arXiv subjects

Bart de Leeuw

Publications and source records attributed to Bart de Leeuw.

3 recordsLinked to original sources

arXiv2020

Shadowing-based data assimilation method for partially observed models

In this article we develop further an algorithm for data assimilation based upon a shadowing refinement technique [de Leeuw et al., SIAM J. Appl. Dyn. Sys., 17 (2018)] to take partial observations into account. Our method is based on regularized Gauss-Newton method. We prove local convergence to the solution manifold and provide a lower bound on the algorithmic time step. We use numerical experiments with the Lorenz 63 and Lorenz 96 models to illustrate convergence of the algorithm and show that the results compare favourably with a variational technique (weak-constraint four-dimensional variational method) and a shadowing technique (pseudo-orbit data assimilation). Numerical experiments show that a preconditioner chosen based on a cost function allows the algorithm to find an orbit of the dynamical system in the vicinity of the true solution.

math.OC↗

arXiv2017

Projected Shadowing-based Data Assimilation

In this article we develop algorithms for data assimilation based upon a computational time dependent stable/unstable splitting. Our particular method is based upon shadowing refinement and synchronization techniques and is motivated by work on Assimilation in the Unstable Subspace (AUS) and Pseudo-orbit Data Assimilation (PDA). The algorithm utilizes time dependent projections onto the non-stable subspace determined by employing computational techniques for Lyapunov exponents/vectors. The method is extended to parameter estimation without changing the problem dynamics and we address techniques for adapting the method when (as is commonly the case) observations are not available in the full model state space. We use a combination of analysis and numerical experiments (with the Lorenz 63 and Lorenz 96 models) to illustrate the efficacy of the techniques and show that the results compare favorably with other variational techniques.

math.DS↗

arXiv2015

Stability of the X-Y-phase of the two-dimensional C4 point group insulator

Noninteracting insulating electronic states of matter can be classified according to their symmetries in terms of topological invariants which can be related to effective surface theories. These effective surface theories are in turn topologically protected against the effects of disorder. Topological crystalline insulators are, on the other hand, trivial in the sense of the above classification but still possess surface modes. In this work we consider an extension of the Bernevig-Hughes-Zhang model that describes a topological crystalline insulator. We explicitly show that the surface properties of this state can be as robust as in topologically nontrivial insulators, but only if the $S_z$-component of the spin is conserved. However, in the presence of Rashba spin-orbit coupling this protection vanishes and the surface states localize, even if the crystalline symmetries are intact on average.

cond-mat.mes-hall↗