pressure. In this work, the KGD model is simulated in transient and steady analysis for two cases: (1) injection in a single layer formation and (2) injection in tri-layered formation with stress and porepressure contrast between them. The numerical simulation of a hydraulic fracturing is carried out using the finite element method with the zone cohesive model in Abaqus whose results are compared with analytical solutions of toughness-dominated propagation regime for the one layer formation model and Simonson and Fung analytical solutions for tri-layered formations model.
45
Merxhani, Andi. "Analytical and numerical study of poroelastic wave-seabed interactions." Thesis, University of Cambridge, 2014. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.648743.
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Bezekci, Burhan. "Analytical and numerical approaches to initiation of excitation waves." Thesis, University of Exeter, 2016. http://hdl.handle.net/10871/25434.
Full textAbstract:
This thesis studies the problem of initiation of propagation of excitation waves in one- dimensional spatially extended excitable media. In a study which set out to determine an analytical criteria for the threshold conditions, Idris and Biktashev [68] showed that the linear approximation of the (center-)stable manifold of a certain critical solution yields analytical approximation of the threshold curves, separating initial (or boundary) conditions leading to propagation wave solutions from those leading to decay solutions. The aim of this project is to extend this method to address a wider class of ex- citable systems including multicomponent reaction-diffusion systems, systems with non-self-adjoint linearized operators and in particular, systems with moving critical solutions (critical fronts and critical pulses). In the case of one-component excitable systems where the critical solution is the critical nucleus, we also extend the theory to a quadratic approximation for the purpose of improving the accuracy of the linear approximation. The applicability of the approach is tested through five test problems with either traveling front such as Biktashev model, a simplified cardiac excitation model or traveling pulse solutions including Beeler-Reuter model, near realistic cardiac excitation model. Apart from some exceptional cases, it is not always possible to obtain explicit solution for the essential ingredients of the theory due to the nonlinear nature of the problem. Thus, this thesis also covers a hybrid method, where these ingredients are found numerically. Another important finding of the research is the use of the perturbation theory to find the approximate solution of the essential ingredients of FitzHugh-Nagumo system by using the exact analytical solutions of its primitive ver- sion, Zeldovich-Frank-Kamenetsky equation.
47
Gallizio, Federico. "Analytical and numerical vortex methods to model separated flows." Thesis, Bordeaux 1, 2009. http://www.theses.fr/2009BOR13785/document.
Full textAbstract:
Le problème de la mécanique des fluides, concernant les écoulements décollés derrière des obstacles immobiles ou en mouvement, est traité par l’étude de deux sujets: a) recherches sur l’existence de solutions stationnaires des equations d’Euler et Navier-Stokes pour grands nombres de Reynolds, au-delà des corps caractérisés par pointes ou singularités géométriques; b) analyse du sillage non stationnaire derrière une turbine à axe vertical (VAT). L’étude de ces deux différents régimes d’écoulements, concernant le phénomène du détachement derrière corps émoussés ou profils alaires à haut angle d’incidence, a permis la mise au point de plusieurs techniques analytiques et numériques basées sur le champ de vorticitéThe problem of the separated flows dynamics past obstacles at rest or moving bodies is addressed by means of the study of two topics a) investigation on the existence of some steady solutions of the Euler equations and of the Navier-Stokes equations at large Reynolds number, past bodies characterized by a cusp; b) analysis of the unsteady wake behind a Vertical Axis Turbine (VAT). The survey of such different flow regimes related to the separation phenomenon past bluff bodies or bodies at incidence allowed to devise several numerical and analytical techniques based on the evaluation of the vorticity field
48
Åberg, K. Magnus. "Variance Reduction in Analytical Chemistry : New Numerical Methods in Chemometrics and Molecular Simulation." Doctoral thesis, Stockholm University, Department of Analytical Chemistry, 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-283.
Full textAbstract:
This thesis is based on five papers addressing variance reduction in different ways. The papers have in common that they all present new numerical methods.
Paper I investigates quantitative structure-retention relationships from an image processing perspective, using an artificial neural network to preprocess three-dimensional structural descriptions of the studied steroid molecules.
Paper II presents a new method for computing free energies. Free energy is the quantity that determines chemical equilibria and partition coefficients. The proposed method may be used for estimating, e.g., chromatographic retention without performing experiments.
Two papers (III and IV) deal with correcting deviations from bilinearity by so-called peak alignment. Bilinearity is a theoretical assumption about the distribution of instrumental data that is often violated by measured data. Deviations from bilinearity lead to increased variance, both in the data and in inferences from the data, unless invariance to the deviations is built into the model, e.g., by the use of the method proposed in paper III and extended in paper IV.
Paper V addresses a generic problem in classification; namely, how to measure the goodness of different data representations, so that the best classifier may be constructed.
Variance reduction is one of the pillars on which analytical chemistry rests. This thesis considers two aspects on variance reduction: before and after experiments are performed. Before experimenting, theoretical predictions of experimental outcomes may be used to direct which experiments to perform, and how to perform them (papers I and II). After experiments are performed, the variance of inferences from the measured data are affected by the method of data analysis (papers III-V).
