Relevant bibliographies by topics / Thin Film Equation

Academic literature on the topic 'Thin Film Equation'

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Published: 6 September 2023

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Journal articles on the topic "Thin Film Equation"

1

Huang, F. Y., and C. D. Mote. "Derivation of a Thin Film Equation by a Direct Approach." Journal of Applied Mechanics 63, no. 2 (June 1, 1996): 467–73. http://dx.doi.org/10.1115/1.2788891.

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A new model of the thin viscous fluid film, constrained between two translating, flexible surfaces, is presented in this paper: The unsteady inertia of the film is included in the model. The derivation starts with the reduced three-dimensional Navier-Stokes equations for an incompressible viscous fluid with a small Reynolds number. By introduction of an approximate velocity field, which satisfies the continuity equation and the no-slip boundary conditions exactly, into weighted integrals of the three-dimensional equations over the film thickness, a two-dimensional thin film equation is obtained explicitly in a closed form. The 1th thin film equation is obtained when the velocity field is approximated by 21th order polynominals, and the three-dimensional viscous film is described with increasing accuracy by thin film equations of increasing order. Two cases are used to illustrate the coupling of the film to the vibration of the structure and to show that the second thin film equation can be applied successfully to the prediction of a coupled film-structure response in the range of most applications. A reduced thin film equation is derived through approximation of the second thin film equation that relates the film pressure to transverse accelerations and velocities, and to slopes and slope rates of the two translating surfaces.
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Segatti, Antonio, and Juan Luis Vázquez. "On a fractional thin film equation." Advances in Nonlinear Analysis 9, no. 1 (March 26, 2020): 1516–58. http://dx.doi.org/10.1515/anona-2020-0065.

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Abstract This paper deals with a nonlinear degenerate parabolic equation of order α between 2 and 4 which is a kind of fractional version of the Thin Film Equation. Actually, this one corresponds to the limit value α = 4 while the Porous Medium Equation is the limit α = 2. We prove existence of a nonnegative weak solution for a general class of initial data, and establish its main properties. We also construct the special solutions in self-similar form which turn out to be explicit and compactly supported. As in the porous medium case, they are supposed to give the long time behaviour or the wide class of solutions. This last result is proved to be true under some assumptions. Lastly, we consider nonlocal equations with the same nonlinear structure but with order from 4 to 6. For these equations we construct self-similar solutions that are positive and compactly supported, thus contributing to the higher order theory.
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LIU, CHANGCHUN, JINGXUE YIN, and HONGJUN GAO. "A GENERALIZED THIN FILM EQUATION." Chinese Annals of Mathematics 25, no. 03 (July 2004): 347–58. http://dx.doi.org/10.1142/s0252959904000329.

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van Odyck, D. E. A., and C. H. Venner. "Stokes Flow in Thin Films." Journal of Tribology 125, no. 1 (December 31, 2002): 121–34. http://dx.doi.org/10.1115/1.1506317.

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Present understanding of the mechanisms of lubrication and the load carrying capacity of lubricant films mainly relies on models in which the Reynolds equation is used to describe the flow. The narrow gap assumption is a key element in its derivation from the Navier Stokes equations. However, the tendency in applications is that lubricated contacts have to operate at smaller film thickness levels, and because engineering surfaces are never perfectly smooth, locally in the film this narrow gap assumption may violated. In addition to this geometric limitation of the validity of the Reynolds equation may come a piezoviscous and compressibility related limitation. In this paper the accuracy of the predictions of the Reynolds model in relation to the local geometry of the gap is investigated. A numerical solution algorithm for the flow in a narrow gap has been developed based on the Stokes equations. For a model problem the differences between the pressure and velocity fields according to the Stokes model and the Reynolds equation have been investigated. The configuration entails a lower flat surface together with an upper surface (flat or parabolic) in which a local defect (single asperity) of known geometry has been embedded. It is investigated how the magnitude of the differences develops as a function of the geometric parameters of the film and the feature. Finally, it is discussed to what extend for these problems a perturbation approach can provide accurate corrections to be applied to the Reynolds solution.
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Chen, Kuen Tsann, Jui Hsing Chang, and Jiun Yu Wu. "Modified Stoney's Equation for Evaluation of Residual Stresses on Thin Film." Applied Mechanics and Materials 789-790 (September 2015): 25–32. http://dx.doi.org/10.4028/www.scientific.net/amm.789-790.25.

