Related papers: Optimising energy growth as a tool for finding exa…
Background: The generation of potential energy surfaces is a critical step in theoretical models aiming to understand and predict nuclear fission. Discontinuities frequently arise in these surfaces in unconstrained collective coordinates,…
Nonequilibrium statistical models of point vortex systems are constructed using an optimal closure method, and these models are employed to approximate the relaxation toward equilibrium of systems governed by the two-dimensional Euler…
Persistence-based topological optimization deforms a point cloud $X \subset \mathbb{R}^d$ by minimizing objectives of the form $L(X) = \ell(\mathrm{Dgm}(X))$, where $\mathrm{Dgm}(X)$ is a persistence diagram. In practice, optimization is…
Resolvent analysis is a powerful tool for studying coherent structures in turbulent flows. However, its application beyond canonical flows with symmetries that can be used to simplify the problem to inherently three-dimensional flows and…
Four different applications of spectral proper orthogonal decomposition (SPOD): low-rank reconstruction, denoising, frequency-time analysis, and prewhitening are demonstrated on large-eddy simulation data of a turbulent jet. SPOD-based…
This paper analyses a $(1,\lambda)$-Evolution Strategy, a randomised comparison-based adaptive search algorithm, on a simple constraint optimisation problem. The algorithm uses resampling to handle the constraint and optimizes a linear…
We propose a continuous optimization method for solving dense 3D scene flow problems from stereo imagery. As in recent work, we represent the dynamic 3D scene as a collection of rigidly moving planar segments. The scene flow problem then…
We consider two-dimensional homogeneous shear turbulence within the context of optimal control, a multi-scale turbulence model containing the fluctuation velocity and pressure correlations up to the fourth order; The model is formulated on…
Accurately solving PDEs with localised features requires refined meshes that adapt to the solution. Traditional numerical methods, such as finite elements, are linear in nature and often ineffective for such problems, as the mesh is not…
We investigate uncertainty growth and chaotic dynamics in statistically steady, stably stratified three-dimensional turbulence. Using direct numerical simulations of the Boussinesq equations, we quantify the divergence of initially…
Variational phase-field models of brittle fracture pose a local constrained minimization problem of a non-convex energy functional. In the discrete setting, the problem is most often solved by alternate minimization, exploiting the separate…
In this paper we accomplish the development of the fast rank-adaptive solver for tensor-structured symmetric positive definite linear systems in higher dimensions. In [arXiv:1301.6068] this problem is approached by alternating minimization…
We propose a novel framework for approximating the statistical properties of turbulent flows by combining variational methods for the search of unstable periodic orbits with resolvent analysis for dimensionality reduction. Traditional…
This work proposes a novel method for scaling multi-timestep security-constrained optimal power flow in large power grids. The challenge arises from dealing with millions of variables and constraints, including binary variables and…
We present a novel energy-based numerical analysis of semilinear diffusion-reaction boundary value problems. Based on a suitable variational setting, the proposed computational scheme can be seen as an energy minimisation approach. More…
We present efficient deep learning techniques for approximating flow and transport equations for both single phase and two-phase flow problems. The proposed methods take advantages of the sparsity structures in the underlying discrete…
In this work, we study shape optimization problems in the Stokes flows. By phase-field approaches, the resulted total objective function consists of the dissipation energy of the fluids and the Ginzburg--Landau energy functional as a…
Verifying nonlinear stability of a laminar fluid flow against all perturbations is a central challenge in fluid dynamics. Past results rely on monotonic decrease of a perturbation energy or a similar quadratic generalized energy. None show…
This article presents direct numerical simulations of the growth of turbulent spots in the transitional regime of plane Couette flow. A quantitative description of the growth process and of the detail of the quadrupolar flow around the spot…
We develop a numerical scheme to determine which planar snake motions are optimal for locomotory efficiency, across a wide range of frictional parameter space. For a large coefficient of transverse friction, we find that retrograde…