Essays about: "Partial Differential Equations"
Showing result 1 - 5 of 69 essays containing the words Partial Differential Equations.
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1. Do viscous flows slip?
University essay from Göteborgs universitet/Institutionen för matematiska vetenskaperAbstract : In this thesis, the Stokes equation is discussed and solved under different boundary conditions. The Stokes equation governs the flow of viscous liquids, for example honey or syrup. The first chapters in the thesis provides an introduction to multivector algebra and analysis, with the aim of presenting the concept of Hodge decompositions. READ MORE
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2. Evaluation of Physics Informed Neural Networks in engineering simple structural analysis problems
University essay from Uppsala universitet/Institutionen för informationsteknologiAbstract : Neural Networks have found many applications for a long time in Machine Learning in different disciplines, and have especially flourished in the last decade because of the ever-increasing processing power especially from GPUs. Because of their ability to operate as universal function approximators and model nonlinear processes, attempts have been made in recent years to be also used for modeling partial differential equation (PDE) solutions. READ MORE
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3. Gravity water waves over constant vorticity flows: from laminar flows to touching waves
University essay from Lunds universitet/Matematik (naturvetenskapliga fakulteten); Lunds universitet/MatematikcentrumAbstract : In a recent paper, Hur and Wheeler proved the existence of periodic steady water waves over an infinitely deep, two-dimensional and constant vorticity flow and subject to gravity whose profile overhangs, among which, waves whose surface touches at a point, enclosing a bubble of air. We take this further, proving the existence of a continuous curve of water waves from a laminar flow up to a touching wave for fixed non-zero gravity. READ MORE
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4. Axisymmetric capillary water waves on cylindrical fluid jets
University essay from Lunds universitet/Matematik (naturvetenskapliga fakulteten); Lunds universitet/MatematikcentrumAbstract : In their paper, Vanden-Broeck, Miloh and Spivack (Wave Motion 27, 1998) describe two limiting behaviours of irrotational, axisymmetric capillary water waves using numerical methods. They found a two-parameter family of nontrivial solutions. Some solutions of small amplitude approach a uniform stream, while others approach a static configuration. READ MORE
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5. Implementation and study of boundary integral operators related to PDE:s in the plane
University essay from Lunds universitet/Matematik LTHAbstract : The method of solving boundary value problems of partial differential equations numerically by first reformulating the problem as a boundary integral equation has many advantages over other methods, but also some unique difficulties. Some of these difficulties stem from problems in evaluating singular or nearly singular integral operators, and solving these difficulties is an active field of research. READ MORE