Searched for: subject%3A%22Partial%255C%2BDifferential%255C%2BEquations%22
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Hadjisotiriou, George (author)
Compositional simulation is computationally intensive for high-fidelity models due to thermodynamic equilibrium relations and the coupling of flow, transport and mass transfer. In this report, two methods for accelerated compositional simulation are outlined and demonstrated for a gas vaporization problem. The first method uses a proxy model...
master thesis 2022
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Titulaer, Björn (author)
Spatiotemporal stochastic processes have applications in various fields, but they can be difficult to numerically approximate in a reasonable time, in particular, in the context of statistical inference for large datasets. <br/>Recently, a new approach for efficient spatiotemporal statistical modeling has been proposed, where the space-time...
master thesis 2022
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Ul Haq, Rana (author)
Convection-dominated flow problems are well-known to have non-physical oscillations near steep gradients or discontinuities in the solution when solved with standard numerical methods, such as finite elements or finite difference methods. To overcome this limitation, algebraic flux correction (AFC) can be used, which is a stabilization method....
master thesis 2022
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Daemen, Mieke (author)
The main aim of the research presented in this report is investigating analytical methods to model fluid-structure interaction in large-scale offshore floating photovoltaics. The model that was attempted to be solved analytically is based on a model presented by Pengpeng Xu (2022).<br/>The dimensions in the equations were removed. Applying a...
bachelor thesis 2022
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Zegers, Samuel (author)
In several experiments, enzymes have shown an in increase in diffusivity in the presence of their substrate. The enhancement in diffusivity ranged from as low as 28% for urease to 80% in the case of alkaline phosphatase. There are two main competing theories. One asserts that catalytically driven boosts propel the enzyme forward in ‘leaps’,...
bachelor thesis 2022
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Oliveira de Almeida, S. (author), Chapiro, Grigori (author), Zitha, P.L.J. (author)
Electromagnetic (EM) heating is an emerging method for storing renewable energy, such as photovoltaic solar and wind electric power, into aquifers. We investigate how the captured energy increases the temperature of a prototypical deep aquifer for a six-month period and then to which extent the stored energy can be recovered during the...
journal article 2022
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Tosti Balducci, G.B.L. (author), Chen, B. Y. (author), Möller, M. (author), Gerritsma, M.I. (author), De Breuker, R. (author)
Structural mechanics is commonly modeled by (systems of) partial differential equations (PDEs). Except for very simple cases where analytical solutions exist, the use of numerical methods is required to find approximate solutions. However, for many problems of practical interest, the computational cost of classical numerical solvers running on...
review 2022
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Hendriks, Leo (author)
This essay shows a two dimensional implementation of the finite element method for the Westervelt equation. To do this the finite element method is first applied to the linear wave equation, then to non-linear diffusion and finally to the Westervelt equation. Both an element by element and a faster vectorized implementation are given for the...
bachelor thesis 2021
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Westdorp, Rik (author)
In this thesis, a variation on the nonlinear Schrödinger (NLS) equation with multiplicative noise is studied. In particular, we consider a stochastic version of the parametrically-forced nonlinear Schrödinger equation (PFNLS), which models the effect of linear loss and the compensation thereof by phase-sensitive amplification in pulse...
master thesis 2021
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Vural, Asya (author)
The porous medium equation $\dv{t}u=\dv{x}(k(u)\dv{x}u)$ is a non-linear degenerate parabolic partial differential equation. Consequently, existence and uniqueness of its solutions is not immediately evident.<br/>This bachelor thesis presents a detailed discussion of Atkinson's and Peletier's 1971 article ``Similarity profiles of flows through...
bachelor thesis 2021
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Leeuwis, Toby (author)
When transforming PDE problems using Fourier and Laplace transforms, we can find functions that represent the problem, and which can be used to determine properties of the problem. We define such functions as symbols $P(\lambda,z)$. In general, we define the class of symbols $S(L_t\times L_x)$ are all functions which are represented by a...
bachelor thesis 2021
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Frima, Erik (author)
In (mathematical) physics one can encounter problems with a fase change, the so called Stefan problems. Numerical methods to solve these problems often use a level-set function which indicates the distance to the fase boundary. Problems can arise in the medial axis points of the zero set. Therefore it can be usefull to calculate this medial axis...
bachelor thesis 2021
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Vos, Bart (author)
In recent years many automatic differentiable programming frameworks have been developed in which numerical programs can be differentiated through automatic differentiation (AD). Examples of these frameworks are Theano, TensorFlow and Pytorch. These frameworks are widely used in Machine Learning. AD also finds applications in the field of...
bachelor thesis 2021
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Barbaro, Alethea (author), Rodriguez, Nancy (author), Yoldas, H. (author), Zamponi, Nicola (author)
We study a two-species cross-diffusion model that is inspired by a system of convectiondiffusion equations derived from an agent-based model on a two-dimensional discrete lattice. The latter model has been proposed to simulate gang territorial development through the use of graffiti markings. We find two energy functionals for the system that...
journal article 2021
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Jongbloed, Henk (author)
Reliable and efficient modelling of magnetic hysteresis in inhomogeneous and aniso-tropic media is an important step in developing a state-of-the-art closed-loop degaussing system for naval ships and submarines, to be developed by TNO and to be used by the Royal Netherlands Navy in an updated generation of naval vessels and submarines. Different...
master thesis 2019
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Shachor, Benny (author)
Understanding the permeability of the subsurface is a crucial step to simulate fluid flow in the subsurface. A parameter estimation problem for the flow equations can be solved to find the permeability. The robust identification of material parameters remains a significant challenge. In classical approaches, the non-linear least-squares problem...
master thesis 2019
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Keetch, Blaine (author), van Gennip, Y. (author)
The Max-Cut problem is a well known combinatorial optimization problem. In this paper we describe a fast approximation method. Given a graph G, we want to find a cut whose size is maximal among all possible cuts. A cut is a partition of the vertex set of G into two disjoint subsets. For an unweighted graph, the size of the cut is the number...
journal article 2019
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van de Kamp, Carsten T. (author)
We consider adaptive network models with discrete and continuous state sets obeying dynamical rules that enable application to swarming systems. The 2-state adaptive network contains a supercritical pitchfork bifurcation in the transition between ordered and disordered stationary solutions. We derive an adaptive network model that works on a...
bachelor thesis 2019
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van der Meer, Remco (author)
Recent works have shown that neural networks can be employed to solve partial differential equations, bringing rise to the framework of physics informed neural networks.The aim of this project is to gain a deeper understanding of these novel methods, and to use these insights to further improve them. We show that solving a partial differential...
master thesis 2019
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Verbist, Victor (author)
A model is developed to simulate NaCl concentrations across a cation exchange membrane in the transient regime. The convectionless Nersnt-Planck equation is combined with the continuity equation to obtain a partial dierential equation in time and space. The boundary conditions at the edges of the cell for this equationare a constant bulk...
bachelor thesis 2019
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