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In the article, a simple method for the modification of the Stoney's equation was presented. The Stoney's equation is proposed from the assumption of equi-biaxial residual stresses in thin films. In this present method, biaxial stresses are different in x-axis and y-axis on thin film. The location of neutral axis depends on the material parameters and the film thickness. The finite element method (FEM) was used to simulate the thermal stress on the thin film. The results of the modified methods are compared with the results of FEM and other literatures. The present method is more accurate than the Stoney's equation in the evaluation of such films.
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Ruschak, Kenneth J., and Steven J. Weinstein. "Viscous Thin-Film Flow Over a Round-Crested Weir." Journal of Fluids Engineering 121, no. 3 (September 1, 1999): 673–77. http://dx.doi.org/10.1115/1.2823522.

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Gravity-driven flow over a round-crested weir is analyzed for viscous flow. An equation for the entire flow profile is obtained by simplifying the equations for slowly varying film thickness, assuming a velocity profile, and integrating across the film. Solution of the resulting first order, ordinary differential equation requires a boundary condition generated at a critical point of the flow, beyond which waves cannot propagate upstream. Results for the relationship between head and flow rate are consolidated on a dimensionless master curve represented by an empirical equation.
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Ruschak, Kenneth J., and Steven J. Weinstein. "Laminar, Gravitationally Driven Flow of a Thin Film on a Curved Wall." Journal of Fluids Engineering 125, no. 1 (January 1, 2003): 10–17. http://dx.doi.org/10.1115/1.1522412.

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Gravitationally driven flow of a thin film down an arbitrarily curved wall is analyzed for moderate Reynolds number by generalizing equations previously developed for flow on a planar wall. In the analysis, the ratio of the characteristic film thickness to the characteristic dimension of the wall is presumed small, and terms estimated to be first order in this parameter are retained. Partial differential equations are reduced to ordinary differential equations by the method of von Ka´rma´n and Pohlhausen; namely, an expression for the velocity profile is assumed, and the equation for conservation of linear momentum is averaged across the film. The assumed velocity profile changes shape in the flow direction because a self-similar profile, one of fixed shape but variable magnitude, leads to an equation that typically fails under critical conditions. The resulting equations for film thickness routinely accommodate subcritical-to-supercritical transitions and supercritical-to-subcritical transitions as classified by the underlying wave propagation. The more severe supercritical-to-subcritical transition is manifested by a standing wave where the film noticeably thickens; this standing wave is a simple analogue of a hydraulic jump. Predictions of the film-thickness profile and variations in the velocity profile compare favorably with those from the Navier-Stokes equation obtained by the finite element method.
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Abd Alsamieh, M. F. "Non-Newtonian Film Thickness Formation in Ultra-thin Film." International Journal of Automotive and Mechanical Engineering 16, no. 1 (March 21, 2019): 6230–44. http://dx.doi.org/10.15282/ijame.16.1.2019.11.0473.

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This paper aims to show the characteristics of ultra-thin films for non-Newtonian fluid using Ree-Eyring model where intermolecular forces of solvation and Van der Waal's are considered in addition to the hydrodynamic action to fulfill an identified need for such a conjunction. In this case, the film thickness and pressure distribution are obtained by simultaneous solution of the modified Reynolds’ equation incorporating the effect of non-Newtonian fluid, film thickness equation including elastic deformation caused by all contributing pressures and the load balance equation using Newton-Raphson method with Gauss-Seidel iterations. Effect of changing the operating conditions of speed, load, Eyring shear stress and slide-roll ratio on the characteristic of the contact has been studied. The results show that, for the case where the hydrodynamic action is the only pressure acting to support the applied load capacity, the film thickness and the pressure gradient at the exit of the contact obtained using non-Newtonian model is different than that formed using the Newtonian model especially for the increased value of slide-roll ratio. The main results of this study are that for ultra-thin film, the film thickness formed using non-Newtonian model is smaller compared to that obtained using Newtonian case and the discretization of the film thickness as the gap is reduced occurs similar to the results obtained using Newtonian model. The pressure shape shows no difference compared to that formed using the Newtonian case in which an oscillation around the Hertizan contact pressure shape due to the solvation effect appears. The results also show that for ultra-thin film, changing the Eyring shear stress does not affect the film thickness formation.
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van Odyck, D. E. A., and C. H. Venner. "Compressible Stokes Flow in Thin Films." Journal of Tribology 125, no. 3 (June 19, 2003): 543–51. http://dx.doi.org/10.1115/1.1539058.

