Dissertations / Theses on the topic 'Thin Film Equation'
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Walker, Tanya L. M. "Symmetry-enhancing for a thin film equation." Thesis, View thesis, 2008. http://handle.uws.edu.au:8081/1959.7/43978.
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This thesis is concerned with the construction of new one-parameter symmetry groups and similarity solutions for a generalisation of the one-dimensional thin film equation by the method of symmetry-enhancing constraints involving judicious equation-splitting. Firstly by Lie classical analysis we obtain symmetry groups and similarity solutions of this thin film equation. Via the Bluman-Cole non-classical procedure, we then construct non-classical symmetry groups of this thin film equation and compare them to the classical symmetry groups we derive for this equation. Next we apply the method of symmetry-enhancing constraints to this thin film equation, obtaining new Lie symmetry groups for this equation. We construct similarity solutions for this thin film equation in association with these new groups. Subsequently we retrieve further new symmetry groups for this thin film equation by an approach combining the method of symmetry-enhancing constraints and the Bluman-Cole non-classical procedure. We derive similarity solutions for this thin film equation in connection with these new groups. Then we incorporate nontrivial functions into a partition (of this thin film equation) which has previously led to new Lie symmetry groups. The resulting system admits new Lie symmetry groups. We recover similarity solutions for this system and hence for the thin film equation in question. Finally we attempt to derive potential symmetries for this thin film equation but our investigations reveal that none occur for this equation.
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Walker, Tanya L. M. "Symmetry-enhancing for a thin film equation." View thesis, 2008. http://handle.uws.edu.au:8081/1959.7/43978.
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Thesis (Ph.D.)--University of Western Sydney, 2008.A thesis presented to the University of Western Sydney, College of Health and Science, School of Computing and Mathematics, in fulfilment of the requirements for the degree of Doctor of Philosophy - Science. Includes bibliographies.
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Lattimer, Timothy Richard Bislig. "Singular partial integro-differential equations arising in thin aerofoil theory." Thesis, University of Southampton, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.243192.
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Nana, Sandjo Albert [Verfasser]. "Solutions for fourth-order parabolic equation modeling epitaxial thin film growth / Albert Nana Sandjo." Aachen : Hochschulbibliothek der Rheinisch-Westfälischen Technischen Hochschule Aachen, 2012. http://d-nb.info/1025882253/34.
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Fischer, Julian [Verfasser], and Günther [Akademischer Betreuer] Grün. "Optimal Estimates on Front Propagation for the Thin-Film Equation and Other Fourth-Order Parabolic Equations / Julian Fischer. Betreuer: Günther Grün." Erlangen : Universitätsbibliothek der Universität Erlangen-Nürnberg, 2013. http://d-nb.info/1036774899/34.
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Brown, Robert Winston, and rwb@rmit edu au. "Electrical and Thermal Modelling of Low Power Metallised Polypropylene Capacitors." RMIT University. Electrical and Computer Engineering, 2007. http://adt.lib.rmit.edu.au/adt/public/adt-VIT20080130.155318.
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Metallised polypropylene (MPP) capacitors, the dominant capacitor type used in a wide range of power and electronic circuit applications, offer high volumetric capacitor density, low cost, excellent frequency characteristics and a unique ability to recover from point failures in the dielectric film. However MPP capacitors have a generic weakness that is not well understood, failure of the self-healing process leading to ongoing catastrophic failure. The work described in this thesis includes the derivation of an improved electrical model of a capacitor and the uncovering of a mechanism for the catastrophic failure mode. Corrosion of the thin metallic field is firmly linked to drastic increases in metal film current densities and generation of hot spots in capacitors. In the work, novel formulae were derived relating capacitor parameters such as equivalent series resistance and equivalent series capacitance to frequency and physical characteristics such as metal film resistivity and physical dimensions of multiple layer capacitors. Modelling using numerical methods and diffusion equation showed that capacitors with double-end connection topology have more uniform voltage and power distribution than single-end connected capacitors. External characteristics of both connection topologies were shown to be virtually identical up to frequencies well above typical self-resonance. The aggregate spatial distribution of power from both layers and the voltage across the dielectric were found to be fundamentally different in the two circuit connection topologies. In this work it was shown that above singularity frequencies defined by distributed capacitance and metal film spreading resistance, equivalent series resistance and capacitance both fall with the square root of frequency Analysis of the inductance of typical MPP capacitors for single-end and double-end connected topologies and for circumferentially connected capacitor metallization showed that the magnitude and effect of distributed inductance in typical MPP power capacitors was insignificant compared to packaging inductance. Thermal and electrical modelling and experimental measurements showed that corrosion effects could readily account for the generic catastrophic failure mode of metallised polypropylene capacitors. Modelling showed that remnant vestiges of metal bridging corrosion gaps between the schooping and the metallic film could also pose serious thermal danger to the affected capacitor. Fusing current modelling and experimental measurement showed that fusing in metallic films typically occurred for current densities of several hundred thousand amperes per square centimetre. The partial disconnection of the metallic layers from the schooping edge by corrosion for example, was shown to result in large increases in dissipation factor and power loss in a capacitor readily explaining how capacitors
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Mittal, Arpit. "Monte-Carlo Study of Phonon Heat Conduction in Silicon Thin Films." The Ohio State University, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=osu1259602975.
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John, Dominik [Verfasser]. "Uniqueness and Stability near Stationary Solutions for the Thin-Film Equation in Multiple Space Dimensions with Small Initial Lipschitz Perturbations / Dominik John." Bonn : Universitäts- und Landesbibliothek Bonn, 2013. http://d-nb.info/104527626X/34.
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Hubartt, Bradley C. "Nucleation and Growth, Defect Structure, and Dynamical Behavior of Nanostructured Materials." University of Toledo / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1416828345.
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Bara, Richard J. "Rupture point movement in journal bearings." Link to electronic thesis, 2004. http://www.wpi.edu/Pubs/ETD/Available/etd-0607104-105624/.
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Fabricius, John. "Homogenization of some problems in hydrodynamic lubrication involving rough boundaries." Doctoral thesis, Luleå tekniska universitet, Matematiska vetenskaper, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-25734.
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This thesis is devoted to the study of some homogenization problems with applications in lubrication theory. It consists of an introduction, five research papers (I–V) and a complementary appendix.Homogenization is a mathematical theory for studying differential equations with rapidly oscillating coefficients. Many important problems in physics with one or several microscopic scales give rise to this kind of equations, whence the need for methods that enable an efficient treatment of such problems. To this end several mathematical techniques have been devised. The main homogenization method used in this thesis is called multiscale convergence. It is a notion of weak convergence in Lp spaces which is designed to take oscillations into account. In paper II we extend some previously obtained results in multiscale convergence that enable us to homogenize a nonlinear problem with a finite number of microscopic scales. The main idea in the proof is closely related to a decomposition of vector fields due to Hermann Weyl. The Weyl decomposition is further explored in paper III.Lubrication theory is devoted to the study of fluid flows in thin domains. More generally, tribology is the science of bodies in relative motion interacting through a mechanical contact. An important aspect of tribology is to explain the principles of friction, lubrication and wear. The mathematical foundations of lubrication theory are given by the Navier–Stokes equation which describes the motion of a viscous fluid. In thin domains several simplifications are possible, as shown in the introduction of this thesis. The resulting equation is named after Osborne Reynolds and is much simpler to analyze than the Navier--Stokes equation.The Reynolds equation is widely used by engineers today. For extremely thin films, it is well-known that the surface micro-topography is an important factor in hydrodynamic performance. Hence it is important to understand the influence of surface roughness with small characteristic wavelengths upon the solution of the Reynolds equation. Since the 1980s such problems have been increasingly studied by homogenization theory. The idea is to replace the original equation with a homogenized equation where the roughness effects are “averaged out”. One problem consists of finding an algorithm for computing the solution of the homogenized equation. Another problem consists of showing, on introducing the appropriate mathematical definitions, that the homogenized equation is the correct method of averaging. Papers I, II, IV and V investigate the effects of surface roughness by homogenization techniques in various situations of hydrodynamic lubrication. To compare the homogenized solution with the solution of the deterministic Reynolds equation, some numerical examples are also included.Godkänd; 2011; 20110408 (johfab); DISPUTATION Ämnesområde: Matematik/Mathematics Opponent: Professor Guy Bayada, Institut National des Sciences Appliquées de Lyon (INSA-LYON), Lyon, France, Ordförande: Professor Lars-Erik Persson, Institutionen för teknikvetenskap och matematik, Luleå tekniska universitet Tid: Tisdag den 7 juni 2011, kl 10.00 Plats: D2214/15, Luleå tekniska universitet
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McKinley, Iain Stewart. "Studies in thin film flows." Thesis, University of Strathclyde, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.366911.
