Essays about: "Partial differential equations"
Showing result 1 - 5 of 89 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. Data Assimilation for Systems with Multiple Timescales
University essay from KTH/Skolan för teknikvetenskap (SCI)Abstract : This text provides an overview of problems in the field of data assimilation. We explore the possibility of recreating unknown data by continuously inserting known data into certain dynamical systems, under certain regularity assumptions. READ MORE
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3. 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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4. Application of Physics-Informed Neural Networks for Galaxy Dynamics
University essay from Linnéuniversitetet/Institutionen för fysik och elektroteknik (IFE)Abstract : Developing efficient and accurate numerical methods to simulate dynamics of physical systems has been an everlasting challenge in computational physics. Physics-Informed Neural Networks (PINNs) are neural networks that encode laws of physics into their structure. READ MORE
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5. 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