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A multigrid numerical solution algorithm has been developed for the laminar (Stokes) flow of a compressible medium in a thin film. The solver has been applied to two model problems each representative of lubrication problems in a specific way. For both problems the solutions of the Stokes equations are compared with the solutions of the Reynolds equation. The configurations of both model problems were chosen such that based on the ratio film thickness to contact length (H/L) the difference between the Reynolds and the Stokes solutions will be very small, so the geometry of the gap itself does not lead to a significant cross film dependence of the pressure. It is shown that in this situation the compressibility can still lead to a cross-film pressure dependence which is predicted by the Stokes solution and not by the Reynolds solution. The results demonstrate that limitations exist to the validity of the Reynolds equation related to the compressibility of the medium.
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Fabes, B. D., W. C. Oliver, R. A. McKee, and F. J. Walker. "The determination of film hardness from the composite response of film and substrate to nanometer scale indentations." Journal of Materials Research 7, no. 11 (November 1992): 3056–64. http://dx.doi.org/10.1557/jmr.1992.3056.

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Two equations for determining the hardness of thin films from depth-sensing indentation data are examined. The first equation is based on an empirical fit of hardness versus indenter displacement data obtained from finite element calculations on a variety of hypothetical films. The second equation is based on a model which assumes that measured hardness is determined by the weighted average of the volume of plastically deformed material in the coating and that in the substrate. The equations are evaluated by fitting the predicted hardness versus contact depth to data obtained from titanium coatings on a sapphire substrate. Only the volume fractions model allows the data to be fitted with a single adjustable parameter, the film hardness; the finite element equation requires two thickness-dependent parameters to obtain acceptable fits. It is argued that the difficulty in applying the finite element model lies in the use of an unrealistic area function for the indenter. For real indenters, which have finite radii, the area function must appear explicitly in the final equation. This is difficult to do with the finite element approach, but is naturally incorporated into the volume fractions equation. Finally, using the volume fractions approach the hardnesses of the titanium films are found to be relatively insensitive to film thickness. Thus, the apparent increase in hardness with decreasing film thickness for the titanium films is most likely due to increased interactions between the film and substrate for the thinner films rather than to a change in the basic structure of the titanium films.
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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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Books on the topic "Thin Film Equation"

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Brown, James L. The thin oil film equation. Moffett Field, Calif: National Aeronautics and Space Administration, Ames Research Center, 1999.

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A, Goldman J., Brennan K. F, and United States. National Aeronautics and Space Administration., eds. Theoretical and material studies of thin-film electroluminescent devices: Sixth six-monthly report for the period 1 November 1987 - 30 April 1988. Atlanta, GA: Georgia Institute of Technology ; [Washington, DC, 1988.

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F, Brennan K., and United States. National Aeronautics and Space Administration., eds. Theoretical and material studies of thin-film electroluminescent devices: Second six monthly report for the period 1 October 1985 - 31 March 1986. [Washington, DC: National Aeronautics and Space Administration, 1986.

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United States. National Aeronautics and Space Administration., ed. Fast methods to numerically integrate the Reynolds equation for gas fluid films. [Washington, DC]: National Aeronautics and Space Administration, 1992.

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Krishnamoorthy, S. Full-scale direct numerical simulation of two- and three-dimensional instabilities and rivulet formation in heated falling films. [Washington, D.C.]: National Aeronautics and Space Administration, 1995.

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Krishnamoorthy, S. Full-scale direct numerical simulation of two- and three-dimensional instabilities and rivulet formation in heated falling films. [Washington, D.C.]: National Aeronautics and Space Administration, 1995.

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ZnO bao mo zhi bei ji qi guang, dian xing neng yan jiu. Shanghai Shi: Shanghai da xue chu ban she, 2010.

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Theoretical and material studies of thin-film electroluminescent devices: Final report. [Washington, DC: National Aeronautics and Space Administration, 1990.

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Eriksson, Olle, Anders Bergman, Lars Bergqvist, and Johan Hellsvik. Atomistic Spin Dynamics. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198788669.001.0001.