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Brüll, Gabriele [Verfasser]. "Two-phase thin film equations with insoluble surfactant / Gabriele Brüll." Hannover : Technische Informationsbibliothek und Universitätsbibliothek Hannover (TIB), 2015. http://d-nb.info/1076059619/34.
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Alharbi, Abdulghani Ragaa. "Numerical solution of thin-film flow equations using adaptive moving mesh methods." Thesis, Keele University, 2016. http://eprints.keele.ac.uk/2356/.
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Thin liquid films are found everywhere in nature. Their flows play a fundamental role in a wide range of applications and processes. They are central to a number of biological, industrial, chemical, geophysical and environmental applications. Thin films driven by external forces are susceptible to instabilities leading to the break-up of the film into fingering-type patterns. These fingering-type patterns are usually undesirable as they lead to imperfections and dry spots. This behaviour has motivated theoreticians to try to understand the behaviour of the flow and the mechanisms by which these instabilities occur. In the physically relevant case when surface tension is large, the film’s free surface exhibits internal layers where there is rapid spatial variation in the film’s curvature over very short lengthscales and away from these internal layers the film’s curvature is almost negligible. This provides the main motivation for this thesis which is to develop adaptive numerical solution techniques for thin film flow equations that fully resolve such internal layers in order to obtain accurate numerical solutions. We consider two thin film flow problems in one and two-dimensions to test the adaptive numerical solution techniques developed in this thesis. The first problem we consider is related to a liquid sheet or drop spreading down an inclined pre-wetted plane due to influence of gravity. The second problem we consider is also related to the spreading of a liquid sheet or drop down an inclined pre-wetted plane including surfactant-related effects in addition to gravity. We follow the r-adaptive moving mesh technique which uses moving mesh partial differential equations (MMPDEs) to adapt and move the mesh coupled to the underlying PDE(s). We show how this technique can accurately resolve the various one and two-dimensional structures observed in the above test problems as well as reduce the computational effort in comparison to numerical solutions using a uniform mesh.
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Beerman, Michael. "Transverse freezing of thin liquid films /." Thesis, Connect to this title online; UW restricted, 2007. http://hdl.handle.net/1773/10573.
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Groh, Christian Michael. "Asymptotic and numerical studies of nonlinear evolution equations of viscous thin-film flows." Thesis, University of Leeds, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.534751.
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Goodnight, Randall James Truett. "Derivation of an Evolution Equation for Two-Dimensional Waves on Thin Films." Thesis, Virginia Tech, 2013. http://hdl.handle.net/10919/23125.
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We examine wave propagation on thin liquid films subjected to gravity, fluid friction, surface tension, and Marangoni effects. The physical configuration is a thin liquid layer on a planar incline. Following previous studies, the Marangoni effect is incorporated by a constant surface tension gradient and yields a non-convex flux function in our thin film equation. We extend previous studies by deriving the thin film equation governing two-dimensional waves on the liquid layer. We then derive a simplified evolution equation governing weakly nonlinear, quasi-planar, and weakly dissipative waves on the layer. When the undisturbed state is in the vicinity of an inflection point in the streamwise component of the flux function, the mixed nonlinearity, fourth order dissipation and the transverse modulations interact over time scales on the order of the scaled amplitude to the negative second power. The effect the transverse modulations is found to be intrinsically nonlinear.Master of Science
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Ulusoy, Suleyman. "The Mathematical Theory of Thin Film Evolution." Diss., Georgia Institute of Technology, 2007. http://hdl.handle.net/1853/16213.
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We try to explain the mathematical theory of thin liquid film evolution. We start with introducing physical processes in which thin film evolution plays an important role. Derivation of the classical thin film equation and existing mathematical theory in the literature are also introduced.
To explain the thin film evolution we derive a new family of degenerate parabolic equations. We prove results on existence, uniqueness, long time behavior, regularity and support properties of solutions for this equation.
At the end of the thesis we consider the classical thin film Cauchy problem on the whole real line for which we use asymptotic equipartition to show H^1(R) convergence of solutions to the unique self-similar solution.
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Peschka, Dirk. "Self-similar rupture of thin liquid films with slippage." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2009. http://dx.doi.org/10.18452/15923.
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In der vorliegenden Arbeit wird das Entstehen von Singularitäten an Oberflächen von dünnen Flüssigkeitsfilmen studiert. Unter einer Singularität versteht man hier das plötzliche Aufreißen einer Flüssigkeitsoberfläche an einer Stelle. Nach einer Diskussion physikalischer Phänomene, wird ein 2D Modell zur Beschreibung von Flüssigkeitsfilmen hergeleitet. Dieses Modell beinhaltet u.a. Oberflächenspannung, van der Waals''sche Kräfte und eine Navier-slip Randbedingung (Schlupf-Randbedingung) zwischen Substrat und Flüssigkeit, d.h. die Flüssigkeite haftet nicht an der Grenzfläche zum Substrat. Dieses Phänomen wird vor allen Dingen im Nano- und Mikrometerbereich beobachtet. Dieses Modell wird vereinfacht und man erhält die sogenannte "strong-slip" Gleichung. In dieser Dissertation werden verschiedene Ansätze verfolgt, um die Singularität der Flüssigkeitsoberfläche zu beschreiben. Der Entstehungsprozess der Singularität wird durch die lineare Stabilitätsuntersuchung beschrieben. Da die Linearisierung schnell ihre Gültigkeit verliert, wird das nichtlineare Verhalten der Singularität mit einem numerischen Verfahren beschrieben. Das dazu hier konstruierte Finite-Differenzen-Schema besitzt eine hohe räumliche und zeitliche Genauigkeit. Dadurch können verschiedene Regime, in denen die Singularität eine selbstähnliche Dynamik besitzt, untersucht und beschrieben werden. Im zweiten Teil der Arbeit werden die Gleichungen weiter vereinfacht. Dadurch können qualitative Eigenschaften der Singularitätsentstehung bewiesen werden. Weiterhin kann so eine Verbindung zu Modellen der Ostwald-Reifung hergestellt werden und man gelangt zu ähnlichen mathematischen Aussagen wie für selbstähnliche Vergröberungsprozesse. Insbesondere wird in der Arbeit gezeigt, dass die Singularität nach endlicher Zeit auftritt. Für das vereinfachte Problem werden hinreichende und notwendige Bedingungen für selbstähnliches Verhalten angegeben.In this thesis we study the formation of surface singularites of thin liquid films, i.e., rupture of thin liquid films. First, important physical phenomena are discussed and a two-dimensional model for thin-film rupture is derived . That model contains surface tension, van der Waals forces between a liquid and a underlying substrate, and a Navier-slip condition. Using the thin-film hypothesis, this model is simplified and one obtains the so-called strong-slip equation. The phenomenon slip, where the velocity of the liquid is non-zero at a fluid-solid interface, is particularly important at microscopic length scales. In this text we study interfacial singularities with various approaches. The creation of a singularity is described by a linear stability analysis. The non-linear behavior is investigated by a numerical analysis. A finite-difference scheme is used to study the non-linear self-similar dynamics of the singularity. In the second part of this thesis the equations are further simplified. This allows to study qualitative properties of the singularity formation. Furthermore, we can establish a correspondence to models for Ostwald rippending and obtain similar mathematical statements as they are known for self-similar coarsening processes. In particular it is shown that rupture happens after a finite time. In addition, necessary and sufficient condition for self-similar rupture are proven.
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Carballo, Jose M. "Residual Stress Analysis in 3C-SiC Thin Films by Substrate Curvature Method." Scholar Commons, 2010. https://scholarcommons.usf.edu/etd/1590.
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Development of thin films has allowed for important improvements in optical, electronic and electromechanical devices within micrometer length scales. In order to grow thin films, there exist a wide variety of deposition techniques, as each technique offers a unique set of advantages. The main challenge of thin film deposition is to reach smallest possible dimensions, while achieving mechanical stability during operating conditions (including extreme temperatures and external forces, complex film structures and device configurations). Silicon carbide (SiC) is attractive for its resistance to harsh environments, and the potential it offers to improve performance in several microelectronic, micro-electromechanical, and optoelectronic applications. The challenge is to overcome presence of high defect densities within structure of SiC while it is grown as a crystalline thin film. For this reason is important to monitor levels of residual stress, inherited from such grown defects, and which can risk the mechanical stability of SiC- made thin film devices.
