Numerical pancake droplets: from capturing to versatile microfluidics
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This thesis focuses on the numerical analysis of partial differential equations (PDEs) with an emphasis on first and second-order fully nonlinear PDEs. The main goal is the design of numerical methods to solve a variety of equations such as orthogonal maps ...
We study the large deviations of the power injected by the active force for an active Ornstein-Uhlenbeck particle (AOUP), free or in a confining potential. For the free-particle case, we compute the rate function analytically in d-dimensions from a saddle- ...
Multiscale problems, such as modelling flows through porous media or predicting the mechanical properties of composite materials, are of great interest in many scientific areas. Analytical models describing these phenomena are rarely available, and one mus ...
In this thesis we consider inverse problems involving multiscale elliptic partial differential equations. The name multiscale indicates that these models are characterized by the presence of parameters which vary on different spatial scales (macroscopic, m ...
Analysis-suitable T-splines (ASTS) including both extraordinary points and T-junctions are used to solve Kirchhoff-Love shell problems. Extraordinary points are required to represent surfaces with arbitrary topological genus. T-junctions enable local refin ...
The experimental and numerical investigation presented by Bertsch et al. (Phys. Rev. Fluids, vol. 5, 2020a, p. 054202) describes the self-sustained oscillations induced by the interaction of two impinging jets in microfluidic devices. While the oscillatory ...
Stabilized Runge–Kutta (aka Chebyshev) methods are especially efficient for the numerical solution of large systems of stiff differential equations because they are fully explicit; hence, they are inherently parallel and easily accommodate nonlinearity. Fo ...
We present a numerical method for the solution of nonlinear geomechanical problems involving localized deformation along shear bands and fractures. We leverage the boundary element method to solve for the quasi-static elastic deformation of the medium whil ...
The basis of the discrete element method is to model masses interacting with each other through different forces and constraints. On each mass, the second law of Newton is applied to obtain a differential equation. From this equation and boundary condition ...
The numerical solution of the stepped pressure equilibrium (Hudson et al 2012 Phys. Plasmas 19 112502) requires a fast and robust solver to obtain the Beltrami field in three-dimensional geometry such as stellarators. The spectral method implemented in the ...