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The purpose of this book is to provide a theoretical foundation and an understanding of atomistic spin-dynamics, and to give examples of where the atomistic Landau-Lifshitz-Gilbert equation can and should be used. The contents involve a description of density functional theory both from a fundamental viewpoint as well as a practical one, with several examples of how this theory can be used for the evaluation of ground state properties like spin and orbital moments, magnetic form-factors, magnetic anisotropy, Heisenberg exchange parameters, and the Gilbert damping parameter. This book also outlines how interatomic exchange interactions are relevant for the effective field used in the temporal evolution of atomistic spins. The equation of motion for atomistic spin-dynamics is derived starting from the quantum mechanical equation of motion of the spin-operator. It is shown that this lead to the atomistic Landau-Lifshitz-Gilbert equation, provided a Born-Oppenheimer-like approximation is made, where the motion of atomic spins is considered slower than that of the electrons. It is also described how finite temperature effects may enter the theory of atomistic spin-dynamics, via Langevin dynamics. Details of the practical implementation of the resulting stochastic differential equation are provided, and several examples illustrating the accuracy and importance of this method are given. Examples are given of how atomistic spin-dynamics reproduce experimental data of magnon dispersion of bulk and thin-film systems, the damping parameter, the formation of skyrmionic states, all-thermal switching motion, and ultrafast magnetization measurements.
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Aspell, Luke. Shivers. Liverpool University Press, 2019. http://dx.doi.org/10.3828/liverpool/9781911325970.001.0001.

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Shivers (1975) was David Cronenberg's first commercial feature and his first horror film. In a modern apartment block, a scientific project to unleash the id results in the equation of passion with contagion and predation. Because the writer-director's imaginative landscape arrived in the genre fully formed, the unique forms of this début have often been overlooked or mistaken for shortcomings. Cronenberg's most comedic film until Map to the Stars, Shivers is also his most spectacularly unnerving, throwing more images of extreme behavior at us than any of his subsequent films; it remains, with Crash, his most disquieting and transgressive film to date. This book's analysis addresses all channels of communication available to the 35mm sync-sound narrative feature, including shot composition, lighting, cinematographic texture, sound, the use of stock music, editing, costume, makeup, optical work, the screenplay, the casting, and the direction of the actors. This tour of Shivers as “cognitive territory” takes in architecture, cultural context, critical reception, and artistic legacy.
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Book chapters on the topic "Thin Film Equation"

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Hulshof, Josephus. "Some Aspects of the Thin Film Equation." In European Congress of Mathematics, 291–301. Basel: Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8266-8_25.

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Taranets, Roman M. "Strong Solutions of the Thin Film Equation in Spherical Geometry." In Understanding Complex Systems, 181–92. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-96755-4_11.

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Matsunaga, Naoki, Go Sakai, Kengo Shimanoe, and Noboru Yamazoe. "Diffusion Equation-Based Study of Thin Film Semiconductor Gas Sensor -Response Transient-." In Transducers ’01 Eurosensors XV, 1652–55. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-642-59497-7_390.

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Sakai, Go, Naoki Matsunaga, Kengo Shimanoe, and Noboru Yamazoe. "Diffusion equation-based analysis of thin film semiconductor gas sensor -sensitivity dependence on film thickness and operating temperature-." In Transducers ’01 Eurosensors XV, 1694–97. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-642-59497-7_400.

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Eneeva, Liana, Arsen Pskhu, Alexander Potapov, Tianhua Feng, and Sergo Rekhviashvili. "Lyapunov Inequality for a Fractional Differential Equation Modeling Damped Vibrations of Thin Film MEMS." In Advances in Intelligent Systems and Computing, 454–57. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-5887-0_65.

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Vvedensky, Dimitri D. "Stochastic Equations for Thin Film Morphology." In Handbook of Materials Modeling, 2351–61. Dordrecht: Springer Netherlands, 2005. http://dx.doi.org/10.1007/1-4020-3286-2_122.

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Vvedensky, Dimitri D. "Stochastic Equations for Thin Film Morphology." In Handbook of Materials Modeling, 2351–61. Dordrecht: Springer Netherlands, 2005. http://dx.doi.org/10.1007/978-1-4020-3286-8_122.

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King, John R. "Thin-Film Flows And High-Order Degenerate Parabolic Equations." In Fluid Mechanics and Its Applications, 7–18. Dordrecht: Springer Netherlands, 2001. http://dx.doi.org/10.1007/978-94-010-0796-2_2.