Stoney's equation is the theoretical foundation of the curvature method for measuring thin film residual stress. It connects residual film stress with substrate curvature through thin plates bending mechanics. Important assumptions and vii simplifications are made about the film-substrate system material properties, dimensions and loading conditions; however, accuracy is reduced upon applying such simplifications. In recent studies of cubic SiC growth, certain Stoney's equation assumptions are violated in order to obtain approximate values of residual stress average. Furthermore, several studies have proposed to expand the scope of Stoney's equation utility; however, such expansions demand of more extensive substrate deflection measurements to be made, before and after film deposition.
The goal of this work is to improve the analysis of substrate deflection data, obtained by mechanical profilometry, which is a simple and inexpensive technique. Scatter in deflection data complicates the use of simple processes such as direct differentiation or polynomial fitting. One proposed method is total variation regularization of differentiation process; and results are promising for the adaptation of mechanical profilometry for complete measurement of all components of non-uniform substrate curvature.
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Hurst, Jerome. "Ultrafast spin dynamics in ferromagnetic thin films." Thesis, Strasbourg, 2017. http://www.theses.fr/2017STRAE004/document.
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Dans cette thèse, on s’intéresse à l'étude théorique et à la simulation numérique de la dynamique de charges et de spins dans des nano-structures métalliques. Ces dernières années la physique des nano-structures métalliques à connu un intérêt croissant, aussi bien d'un point de vue de la physique fondamental que d'un point de vue des applications technologiques. Il est donc essentiel d'avoir des modèles théoriques nous permettant de décrire correctement ce type d'objets. Cette thèse comporte deux études distinctes. Dans un premier temps on utilise un modèle semi-classique dans l'espace des phases afin d'étudier la dynamique de charges et de spins dans des films ferromagnétiques(Nickel). On décrit dans le même modèle le magnétisme itinérant et le magnétisme localisé. On montre qu'il est possible, en excitant le système avec un laser pulsé femtoseconde dans le domaine du visible, de créer un courant de spin oscillant dans la direction normal du film sur des temps ultrarapides(femtoseconde). Dans un second temps on s’intéresse à la dynamique de charge d'électrons confinés dans des nano-particules d'Or ou bien encore par des potentiels anisotropes. On montre que de telles systèmes sont des candidats intéressant pour faire de la génération d'harmoniquesIn this thesis we focus on the theoritical description and on the numerical simulation of the charge and spin dynamics in metallic nano-structures. The physics of metallic nano-structures has stimulated a huge amount of scientific interest in the last two decades, both for fundamental research and for potential technological applications. The thesis is divided in two parts. In the first part we use a semiclassical phase-space model to study the ultrafast charge and spin dynamics in thin ferromagnetic films (Nickel). Both itinerant and localized magnetism are taken into account. It is shown that an oscillating spin current can be generated in the film via the application of a femtosecond laser pulse in the visible range. In the second part we focus on the charge dynamics of electrons confined in metallic nano-particles (Gold) or anisotropic wells. We show that such systems can be used for high harmonic generation
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Rouxel, Yann. "Coévaporation avec masquage mécanique de ZnSe et de LaF3, pour la réalisation de couches minces à profils d'indice continus périodiques." Université Joseph Fourier (Grenoble), 1996. http://www.theses.fr/1996GRE10096.
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Dans une etude theorique des structures a profil d'indice continu, il est montre que l'essentiel des proprietes spectrales des filtres a profil d'indice sinusoidal peut etre etudie de maniere analytique a partir de certaines proprietes de l'equation de mathieu. L'etude experimentale de ces structures a ete realisee a l'aide d'une technique de coevaporation par masquage mecanique. L'equipement de depot realisant la coevaporation a ete developpe pour permettre la realisation de couches sur substrat chaud pour des profils d'indice quelconques. Un systeme de mesure optique multispectral in-situ en reflectivite a egalement ete mis au point. Les proprietes des couches minces de melanges de znse et de laf3 ont ete etudiees pour toute la gamme de composition. Un schema d'evolution de la structure cristalline et de la porosite des couches en fonction de leur composition est propose. Les contraintes qui s'y developpent sont aussi analysees ainsi que leur evolution en fonction de l'environnement. L'etude des proprietes optiques a permis de definir les lois de melange ainsi que de mettre en evidence l'existence d'une birefringence evoluant avec la composition des melanges. Enfin, plusieurs types de structures periodiques ont ete realisees, comportant jusqu'a 20 periodes pour une epaisseur superieure a 5m. Les resultats ont permis de montrer que la modulation par masquage mecanique est une technique fiable et precise et que c'est le choix du couple de materiaux qui va conditionner la precision du controle du profil d'indice
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Noakes, Caroline. "The dynamics of liquid films on rotating surfaces." Thesis, University of Nottingham, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.368933.
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Heryudono, Alfa R. H. "Adaptive radial basis function methods for the numerical solution of partial differential equations, with application to the simulation of the human tear film." Access to citation, abstract and download form provided by ProQuest Information and Learning Company; downloadable PDF file, 178 p, 2008. http://proquest.umi.com/pqdweb?did=1601513551&sid=5&Fmt=2&clientId=8331&RQT=309&VName=PQD.
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Qiqi, Kristos. "Finite Element Approximation of a Moving Boundary Problem Arising in the Modeling of the Spin Coating Process for Thin Films." Thesis, Karlstads universitet, Institutionen för matematik och datavetenskap (from 2013), 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-78234.
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Using the Navier-Stokes equations along with a continuity equation, a one-dimensional model is developed to describe the spin coating process of thin polymeric films. The resulting model is a system of a parabolic partial differential equation coupled with an integral equation as well as with an ordinary differential equation describing the motion of a moving boundary. Viscosity and diffusivity are allowed to be varied in the model. To be able to perform the finite element approximation of the model equations, the moving boundary is fixed. Then the finite element method is applied along with the so called Method of Lines resulting in a semi-discrete problem, a large system of ordinary differential equations which is then solved with MATLAB. We present an existence and uniqueness result what concerns the semi-discrete solutions. Finally, we illustrate numerically the behavior of the solutions to our model.
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Alriyabi, Ali. "Analyse de quelques équations différentielles à retard et EDP modélisant les instabilités de surfaces." Thesis, Poitiers, 2013. http://www.theses.fr/2013POIT2255/document.
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Cette thèse est divisée en deux parties principales : La première partie concerne la déformation plastique d'un matériau contraint. Nous commençons cette partie par une introduction physique sur la dislocation et son rôle dans l'étude de la déformation plastique. Nous exposons ensuite deux types de modélisation de la déformation plastique ce qui nous conduit à deux équations différentielles à retard de Mecking-Lüke-Grilhé. Nous présentons une analyse mathématique complète des deux modèles linéaire et non linéaire. Nous terminons cette partie par des tests numériques et une comparaison des deux modèles. La deuxième partie de la thèse traite l'instabilité de Rayleigh-Plateau. Cette étude porte sur les instabilités de surface d'un pore cylindrique sans contraintes. Nous nous intéressons à une EDP parabolique non linéaire d'ordre quatre, obtenue à partir d'une équation d'évolution des films minces. Le résultat principal est l'existence globale de la solution et la convergence vers la valeur moyenne de la donnée initiale en temps long. L'étude théorique est aussi appuyée comme dans la première partie par une validation numériqueThis thesis is divided into two main parts: The first part relates to the plastic deformation of a constrained material. We begin this part by physical introduction on the dislocation and its role in the study of plastic deformation. We also present two types modelling for the plastic deformation, which leads to two delayed differential equations of Mecking-Lücke-Grilhé. We present a complete mathematical analysis of linear and nonlinear models. We conclude this part by numerical tests and a comparison of the two models. The second part of the thesis treats the Rayleigh-Plateau instability. This study focuses on the surface instabilities of a cylindrical pore without constraints. We are interested in a nonlinear parabolic PDE of fourth order, obtained from an evolution equation model of thin films. The main result is the global existence of the solution and the convergence to the average value of the initial data in long time. Numerical validation of the theoretical results is also presented in this part
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Anderson, Tom Harper. "Optoelectronic simulation of nonhomogeneous solar cells." Thesis, University of Edinburgh, 2016. http://hdl.handle.net/1842/25892.