49
Liang, Xiangdong Ph D. Massachusetts Institute of Technology. "Modeling of fluids and waves with analytics and numerics." Thesis, Massachusetts Institute of Technology, 2013. http://hdl.handle.net/1721.1/83696.
Full textAbstract:
Thesis (Ph. D.)--Massachusetts Institute of Technology, Department of Mathematics, 2013.Cataloged from PDF version of thesis.
Includes bibliographical references (pages 133-142).
Capillary instability (Plateau-Rayleigh instability) has been playing an important role in experimental work such as multimaterial fiber drawing and multilayer particle fabrication. Motivated by complex multi-fluid geometries currently being explored in these applications, we theoretically and computationally studied capillary instabilities in concentric cylindrical flows of N fluids with arbitrary viscosities, thicknesses, densities, and surface tensions in both the Stokes regime and for the full Navier-Stokes problem. The resulting mathematical model, based on linear-stability analysis, can quickly predict the breakup lengthscale and timescale of concentric cylindrical fluids, and provides useful guidance for material selections and design parameters in fiber-drawing experiments. A three-fluid system with competing breakup processes at very different length scales is demonstrated with a full Stokes flow simulation. In the second half of this thesis, we study large-scale PDE-constrained microcavity topology optimization. Applications such as lasers and nonlinear devices require optical microcavities with long lifetimes Q and small modal volumes V. While most microcavities are designed mostly by hand using some understanding of the physical principles of the confinement, we let the computer discover its own structures. We formulate and solve a full 3d optimization scheme over all possible 2d-lithography patterns in a thin dielectric film. The key to our formulation is a frequency-averaged local density of states (LDOS), where the frequency averaging corresponds to the desired bandwidth, evaluated by a novel technique: solving a single electromagnetic wave scattering problem at a complex frequency.
by Xiangdong Liang.
Ph.D.
50
Liu, Zhenhui. "Analytical and numerical analysis of iceberg collisions with ship structures." Doctoral thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for marin teknikk, 2011. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-15790.
Full textAbstract:
The scope of the present Ph.D. thesis was to investigate the mechanics of collisions between icebergs and ship structures. Large reservoirs of oil and gas and new sailing routes in the Arctic area are two large motivations for the present research. Human activity in the Arctic demands well-designed naval architectures for facing different kinds of ice loads. According to modern design codes, ship and offshore structures are usually designed under the ultimate limit state (ULS) methods and checked with the accidental limit state (ALS) methods. The methods and assumptions presented in this thesis are only valid for ALS design. This thesis considers three topics related to the iceberg collisions with ship structures: external mechanics, internal mechanics and residual strength assessments. Collisions between icebergs and ship structures are quite complicated processes. For simplicity, this problem was split into its external and internal mechanics. External mechanics talks about the translational and rotational momentum balance. It is believed that the impact mechanics of iceberg collisions with ship structures should be presented in three dimensions. Thus, a new formulation of impact mechanics was proposed that describes the impact in three dimensions. All forces except for impact force are neglected. This new three-dimensional method degrades to existing two dimension (2D) method. It was successfully applied to the calculation of the demanded dissipated energy for iceberg and ship collisions. Internal mechanics deal with both deformations of icebergs and ship structures. Nonlinear finite-element analysis (NLFEA) was used in this research. The commercial code LS-DYNA 971 was used to assess the internal mechanics of both icebergs and ship structures. Deformations of both icebergs and ship structures should be well captured by numerical simulations. However, due to the difficulties of simulating ice, NLFEA is not straightforward. To facilitate such simulations, a plasticity-based material model for icebergs was developed in this thesis. Iceberg crack propagation was simulated by element erosion. An empirical failure criterion for detecting those failed ice elements is proposed. Numerical examples showed that the new iceberg model gives good results. The model was successfully implemented in LS-DYNA 971 through a user-defined subroutine. Subsequently, the integrated numerical analysis of iceberg-ship collisions was then successfully performed. Efforts were made to investigate the internal mechanics of both icebergs and ship structures during collision, such as local structural behaviours and ice failure. Two scenarios of iceberg-ship collisions were investigated: iceberg collisions with foreship and side-ship structures. In the first scenario, efforts focused on the investigation of the detailed internal mechanics of the icebergs and ship structures. The strength of ship structures was varied by adjusting the parameters of the steel material model, thereby varying the relative strength of icebergs and ship structures. A comprehensive discussion is based on the simulation results. The discussion addresses contact pressure, iceberg shapes and collision locations. In the second scenario, investigations focused on the influences of the iceberg shapes. Simple iceberg shapes representing “sharp” and “blunt” icebergs were used. The results show that “blunt” icebergs may behave as rigid bodies. Finally, the residual strengths of the ship structures after impact, which may be caused by the icebergs, was assessed. A simple plasticity method and a single stiffener model were developed to quantify the residual strengths of the damaged ship structures. In the simple plasticity method, elastic and rigid-plastic methods were combined to derive the end-shortening curve for damaged stiffeners. In the single stiffener model, proper boundary conditions were proposed. Both methods were verified against numerical simulations. Generally, good results were obtained. From this work, a rapid method to assess the residual strength of damaged ship structures is suggested.