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Derezin, Svyatoslav. "Gauss-Codazzi Equations for Thin Films and Nanotubes Containing Defects." In Shell-like Structures, 531–48. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-21855-2_35.

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Stone, H. A. "Partial Differential Equations in Thin Film Flows in Fluid Dynamics and Rivulets." In Nonlinear PDE’s in Condensed Matter and Reactive Flows, 297–312. Dordrecht: Springer Netherlands, 2002. http://dx.doi.org/10.1007/978-94-010-0307-0_12.

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Conference papers on the topic "Thin Film Equation"

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Yu, Jian, Yunong Ling, Jinglan Sun, Xiangjian Meng, Junhao Chu, and Dingyuan Tang. "Theoretical study of monolithic pyroelectric sensor arrays by thermal diffusion equation." In 4th International Conference on Thin Film Physics and Applications, edited by Junhao Chu, Pulin Liu, and Yong Chang. SPIE, 2000. http://dx.doi.org/10.1117/12.408357.

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Hijikata, Kunio, Koji Miyazaki, Takayoshi Inoue, and Osamu Nakabeppu. "Nucleation in Thin Film Processing." In ASME 1996 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1996. http://dx.doi.org/10.1115/imece1996-1039.

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Abstract In this study, the stability of a very thin film at the initial stage of deposition was investigated using perturbation theory. It is assumed that the critical wave length of perturbation on a continuous thin film corresponds to the nuclei diameter and we also propose that the surface tension of a thin film changes with the film thickness. With these assumptions, it can be shown that the nucleus diameter grows linearly with deposition time. It is interesting to note that the resulting equation is similar to the well-known contact angle equation. To confirm the result of the analysis, a vacuum deposition experiment was conducted. Copper nuclei on the substrate were observed using a transmission electron microscope (TEM) and diameters of island nuclei were measured. The results clearly show that the effective nuclei diameter grows linearly with deposition time. The good agreement between analysis and the experiment suggests the validity of this analysis.
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Sayed, Khairy, Mazen Abdel-Salam, Mahmoud Ahmed, and Adel A. Ahmed. "Numerical Simulation of Thin-Film Photovoltaic Solar Cells." In ASME 2011 International Mechanical Engineering Congress and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/imece2011-62352.

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The objective of this work is to develop a detailed numerical simulation of solar photovoltaic cells in one, two, and three-dimensions. Such kind of numerical simulation can be used as a flexible research tool for the design and analysis of solar cells. The developed in-house simulation code has the advantage of conducting modifications of the suggested configurations to include effects not covered by the commercial simulation models. In addition, this tool is to serve as a test-bed simulator for the development of solar cells modeling and to design new material models. The photovoltaic solar cells governing equations are Poisson’s equation, the hole and electron continuity equations. Poisson equation is generally used to get the voltages across the device. However, in the present work, it is used to obtain the value of the electrical charge. The governing equations along with the appropriate boundary conditions are solved numerically using a finite difference based method. The resulting system of coupled nonlinear equations is then solved using Newton method for nonlinear systems. The predicted results include illuminated current-voltage characteristic, and dark current-voltage characteristics of photovoltaic module. Comparisons between predicted results and corresponding measured values by manufacturer are conducted in order to validate the numerical simulation. A good agreement between predicted and measured results was prevailed.
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4

Szeri, Andras Z. "Stokes Flow, Reynolds Flow, Molecular Flow: Restrictions on Modeling Thin Films." In ASME 2000 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2000. http://dx.doi.org/10.1115/imece2000-1937.

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Abstract Under ordinary conditions fluids are modeled as continua and the Navier -Stokes equation and the equation of continuity can be employed to study their motion. However, to find solutions to these equations is far from elementary, and in applications we look for ways to simplify them. Such simplification is made particularly easy for thin films. We make use of thin film geometry to derive the Reynolds theory of lubrication. The Reynolds equation is employed extensively in various technical fields; it breaks down, however, when there are sudden changes in film thickness or when the film is too thin for the continuum model to apply. In case of a sudden change of film thickness, the essentially two-dimensional flow approximation inherent in the Reynolds theory is no longer valid and the Stokes equation must be employed. If the film is made progressively thinner, the continuum assumption becomes less accurate, eventually losing its validity. For gas flows the non-dimensional group that characterizes deviation from continuum flow is the Knudsen number, Kn, the ratio of the length of the mean free path to the thickness of the channel. For small values of Kn continuum model with no-slip boundary conditions applies, for intermediate values the Reynolds equation may still be employed when specifying slip at the solid boundaries. For larger values of the Knudsen number molecular modeling is required. For liquids the Knudsen number is not available. Nevertheless, it has been shown that down to 10 nm in film thickness the flow is well modeled by the Reynolds equation.
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5