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This thesis investigates the possibility of enhancing the efficiency of thin film solar cells by including periodic material nonhomogeneities in combination with periodically corrugated back reflectors. Two different types of solar cell are investigated; p-i-n junctions solar cells made from alloys of hydrogenated amorphous silicon (a-Si:H) (containing either carbon or germanium), and Schottky barrier junction solar cells made from alloys of indium gallium nitride (InξGa1-ξN). Material nonhomogeneities are produced by varying the fractions of the constituent elements of the alloys. For example, by varying the content of carbon or germanium in the a-Si:H alloys, semiconductors with bandgaps ranging from 1:3 eV to 1:95 eV can be produced. Changing the bandgap alters both the optical and electrical properties of the material so this necessitates the use of coupled optical and electrical models. To date, the majority of solar cell simulations either prioritise the electrical portion of the simulation or they prioritise the optical portion of the simulation. In this thesis, a coupled optoelectronic model, developed using COMSOL Multiphysics®, was used to simulate solar cells: a two-dimensional finite-element optical model, which solved Maxwell's equations throughout the solar cells, was used to calculate the absorption of incident sunlight; and a finite-element electrical drift-diffusion transport model, either one- or two-dimensional depending on the symmetries of the problem, was used to calculate the steady state current densities throughout the solar cells under external voltage biases. It is shown that a periodically corrugated back reflector made from silver can increase efficiency of an a-Si:H alloy single p-i-n junction solar cell by 9:9% compared to a baseline design, while for a triple junction the improvement is a relatively meagre 1:8%. It is subsequently shown that the efficiency of these single p-i-n junction solar cells with a back reflector can be further increased by the inclusion of material nonhomogeneities, and that increasing the nonhomogeneity progressively increases efficiency, especially in thicker solar cells. In the case of InξGa1-ξN Schottky barrier junction solar cells, the gains are shown to be even greater. An overall increase in efficiency of up to 26:8% over a baseline design is reported.
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Nery, Fábio. "Minimização da energia de deformação de filmes finos com substratos espessos." Universidade do Estado de Santa Catarina, 2009. http://tede.udesc.br/handle/handle/2000.
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O objetivo deste trabalho é a obtenção de um modelo tridimensional, que descreva as tensões que surgem em filmes finos depositados em substratos espessos planos. Para isto é utilizado o método da minimização da energia de deformação da amostra (filme fino/substrato), já descrito e utilizado na literatura para uma descrição unidimensional do problema. A vantagem deste método é sua maior simplicidade em relação a uma abordagem tensorial do problema, uma vez que envolve uma grandeza escalar (energia de deformação) de identificação mais simples que as diversas componentes de um tensor de tensões. Após a apresentação do problema físico e da metodologia, é feita a aplicação a duas situações de interesse: para uma amostra submetida a valores de tensão menos elevados, adquirindo uma forma proximadamente esférica e para uma amostra submetida a valores mais elevados de tensão, adquirindo uma forma aproximadamente cilíndrica. Nestes dois casos se obteve uma fórmula que relaciona a linha de tensão do filme com a curvatura da amostra, que é então comparada com outras formulações.
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Simon, Amélie. "Modélisation des phénomènes de films liquides dans les turbines à vapeur." Thesis, Lyon, 2017. http://www.theses.fr/2017LYSEC001/document.
Full textAbstract:
Dans la production d'électricité, un des leviers centraux pour réduire les détériorations et les pertes causées par l'humidité dans les turbines à vapeur est l'étude des films liquides. Ces films minces, sont créés par la déposition de gouttes et sont fortement cisaillés. Des gouttes peuvent ensuite être arrachées du film. A l'heure actuelle, aucun modèle complet et valide n'existe pour décrire ce phénomène. Un modèle 2D à formulation intégrale associé à des lois de fermetures a été dérivé pour représenter ce film. Comparé aux équations classiques de Saint-Venant, le modèle prend en compte davantage d'effets : le transfert de masse, l'impact des gouttes, le cisaillement à la surface libre, la tension de surface, le gradient de pression et la rotation. Une analyse des propriétés du modèle (hyperbolicité, entropie, conservativité, analyse de stabilité linéaire, invariance par translation et par rotation) est réalisée pour juger de la pertinence du modèle. Un nouveau code 2D est implémenté dans un module de développement libre du code EDF Code Saturne et une méthode de volumes finis pour un maillage non-structure a été développée. La vérification du code est ensuite effectuée avec des solutions analytiques dont un problème de Riemann. Le modèle, qui dégénère en modèle classique de Saint-Venant pour le cas d'un film tombant sur un plan inclinée, est validé par l'expérience de Liu and Gollub, 1994, PoF et comparé à des modèles de références (Ruyer-Quil and Manneville, 2000, EPJ-B et Lavalle, 2014, PhD thesis). Un autre cas d'étude met en scène un film cisaillé en condition basse-pression de turbine à vapeur et, est validé par l'expérience de Hammitt et al., 1981, I. Enfin, le code film est couplé aux données 3D du champ de vapeur autour d'un stator d'une turbine basse-pression du parc EDF, issues de Blondel, 2014, PhD thesis. Cette application industrielle montre la faisabilité d'une simulation d'un film en condition réelle du turbine à vapeurIn the electricity production, one central key to reduce damages and losses due to wetness in steam turbines is the study of liquid films. These thin films are created by the deposition of droplets and are highly sheared. This film may then be atomized into coarse water. At the moment, no comprehensive and validated model exists to describe this phenomenon. A 2D model based on a integral formulation associated with closure laws is developed to represent this film. Compared to classical Shallow-Water equation, the model takes into account additional effect : mass transfer, droplet impact, shearing at the free surface, surface tension, pressure gradient and the rotation. The model properties (hyperbolicity, entropy, conservativity, linear stability, Galilean invariance and rotational invariance) has been analyzed to judge the pertinence of the model. A new 2D code is implemented in a free module of the code EDF Code Saturne and a finite volume method for unstructured mesh has been developed. The verification of the code is then carried out with analytical solutions including a Riemann problem. The model, which degenerates into classical Shallow-Water equations for the case of a falling liquid film on a inclined plane, is validated by the experiment of Liu and Gollub, 1994, PoF and compared to reference models (Ruyer-Quil and Manneville, 2000, EPJ-B et Lavalle, 2014, PhD thesis). Another study depicts a sheared film under low-pressure steam turbine conditions and is validated by the experiment of Hammitt et al., 1981, FiI. Lastly, the code film is coupled to 3D steam data around a fixed blade of a BP100 turbine, from Blondel, 2014, PhD thesis. This industrial application shows the feasibility of liquid film's simulation in real steam turbine condition
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Volpert, Thibault. "Étude d'un schéma différences finies haute précision et d'un modèle de fil mince oblique pour simuler les perturbations électromagnétiques sur véhicule aérospatial." Thesis, Toulouse, ISAE, 2014. http://www.theses.fr/2014ESAE0042/document.
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Les travaux de cette thèse concerne l’étude d’une méthode élément finis d’ordre spatial élevé que l’on peut assimilé à une extension du schéma de Yee. On parle alors de méthode différences finies d’ordre élevé. Après avoir donné, dans un premier chapitre, un historique non exhaustif des principales méthodes utilisées pour résoudre les équations de Maxwell dans le cadre de problèmes de CEM et montré l’ intérêt de disposer d’un solveur de type "différences finies d’ ordre élevé", nous présentons dans un deuxième chapitre le principe de la méthode. Nous donnons pour cela les caractéristiques du schéma spatial et temporel en précisant les conditions de stabilité de la méthode. En outre, dans une étude purement numérique, nous étudions la convergence du schéma. On se focalise ensuite sur la possibilité d’utiliser des ordres spatiaux variable par cellules dans chaque direction de l’espace. Des comparaisons avec le schéma de Yee et un schéma de Galerkin Discontinu particulier sont ensuite effectuées pour montrer les gains en coûts calcul et mémoire et donc l’intérêt de notre approche par rapport aux deux autres. Dans un troisième chapitre, nous nous intéressons à l’étude de modèles physiques indispensable au traitement d’un problème de CEM. Pour cela, nous nous focalisons particulièrement sur un modèle de fil mince oblique, des modèles de matériaux volumiques et minces et enfin sur la prise en compte de sol parfaitement métallique dans une agression de type onde plane. Chaque modèle est détaillé et validé par comparaison avec des solutions analytiques ou résultant de la littérature, sur des exemples canoniques. Le quatrième chapitre est dédié à une technique d’hybridation entre notre méthode et une approche Galerkin Discontinu en vue de traiter des géométries possédant des courbures. Nous donnons pour cela une stratégie d’hybridation basée sur l’échange de flux qui garantie au niveau continue la conservation d’une énergie. Nous présentons ensuite quelques exemples montrant la validité de notre approche dans une stratégie multi-domaines/multi-méthodes que nous précisons. Enfin le dernier chapitre de cette thèse concerne l’exploitation de notre méthode sur des cas industriels en comparaisons avec d’autres méthodes ou des résultats expérimentauxThis thesis is about the study of a high spatial finite element method whichcan be assimilated at an extension of the Yee schema. In the next, this method is also called high order finite difference method. In the first chapter, we give a non exhaustive recall of the major methods used to treat EMC problems and we show the necessity to have this kind of schema to simulate efficiently some EMC configurations. In the second chapter, the principle of the numerical method is presented and a stability condition is given. A numerical study analysis of the schema convergence is also done. Next, we show the interest to have the possibility to use local spatial order by cell in each direction of the computational domain. Some canonic examples are given to show the advantages interms of CPU time and memory storage of the method by comparison with Yee’s scheme and DG approach. In the third chapter, we define and validate on several examples,some physical models as thin wire, materials and perfectly metallic ground in presence of a plane wave, to have the possibility to treat EMC problems. The fourth chapter is about a hybridization strategy between our high order FDTD method and a DG schema.We focalize our study on a hybrid method which provides an energy conservation of the continuous problem. A numerical example is given to validate the method. Finally, in the last chapter, we present some simulations on industrial problems to show the possibility of the method to treat realistic EMC problems
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Deymier, Nicolas. "Étude d’une méthode d’éléments finis d’ordre élevé et de son hybridation avec d’autres méthodes numériques pour la simulation électromagnétique instationnaire dans un contexte industriel." Thesis, Toulouse, ISAE, 2016. http://www.theses.fr/2016ESAE0038/document.
