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Dissertations / Theses on the topic 'Thin Film Equation'

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Published: 6 September 2023

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1

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

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2

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.<br>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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3

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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4

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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5

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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6

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 fo

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7

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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8

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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10

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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11

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 us

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12

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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13

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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14

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 thes

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15

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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16

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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17

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

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18

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 t

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19

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. D

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20

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 h

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21

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 pha

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22

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

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23

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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24

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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25

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 t

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26

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

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27

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

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28

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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Made available in DSpace on 2016-12-12T20:15:53Z (GMT). No. of bitstreams: 1 RESUMO- Fabio Nery.pdf: 214160 bytes, checksum: a7fa12ba9fb8da2aa6290a30867a85b2 (MD5) Previous issue date: 2009-07-31<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior<br>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 unidimensio

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29

Simon, Amélie. "Modélisation des phénomènes de films liquides dans les turbines à vapeur." Thesis, Lyon, 2017. http://www.theses.fr/2017LYSEC001/document.

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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 dav

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30

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 s

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31

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

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32

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.

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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 incorporat

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33

Stöcker, Christina. "Level set methods for higher order evolution laws." Doctoral thesis, Forschungszentrum caesar, 2007. https://tud.qucosa.de/id/qucosa%3A24054.

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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 incorporat

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34

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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35

"The thin film type parabolic equation." 2003. http://library.cuhk.edu.hk/record=b5891735.

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Shi-Zhong Du.<br>Thesis (M.Phil.)--Chinese University of Hong Kong, 2003.<br>Includes bibliographical references (leaves 56-58).<br>Chapter 1 --- Introduction --- p.5<br>Chapter 2 --- A Nondegenerate Cahn-Hilliard Type Equation --- p.11<br>Chapter 2.1 --- A priori estimation --- p.13<br>Chapter 2.2 --- Long time existence --- p.19<br>Chapter 3 --- The Thin Film Type Equation --- p.31<br>Chapter 3.1 --- Positivity for n>4 --- p.31<br>Chapter 3.2 --- Improved entropy estimates --- p.36<br>Chapter 4 --- Finite Speed of Propagation --- p.43<br>Chapter 4.1 --- Finite speed of propagation --

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36

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.<br>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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37

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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38

"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 d

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39

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.<br>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

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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 effo

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41

"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.<br>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 limit

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42

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 firs

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43

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 condu

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44

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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45

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

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46

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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