Lam, Michael, Linda Cummings, and Lou Kondic. "Video: Large Scale GPU Simulations of the Generalized Thin Film Equation." In 69th Annual Meeting of the APS Division of Fluid Dynamics. American Physical Society, 2016. http://dx.doi.org/10.1103/aps.dfd.2016.gfm.v0048.

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6

Recio, E., S. Anco, and M. S. Bruzón. "Conservation laws and potential systems for a generalized thin film equation." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2016). Author(s), 2017. http://dx.doi.org/10.1063/1.4992433.

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7

Wang, C., H. P. Morvan, S. Hibberd, and K. A. Cliffe. "Thin Film Modelling for Aero-Engine Bearing Chambers." In ASME 2011 Turbo Expo: Turbine Technical Conference and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/gt2011-46259.

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This paper presents a dynamic mathematical model describing the thin film flow in aero-engine bearing chamber. By analyzing the depth averaged continuity equation and momentum equation term by term, the comprehensive physical mechanisms driving thin film flow are revealed. The terms that require extra modeling work are then identified. As a useful first approach, a thin film model based on presumed quadratic velocity profile is adopted. A preliminary study shows that this model can include the main film flow features in aero-engine bearing chamber, whilst maintain simple formulation and work efficiently. Finally, a converging computational strategy is obtained towards the numerical simulation of engine bearing chamber.
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8

Taha, W. M., M. S. M. Noorani, and I. Hashim. "Exact solution of sixth-order thin-film equation by GʹG-expansion method." In INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES AND STATISTICS 2013 (ICMSS2013): Proceedings of the International Conference on Mathematical Sciences and Statistics 2013. AIP, 2013. http://dx.doi.org/10.1063/1.4823945.

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9

Davies, Mark R. D., and Francis K. O’Donnell. "Local Measurement of Loss Using Heated Thin Film Sensors." In ASME 1998 International Gas Turbine and Aeroengine Congress and Exhibition. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/98-gt-380.

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A calibration equation is derived linking the non-dimensional entropy generation rate per unit area with the non-dimensional aerodynamic wall shear stress and free stream pressure gradient. It is proposed that the latter quantities, which can be measured from surface gauges, be used to measure the profile entropy generation rate. It is shown that the equation is accurate for a wide range of well-defined laminar profiles. To measure the dimensional entropy generation rate per unit area requires measurement of the thickness of the boundary layer. A general profile equation is given and used to show the range of accuracy of a further simplification to the calibration. For flows with low free stream pressure gradients, the entropy generation rate is very simply related to the wall shear stress, if both are expressed without units. An array of heated thin film sensors is calibrated for the measurement of wall shear stress, thus demonstrating the feasibility of using them to measure profile entropy generation rate.
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10

Yan, Chunji, Xinxiang Pan, and Xiaowei Lu. "Mechanisms of Thin-Film Evaporation Considering Momentum and Energy Conservation." In ASME 2013 4th International Conference on Micro/Nanoscale Heat and Mass Transfer. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/mnhmt2013-22157.

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A mathematic model, which can be used to predict the evaporation and fluid flow in thin film region, is developed based on momentum and energy conservations and the augmented Young-Laplace equation in this paper. In the model the variations of the enthalpy and kinetics energy of the thin-film along the evaporating region are considered. By theoretical analysis, we have obtained the governing equation for thin film profile. The fluid flow and phase-change heat transfer in an evaporating extended meniscus are numerically studied. The differences between the model considering momentum conservation only and including both momentum and energy conservations are compared. It is found that the maximum heat flux of the thin-film evaporation by using two mathematical models obtained has no change, but when considering the momentum and energy conservations the total heat transfer rate unit width along the thin-film evaporation region is greater than that of only including momentum equation.
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Reports on the topic "Thin Film Equation"

1

Elbehri, Aziz, and Ken Pearson. Implementing Bilateral Tariff Rate Quotas in GTAP using GEMPACK. GTAP Technical Paper, December 2000. http://dx.doi.org/10.21642/gtap.tp18.