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Dans cette thèse, nous nous intéressons à l’amélioration du schéma de Yee pour traiter demanière plus efficace et pertinente les problèmes industriels auxquels nous sommes confrontés à l’heureactuelle. Pour cela, nous cherchons avant tout à diminuer les erreurs numériques de dispersion et àaméliorer les modélisations des géométries courbes ainsi que des réseaux de câbles. Pour répondre àces besoins, une solution basée sur un schéma Galerkin discontinu pourrait être envisagée. Toutefois,l’utilisation d’une telle technique sur la totalité du volume de calcul est relativement coûteuse. De plus,la prise en compte de structures filaires sur un tel schéma n’est pas encore opérationnelle. C’est pourquoi,dans l’optique d’avoir un outil industriel, et après une étude bibliographique, nous nous sommes plutôtorientés sur l’étude d’un schéma éléments finis (FEM) sur maillage cartésien qui possède toutes lesbonnes propriétés du schéma de Yee. Notamment, à l’ordre d’approximation spatiale égal à 0 ce schémaFEM est exactement le schéma de Yee, et, pour des ordres supérieurs, il permet de réduire fortementl’erreur de dispersion numérique de ce dernier. Dans le travail de cette thèse, pour ce schéma, nous avons notamment donné un critère de stabilité théorique, étudié sa convergence théorique et fait une analyse de l’erreur de dispersion. Pour tenircompte des possibilités d’ordre d’approximation spatiale variable par direction, nous avons mis en placeune stratégie d’affectation des ordres suivant le maillage donné. Ceci nous a permis d’obtenir un pas detemps optimal pour une précision souhaitée tout en réduisant les coûts de calcul. Après avoir porté ceschéma sur des machines de production, différents problèmes de CEM, antennes, IEM ou foudre ont ététraités afin de montrer les avantages et le potentiel de celui-ci. En conclusion de ces expérimentationsnumériques, il s’avère que la méthode est limitée par le manque de précision pour prendre en comptedes géométries courbes. Afin d’améliorer cela, nous avons proposé une hybridation entre ce schéma et leschéma GD que l’on peut étendre aux autres schémas comme les méthodes différences finies (FDTD) etvolumes finis (FVTD). Nous avons montré que la technique d’hybridation proposée conserve l’énergie etest stable sous une condition que nous avons évaluée de manière théorique. Des exemples de validationont ensuite été montrés. Enfin, pour tenir compte des réseaux de câbles, un modèle de fils minces d’ordred’approximation spatiale élevé a été proposé. Malheureusement, celui-ci ne peut pas couvrir l’ensembledes cas industriels et pour remédier à cela, nous avons proposé une hybridation de notre approche avecune équation de ligne de transmission. L’intérêt de cette hybridation a été montré sur un certain nombred’exemples, que nous n’aurions pas pu traiter par un modèle de structure filaire simpleIn this thesis, we study the improvement of the Yee’s scheme to treat efficiently and in arelevant way the industrial issues we are facing nowadays. For that, we first of all try to reduce thenumerical errors of dispersion and then to improve the modeling of the curved surfaces and of theharness networks. To answer these needs, a solution based on a Galerkin Discontinuous (GD) methodhas been first considered. However, the use of such method on the entire modeling volume is quite costly ;moreover the wires are not taken into account in this method. That is the reason why, with the objectiveof an industrial tool and after a large bibliographic research, we headed for the study of finite elementsscheme (FEM) on a Cartesian mesh which has all the good properties of the Yee’s scheme. Especially,this scheme is exactly the Yee’s scheme when the spatial order of approximation is set to zero. Forthe higher orders, this new scheme allows to greatly reduce the numerical error of dispersion. In theframe of this thesis and for this scheme, we give a theoretical criterion of stability, study its theoreticalconvergence and we perform an analysis of the error of dispersion. To take into account the possibilityof the variable spatial orders of approximation in each direction, we put in place a strategy of orderaffectation according to the given mesh. This strategy allows to obtain an optimal time step for a givenselected precision while reducing the cost of the calculations. Once this new scheme has been adaptedto large industrial computing means, different EMC, antennas, NEMP or lightning problems are treatedto demonstrate the advantages and the potential of this scheme. As a conclusion of these numericalsimulations we demonstrate that this method is limited by a lack of precision when taking into accountcurved geometries. To improve the treatment of the curved surfaces, we propose an hybridization between this scheme andthe GD scheme. This hybridization can also be applied to other methods such as Finite Differences(FDTD) or Finite Volumes (FVTD). We demonstrate that the technique of hybridization proposed,allows to conserve the energy and is stable under a condition that we study theoretically. Some examplesare presented for validation. Finally and to take into account the cables, a thin wire model with a highorder of spatial approximation is proposed. Unfortunately, this model does not allow to cover all theindustrial cases. To solve this issue we propose an hybridization with a transmission line method. Theadvantage of this hybridization is demonstrated thanks to different cases which would not have beenfeasible with a more simple thin wire method
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Stöcker, Christina. "Level set methods for higher order evolution laws." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2008. http://nbn-resolving.de/urn:nbn:de:bsz:14-ds-1205350171405-81971.
Full textAbstract:
A numerical treatment of non-linear higher-order geometric evolution equations with the level set and the finite element method is presented. The isotropic, weak anisotropic and strong anisotropic situation is discussed. Most of the equations considered in this work arise from the field of thin film growth. A short introduction to the subject is given. Four different models are discussed: mean curvature flow, surface diffusion, a kinetic model, which combines the effects of mean curvature flow and surface diffusion and includes a further kinetic component, and an adatom model, which incorporates in addition free adatoms. As an introduction to the numerical schemes, first the isotropic and weak anisotropic situation is considered. Then strong anisotropies (non-convex anisotropies) are used to simulate the phenomena of faceting and coarsening. The experimentally observed effect of corner and edge roundings is reached in the simulation through the regularization of the strong anisotropy with a higher-order curvature term. The curvature regularization leads to an increase by two in the order of the equations, which results in highly non-linear equations of up to 6th order. For the numerical solution, the equations are transformed into systems of second order equations, which are solved with a Schur complement approach. The adatom model constitutes a diffusion equation on a moving surface. An operator splitting approach is used for the numerical solution. In difference to other works, which restrict to the isotropic situation, also the anisotropic situation is discussed and solved numerically. Furthermore, a treatment of geometric evolution equations on implicitly given curved surfaces with the level set method is given. In particular, the numerical solution of surface diffusion on curved surfaces is presented. The equations are discretized in space by standard linear finite elements. For the time discretization a semi-implicit discretization scheme is employed. The derivation of the numerical schemes is presented in detail, and numerous computational results are given for the 2D and 3D situation. To keep computational costs low, the finite element grid is adaptively refined near the moving curves and surfaces resp. A redistancing algorithm based on a local Hopf-Lax formula is used. The algorithm has been extended by the authors to the 3D case. A detailed description of the algorithm in 3D is presented in this workIn der Arbeit geht es um die numerische Behandlung nicht-linearer geometrischer Evolutionsgleichungen höherer Ordnung mit Levelset- und Finite-Elemente-Verfahren. Der isotrope, schwach anisotrope und stark anisotrope Fall wird diskutiert. Die meisten in dieser Arbeit betrachteten Gleichungen entstammen dem Gebiet des Dünnschicht-Wachstums. Eine kurze Einführung in dieses Gebiet wird gegeben. Es werden vier verschiedene Modelle diskutiert: mittlerer Krümmungsfluss, Oberflächendiffusion, ein kinetisches Modell, welches die Effekte des mittleren Krümmungsflusses und der Oberflächendiffusion kombiniert und zusätzlich eine kinetische Komponente beinhaltet, und ein Adatom-Modell, welches außerdem freie Adatome berücksichtigt. Als Einführung in die numerischen Schemata, wird zuerst der isotrope und schwach anisotrope Fall betrachtet. Anschließend werden starke Anisotropien (nicht-konvexe Anisotropien) benutzt, um Facettierungs- und Vergröberungsphänomene zu simulieren. Der in Experimenten beobachtete Effekt der Ecken- und Kanten-Abrundung wird in der Simulation durch die Regularisierung der starken Anisotropie durch einen Krümmungsterm höherer Ordnung erreicht. Die Krümmungsregularisierung führt zu einer Erhöhung der Ordnung der Gleichung um zwei, was hochgradig nicht-lineare Gleichungen von bis zu sechster Ordnung ergibt. Für die numerische Lösung werden die Gleichungen auf Systeme zweiter Ordnungsgleichungen transformiert, welche mit einem Schurkomplement-Ansatz gelöst werden. Das Adatom-Modell bildet eine Diffusionsgleichung auf einer bewegten Fläche. Zur numerischen Lösung wird ein Operatorsplitting-Ansatz verwendet. Im Unterschied zu anderen Arbeiten, die sich auf den isotropen Fall beschränken, wird auch der anisotrope Fall diskutiert und numerisch gelöst. Außerdem werden geometrische Evolutionsgleichungen auf implizit gegebenen gekrümmten Flächen mit Levelset-Verfahren behandelt. Insbesondere wird die numerische Lösung von Oberflächendiffusion auf gekrümmten Flächen dargestellt. Die Gleichungen werden im Ort mit linearen Standard-Finiten-Elementen diskretisiert. Als Zeitdiskretisierung wird ein semi-implizites Diskretisierungsschema verwendet. Die Herleitung der numerischen Schemata wird detailliert dargestellt, und zahlreiche numerische Ergebnisse für den 2D und 3D Fall sind gegeben. Um den Rechenaufwand gering zu halten, wird das Finite-Elemente-Gitter adaptiv an den bewegten Kurven bzw. den bewegten Flächen verfeinert. Es wird ein Redistancing-Algorithmus basierend auf einer lokalen Hopf-Lax Formel benutzt. Der Algorithmus wurde von den Autoren auf den 3D Fall erweitert. In dieser Arbeit wird der Algorithmus für den 3D Fall detailliert beschrieben
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Stöcker, Christina. "Level set methods for higher order evolution laws." Doctoral thesis, Forschungszentrum caesar, 2007. https://tud.qucosa.de/id/qucosa%3A24054.
Full textAbstract:
A numerical treatment of non-linear higher-order geometric evolution equations with the level set and the finite element method is presented. The isotropic, weak anisotropic and strong anisotropic situation is discussed. Most of the equations considered in this work arise from the field of thin film growth. A short introduction to the subject is given. Four different models are discussed: mean curvature flow, surface diffusion, a kinetic model, which combines the effects of mean curvature flow and surface diffusion and includes a further kinetic component, and an adatom model, which incorporates in addition free adatoms. As an introduction to the numerical schemes, first the isotropic and weak anisotropic situation is considered. Then strong anisotropies (non-convex anisotropies) are used to simulate the phenomena of faceting and coarsening. The experimentally observed effect of corner and edge roundings is reached in the simulation through the regularization of the strong anisotropy with a higher-order curvature term. The curvature regularization leads to an increase by two in the order of the equations, which results in highly non-linear equations of up to 6th order. For the numerical solution, the equations are transformed into systems of second order equations, which are solved with a Schur complement approach. The adatom model constitutes a diffusion equation on a moving surface. An operator splitting approach is used for the numerical solution. In difference to other works, which restrict to the isotropic situation, also the anisotropic situation is discussed and solved numerically. Furthermore, a treatment of geometric evolution equations on implicitly given curved surfaces with the level set method is given. In particular, the numerical solution of surface diffusion on curved surfaces is presented. The equations are discretized in space by standard linear finite elements. For the time discretization a semi-implicit discretization scheme is employed. The derivation of the numerical schemes is presented in detail, and numerous computational results are given for the 2D and 3D situation. To keep computational costs low, the finite element grid is adaptively refined near the moving curves and surfaces resp. A redistancing algorithm based on a local Hopf-Lax formula is used. The algorithm has been extended by the authors to the 3D case. A detailed description of the algorithm in 3D is presented in this work.In der Arbeit geht es um die numerische Behandlung nicht-linearer geometrischer Evolutionsgleichungen höherer Ordnung mit Levelset- und Finite-Elemente-Verfahren. Der isotrope, schwach anisotrope und stark anisotrope Fall wird diskutiert. Die meisten in dieser Arbeit betrachteten Gleichungen entstammen dem Gebiet des Dünnschicht-Wachstums. Eine kurze Einführung in dieses Gebiet wird gegeben. Es werden vier verschiedene Modelle diskutiert: mittlerer Krümmungsfluss, Oberflächendiffusion, ein kinetisches Modell, welches die Effekte des mittleren Krümmungsflusses und der Oberflächendiffusion kombiniert und zusätzlich eine kinetische Komponente beinhaltet, und ein Adatom-Modell, welches außerdem freie Adatome berücksichtigt. Als Einführung in die numerischen Schemata, wird zuerst der isotrope und schwach anisotrope Fall betrachtet. Anschließend werden starke Anisotropien (nicht-konvexe Anisotropien) benutzt, um Facettierungs- und Vergröberungsphänomene zu simulieren. Der in Experimenten beobachtete Effekt der Ecken- und Kanten-Abrundung wird in der Simulation durch die Regularisierung der starken Anisotropie durch einen Krümmungsterm höherer Ordnung erreicht. Die Krümmungsregularisierung führt zu einer Erhöhung der Ordnung der Gleichung um zwei, was hochgradig nicht-lineare Gleichungen von bis zu sechster Ordnung ergibt. Für die numerische Lösung werden die Gleichungen auf Systeme zweiter Ordnungsgleichungen transformiert, welche mit einem Schurkomplement-Ansatz gelöst werden. Das Adatom-Modell bildet eine Diffusionsgleichung auf einer bewegten Fläche. Zur numerischen Lösung wird ein Operatorsplitting-Ansatz verwendet. Im Unterschied zu anderen Arbeiten, die sich auf den isotropen Fall beschränken, wird auch der anisotrope Fall diskutiert und numerisch gelöst. Außerdem werden geometrische Evolutionsgleichungen auf implizit gegebenen gekrümmten Flächen mit Levelset-Verfahren behandelt. Insbesondere wird die numerische Lösung von Oberflächendiffusion auf gekrümmten Flächen dargestellt. Die Gleichungen werden im Ort mit linearen Standard-Finiten-Elementen diskretisiert. Als Zeitdiskretisierung wird ein semi-implizites Diskretisierungsschema verwendet. Die Herleitung der numerischen Schemata wird detailliert dargestellt, und zahlreiche numerische Ergebnisse für den 2D und 3D Fall sind gegeben. Um den Rechenaufwand gering zu halten, wird das Finite-Elemente-Gitter adaptiv an den bewegten Kurven bzw. den bewegten Flächen verfeinert. Es wird ein Redistancing-Algorithmus basierend auf einer lokalen Hopf-Lax Formel benutzt. Der Algorithmus wurde von den Autoren auf den 3D Fall erweitert. In dieser Arbeit wird der Algorithmus für den 3D Fall detailliert beschrieben.
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Streng, Christoph. "Wachstumsanalyse amorpher dicker Schichten und Schichtsysteme." Doctoral thesis, [S.l.] : [s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=972086544.
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"The thin film type parabolic equation." 2003. http://library.cuhk.edu.hk/record=b5891735.
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Shi-Zhong Du.Thesis (M.Phil.)--Chinese University of Hong Kong, 2003.
Includes bibliographical references (leaves 56-58).