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Explicit modeling of tariff rate quotas (TRQs) is important in the current World Trade Organization negotiations. In order to do such modeling with GTAP, extra data is required and extra equations must be added to the model. This paper provides tools for assisting modelers to carry out explicit modeling of bilateral tariff rate quotas in GTAP using GEMPACK. The paper describes how the extra data for sugar TRQ applications was obtained and reconciled with the standard GTAP data. Supplied with the paper is a TABLO Input file TRQDATA.TAB which others can use for reconciling their TRQ data with the usual GTAP data. Supplied with the paper is a module which can be added to the standard TABLO Input files for GTAP. This module contains the extra equations required to model TRQs. Detailed hands-on examples are supplied with the paper, as is a TRQ application relating to a partial liberalization of sugar TRQ. Readers of the paper can replicate these applications. A windows interface TRQmate is supplied with the paper. This is a relatively general-purpose interface which automates the steps in carrying out TRQ applications with GTAP and GEMPACK. If you wish to carry out your own bilateral TRQ applications with GTAP and GEMPACK, the tools supplied with this paper will make it relatively straightforward for you to do so once you have collected the extra data you need.
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2

Walmsley, Terrie. Long Run Simulations With GTAP: Illustrative Results from APEC Trade Liberalisation. GTAP Technical Paper, September 2000. http://dx.doi.org/10.21642/gtap.tp09.

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In static applied general equilibrium models, the exogenous/endogenous split between variables (or closure) is used to infer the time frame over which the effects of a shock are simulated. This paper introduces a long-run closure for the GTAP model (Hertel and Tsigas, 1997) and uses this closure to simulate and compare the short-run and long-run effects of Asia-Pacific trade liberalisation. The approach explored here incorporates some relatively minor changes to existing GTAP theory in order to define a steady state in which growth rates of all real variables are uniform. Such uniformity must apply in the initial database (as well as in the post-shock solution). So to implement the new long run in GTAP a new initial database must first be created. Details concerning the creation of the new database are given, and results under the new approach are compared with those obtained under the old. The emphasis of this paper is on the development of a long-run closure in which the percentage change form equations of the model and the relationships between the levels variables in the GTAP database are consistent. Further research is required into these types of long-run closures to incorporate changes in ownership of capital to ensure that changes in welfare are adequately modelled. In the results reported here, GDP is not a useful guide to national welfare. The long-run closures introduced here are also compared with another comparative static long-run closure developed for GTAP by Francois, MacDonald and Nordström (1996). Technical Paper Number 9 can be downloaded in PDF format. To print this you will need the Adobe Acrobat Reader. For those interested in replicating the results in this technical paper, an associated zip file can be downloaded. The zip file includes a readme file with detailed instructions.
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Oviedo, Daniel, Orlando Sabogal-Cardona, and Lynn Scholl. Ready to ride: security and transit-related determinants of ride-hailing adoption in Latin America. Inter-American Development Bank, February 2023. http://dx.doi.org/10.18235/0004656.

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Previous research on ride-hailing has focused on the effects that the built environment, demographic variables, and personal attitudes have on the frequency of ride-hailing use, finding that adopters are mainly young and highly educated people with increased levels of technology embracement. Despite that some scholars have shown that the convenience of ride-hailing such as their flexibility and major geographical coverage has led to users to prefer services provided by Transportation Network Companies (TNCs) over public transportation for some trips, there is a lack of research on how perceptions of public transit systems and TNCs can induce ride-hailing usage. In this article we extend the understanding of ride-hailing phenomena by proposing that structural gaps in public transit are key explanatory variables in the uptake and willingness to pay for ride-hailing trips. Building on an international survey in Mexico City, Bogotá, and Medellín, we develop a Structural Equation Model (SEM) incorporating latent variables expressing perceptions people have about features of ride-hailing and vulnerabilities in public transit. Results show that these variables are relevant. We also confirm that educational attainment and income are instrumental for ride-hailing trips, and that technology embracement is the most important variable to distinguish among levels of adoption. Findings inform public policy by focusing on the negative experiences of using public transit and how this could be generating more ride-hailing trips. TNCs are an attractive transport alternative that can fill gaps in public transit systems but that are also benefiting from structural problems in the transit systems.
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