Chapter 1 --- Introduction --- p.5
Chapter 2 --- A Nondegenerate Cahn-Hilliard Type Equation --- p.11
Chapter 2.1 --- A priori estimation --- p.13
Chapter 2.2 --- Long time existence --- p.19
Chapter 3 --- The Thin Film Type Equation --- p.31
Chapter 3.1 --- Positivity for n>4 --- p.31
Chapter 3.2 --- Improved entropy estimates --- p.36
Chapter 4 --- Finite Speed of Propagation --- p.43
Chapter 4.1 --- Finite speed of propagation --- p.44
Chapter 4.2 --- The regularity of free boundary --- p.54
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Tekalign, Wondimu Taye. "Evolution equation for a thin epitaxial film on a deformable substrate." 2005. http://wwwlib.umi.com/dissertations/fullcit/3169118.
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Thesis (Ph.D.)--State University of New York at Buffalo, 2005.Title from PDF title page (viewed on Dec. 1, 2005) Available through UMI ProQuest Digital Dissertations. Thesis adviser: Brian J. Spencer. Includes bibliographical references.
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Knüpfer, Hans [Verfasser]. "Classical solutions for a thin film equation / vorgelegt von Hans Knüpfer." 2007. http://d-nb.info/987339788/34.
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"Some results on steady states of the thin-film type equation." Thesis, 2011. http://library.cuhk.edu.hk/record=b6075217.
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In this thesis we study the thin-film type equations in one spatial dimension. These equations arise from the lubrication approximation to the thin films of viscous fluids which is described by the Navier-Stokes equations with free boundary. From the structural point of view, they are fourth-order degenerate nonlinear parabolic equations, with principal term from diffusion and lower order term from external forces. In Chapter one we study the dynamics of the equations when the external force is given by a power law. Classification of steady states of this equation, which is important for the dynamics, was already known. Previous numerical studies show that there is a mountain pass scenario among the steady states. We shall provide a rigorous justification to these numerical results. As a result, a rather complete picture of the dynamics of the thin film is obtained when the power law is in the range (1,3). In Chapter two we turn to the special case of the equation where the external force is the gravity. This is important, but, unfortunately not a power law. We study and classify the steady states of this equation as well as compare their energy levels. Some numerical results are also present.Zhang, Zhenyu.
Asviser: Kai Seng Chou.
Source: Dissertation Abstracts International, Volume: 73-06, Section: B, page: .
Thesis (Ph.D.)--Chinese University of Hong Kong, 2011.
Includes bibliographical references (leaves 103-107).
Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web.
Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web.
Abstract also in Chinese.
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Modhien, Naeemah. "The effect of suction and blowing on the spreading of a thin fluid film: a lie point symmetry analysis." Thesis, 2017. http://hdl.handle.net/10539/23512.
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A thesis submitted to the Faculty of Science, University of the Witwatersrand in
fulfillment of the requirements for the degree of Doctor of Philosophy. Johannesburg, 3 April 2017.The effect of suction and blowing at the base on the horizontal spreading under gravity of a two-dimensional thin fluid film and an axisymmetric liquid drop is in- vestigated. The velocity vn which describes the suction/injection of fluid at the base is not specified initially. The height of the thin film satisfies a nonlinear diffusion equation with vn as a source term. The Lie group method for the solution of partial differential equations is used to reduce the partial differential equations to ordinary differential equations and to construct group invariant solutions. For a group invari- ant solution to exist, vn must satisfy a first order linear partial differential equation. The two-dimensional spreading of a thin fluid film is first investigated. Two models for vn which give analytical solutions are analysed. In the first model vn is propor- tional to the height of the thin film at that point. The constant of proportionality is β (−∞ < β < ∞). The half-width always increases to infinity as time increases even for suction at the base. The range of β for the thin fluid film approximation to be valid is determined. For all values of suction and a small range of blowing the maximum height of the film tends to zero as time t → ∞. There is a value of β corresponding to blowing for which the maximum height remains constant with the blowing balancing the effect of gravity. For stronger blowing the maximum height tends to infinity algebraically, there is a value of β for which the maximum height tends to infinity exponentially and for stronger blowing, still in the range for which the thin film approximation is valid, the maximum height tends to infinity in a finite time. For blowing the location of a stagnation point on the centre line is determined by solving a cubic equation approximately by a singular perturbation method and then exactly using a trigonometric solution. A dividing streamline passes through the stagnation point which separates the flow into two regions, an upper region consisting of fluid descending due to gravity and a lower region consisting of fluid rising due to blowing. For sufficiently strong blowing the lower region fills the whole of the film. In the second model vn is proportional to the spatial gradient of the height with constant of proportionality β∗ (−∞ < β∗ < ∞). The maximum height always decreases to zero as time increases even for blowing. The range of β∗ for the thin fluid film approximation to be valid is determined. The half-width tends to infinity algebraically for all blowing and a small range of weak suction. There is a value of β∗ corresponding to suction for which the half-width remains constant with the suction balancing the spreading due to gravity. For stronger suction the half-width tends to zero as t → ∞. For even stronger suction there is a value of β∗ for which the half-width tends to zero exponentially and a range of β∗ for which it tends to zero in a finite time but these values lie outside the range for which the thin fluid film approximation is valid. For blowing there is a stagnation point on the centre line at the base. Two dividing streamlines passes through the stagnation point which separate fluid descending due to gravity from fluid rising due to blowing. An approximate analytical solution is derived for the two dividing streamlines. A similar analysis is performed for the axisymmetric spreading of a liquid drop and the results are compared with the two-dimensional spreading of a thin fluid film. Since the two models for vn are still quite general it can be expected that general results found will apply to other models. These include the existence of a divid- ing streamline separating descending and rising fluid for blowing, the existence of a strength of blowing which balances the effect of gravity so the maximum height remains constant and the existence of a strength of suction which balances spreading due to gravity so that the half-width/radius remains constant.
MT 2017
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Sellan, Daniel P. "Predicting Phonon Transport in Semiconductor Nanostructures using Atomistic Calculations and the Boltzmann Transport Equation." Thesis, 2012. http://hdl.handle.net/1807/32882.
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The mechanisms of thermal transport in defect-free silicon nanostructures are examined using a combination of lattice dynamics (LD) calculations and the Boltzmann transport equation (BTE). To begin, the thermal conductivity reduction in thin films is examined using a hierarchical method that first predicts phonon transport properties using LD calculations, and then solves the phonon BTE using the lattice Boltzmann method. This approach, which considers all of the phonons in the first Brillouin-zone, is used to assess the suitability of common assumptions used to reduce the computational effort. Specifically, we assess the validity of: (i) neglecting the contributions of optical modes, (ii) the isotropic approximation, (iii) assuming an averaged bulk mean-free path (i.e., the Gray approximation), and (iv) using the Matthiessen rule to combine the effect of different scattering mechanisms. Because the frequency-dependent contributions to thermal conductivity change as the film thickness is reduced, assumptions that are valid for bulk are not necessarily valid for thin films.
Using knowledge gained from this study, an analytical model for the length-dependence of thin film thermal conductivity is presented and compared to the predictions of the LD-based calculations. The model contains no fitting parameters and only requires the bulk lattice constant, bulk thermal conductivity, and an acoustic phonon speed as inputs. By including the mode-dependence of the phonon lifetimes resulting from phonon-phonon and phonon-boundary scattering, the model predictions capture the approach to the bulk thermal conductivity better than predictions made using Gray models based on a single lifetime.
Both the model and the LD-based method are used to assess a procedure commonly used to extract bulk thermal conductivities from length-dependent molecular dynamics simulation data. Because the mode-dependence of thermal conductivity is not included in the derivation of this extrapolation procedure, using it can result in significant error.
Finally, phonon transport across a silicon/vacuum-gap/silicon structure is modelled using lattice dynamics and Landauer theory. The phonons transmit thermal energy across the vacuum gap via atomic interactions between the leads. Because the incident phonons do not encounter a classically impenetrable potential barrier, this mechanism is not a tunneling phenomenon. The heat flux due to phonon transport can be 4 orders of magnitude larger than that due to photon transport predicted from near-field radiation theory.
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"A comparison of design techniques for gradient-index thin film optical filters." Thesis, 2012. http://hdl.handle.net/10210/5453.
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M.Ing.This work comprises the implementation and comparison of five design techniques for the design of gradient-index thin film optical filters: classical rugate, inverse Fourier transform, a wavelet-based design procedure, as well as the flip-flop and the genetic optimization techniques. Designs for a high-reflectance filter, a beamsplitter, a discrete level filter, a distributed filter, and an anti-reflection coating were used to compare the various filter synthesis techniques. The optical thickness of the various examples was maintained below 30 and the refractive index excursion limits were between 1.5 and 3.2. The overall performance of a specific design was evaluated by a weighted merit function. The classical rugate filter uses a sinusoidal refractive index modulation that produces a single reflection band. More complex filters are realized by linear superposition of these elementary profiles. Sidelobe and ripple suppression are obtained by applying quintic windowing functions to the refractive index profile and adding matching layers at the edges of the filter. This filter design procedure has the best figure of merit of 3.73 for the discrete level filter, and the second best of 3.09 for the high-reflectance filter. The inverse Fourier transform links the refractive index profile and reflection spectrum of an optical filter by an approximate relation. It is self-correcting and iterative in nature. It produces filters with the highest optical density. The procedure excels in the design of the distributed filter with a figure of merit of 4.17. Mortlett's wavelet is used as the basis of the wavelet design technique. A single wavelet yields a single reflection band, similar to the classical rugate filter. Sidelobe suppression is an inherent property of the method, but matching layers are needed for passband ripple suppression. The optical density of the high reflection filter is larger for a filter designed with this method than for the equivalent classical rugate filter. The figure of merit of 1.75 for the high-reflectance filter is the best for any of the designs. Flip-flop refinement is a brute force approach to filter design. The layers of a starting design are flipped between two values of refractive index, the change in figure of merit evaluated and the best case saved. This process is repeated for a fixed number of iterations. It is computationally intensive and lacks ripple suppression characteristics. The flip-flop method does not compare well with any of the other techniques. It yields filters with the worst figures of merit for most of the design examples. However, it was applied successfully to the anti-reflection coating. The peak ripple for the anti-reflection filter in the 400 nm to 1100 nm wavelength band is 9.62 % compared to the inverse Fourier transform's 57.30 %. The genetic algorithm operates on the principle of "survival of the fittest". It is a stochastic procedure and yields quasi-random refractive index profiles. It excels with the antireflection coating. The peak ripple in the passband of the anti-reflection coating is 3.29%. The figure of merit for the anti-reflection coating designed with the genetic algorithm is 2.09.
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Ziade, Elbara Oussama. "Thermal transport in thin films and across interfaces." Thesis, 2017. https://hdl.handle.net/2144/23569.
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Heat dissipation is a critical bottleneck for microelectronic device performance and longevity. At micrometer and nanometer length scales heat carriers scatter at the boundaries of the material reducing its thermal conductivity. Additionally, thermal boundary conductance across dissimilar material interfaces becomes a dominant factor due to the increase in surface area relative to the volume of device layers. Therefore, techniques for monitoring spatially varying temperature profiles, and methods to improve thermal performance are critical to future device design and optimization.
The first half of this thesis focused on frequency domain thermoreflectance (FDTR) to measure thermal transport in nanometer-thick polymer films and across an organic-inorganic interface. Hybrid structures of organic and inorganic materials are widely used in devices such as batteries, solar cells, transistors, and flexible electronics. The Langmuir-Blodgett (LB) technique was used to fabricate nanometer-thick polymer films ranging from 2 - 30 nm. FDTR was then used to experimentally determine the thermal boundary conductance between the polymer and solid substrates.
The second half of the thesis focused on developing a fundamental understanding of thermal transport in wide-bandgap (WBG) materials, such as GaN, and ultrawide-bandgap (UWBG) materials, such as diamond, to improve thermal dissipation in power electronic devices. Improvements in WBG materials and device technologies have slowed as thermal properties limit their performance. UWBG materials can provide a dramatic leap in power electronics technologies while temporarily sidestepping the problems associated with their WBG cousins. However, for power electronic devices based on WBG- and UWBG-materials to reach their full potential the thermal dissipation issues in these hard-driven devices must be understood and solved. FDTR provides a comprehensive pathway towards fully understanding the physics governing phonon transport in WBG- and UWBG-based devices. By leveraging FDTR imaging and measuring samples as a function of temperature, defect concentration, and thickness, in conjunction with transport models, a well-founded understanding of the dominant thermal-carrier scattering mechanisms in these devices was achieved. With this knowledge we developed pathways for their mitigation.
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Nicolaou, Zachary George. "Symmetry and Variational Analyses of Fluid Interface Equations in the Thin Film Limit." Thesis, 2017. https://thesis.library.caltech.edu/9919/7/20160906_zgnsymmetry.zip.
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This thesis concerns a class of nonlinear partial differential equations up to fourth order in spatial derivatives that models thin viscous films. In Chapter 1, we review the derivations of thin film equations from the fundamental transport equations. Section 1.1 contains the derivation for a thermocapillary driven film to familiarize the reader with the key long-wavelength approximation that has been successful in modeling a myriad of thin viscous films. In Section 1.2, we consider the coupling between a thin viscous layer and a much thicker fluid layer with much larger viscosity and conductivity and show how a novel, non-local thermocapillary thin film equation can be derived to model such a system. We then review the wider class of thin film equations in Section 1.3, note the important Cahn-Hilliard variational form of these equations, and demonstrate that classic mathematical results concerning the inverse problem of the calculus of variations permit an algorithmic procedure for discovering Lyapunov functionals. In Chapter 2, we review applications of symmetry methods to partial differential equations. Section 2.1 contains an original geometrical motivation for the study of self-similar reductions which draws an analogy with the fixed points of dynamical systems. In Section 2.2, we derive for the first time the full set of symmetries of the fully two-dimensional thin film equations. We then enumerate the possible symmetry reductions of the thin film equations, and discover several which have not been previously recognized. In Chapter 3, we consider rotationally invariant, steady droplet solutions and their stability. In Section 3.1, we derive stability criteria for thermocapillary-driven droplets, and show a novel correspondence between droplet stability, droplet volume, and droplet Lyapunov energy. We consider thin films under other forces in Section 3.2 and make new predictions about conditions under which such films develop into droplets, columns, or jets of fluid. In Chapter 4, we consider the scale invariant symmetry reductions of thin film equations. In Section 4.1 we describe the extraordinarily rich variety of such solutions in the spreading of a insoluble surfactant on a thin viscous film, identify previously unrecognized scale invariant solutions which are well-behaved at the origin, and demonstrate their relevance with finite element simulations. Lastly, in Section 4.2, we illustrate for capillary driven films some numerical solutions to the novel reductions we uncovered in Chapter 2. Each chapter concludes with a Notes section which summarizes the new results contained therein and relates them to the wider literature.
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Levy, Rachel. "Partial differential equations of thin liquid films analysis and numerical simulation /." 2005. http://www.lib.ncsu.edu/theses/available/etd-04222005-162444/unrestricted/etd.pdf.
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Nemadjieu, Simplice Firmin. "Finite Volume Methods for Advection Diffusion on Moving Interfaces and Application on Surfactant Driven Thin Film Flow." Phd thesis, 2012. http://tel.archives-ouvertes.fr/tel-00731479.
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Cette thèse est scindée en deux parties. Dans un premier temps, nous présentons deux schémas volumes finis pour la discrétisation des problèmes de diffusion-convection-réaction sur les surfaces mouvantes. Le premier schéma présente une extension du schéma volumes finis avec flux à deux points sur les surfaces mouvantes. Le deuxième développe une méthode de type O-méthode. Cette dernière consiste à construire à partir des inconnus au centre des mailles, des solutions linéaires autour des nœuds de maillage qui intègrent la continuité des flux aux interfaces de mailles. La méthode permet aussi la construction des décentrages amont d'ordre 2 et ainsi, offre au procédé l'ordre 2 de convergence sur tout maillage non dégénéré. Ensuite, nous modélisons l'écoulement du couplage filme mince-surfactant (surface active agent) sur les surfaces mouvantes et simulons à l'aide des schémas volumes finis précédemment définis. Ici, l'utilisation du calcul tensoriel et de la méthode d'approximation par la lubrification permettent de réduire les équations de Navier-Stokes caractérisant le mouvement du filme mince en dimension 3 en un système d'équations définies sur la surface courbe mouvante dont l'inconnu est la hauteur du fluide. Le surfactant supposé insoluble est modélisé par une équation de diffusion convection à la l'interface fluid-air. Nous simulons l'ensemble en utilisant une méthode dite de capture d'interface (Interface tracking method) dérivée des volumes finis définis plus haut. Plusieurs exemples illustrent à suffisance l'efficacité et la précision des différentes méthodes.
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Mayr, Stefan Georg. "Wachstum amorpher Schichten: Vergleich von Experiment und Simulation im Bereich Oberflächenrauhigkeit und mechanische Spannungen." Doctoral thesis, 2000. http://hdl.handle.net/11858/00-1735-0000-0006-B40E-C.
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