2 citations · 4 across the 4 of their papers we have counts for
6 papers
Excitation and Identifiability in the 2D Navier-Stokes equations
Vincent R. Martinez, Sarah Strikwerda, Xiang Wan
Convergence in parameter estimation classically requires ``persistency of excitation," which is a non-degeneracy condition on a trajectory-dependent signal. This paper develops, to…
Determining Modes, State Reconstruction, and Intertwinement: Existence of Self-Synchronizing Intertwinements
Elizabeth Carlson, Aseel Farhat, Vincent R. Martinez +1
In the companion paper of the authors, a general synchronization framework was developed in the paradigmatic context of the 2D Navier-Stokes equations that allows one to precisely…
Relaxation-based schemes for on-the-fly parameter estimation in dissipative dynamical systems
Vincent R. Martinez, Jacob Murri, Jared P. Whitehead
This article studies two particular algorithms, a Relaxation Least Squares (RLS) algorithm and a Relaxation Newton Iteration (RNI) scheme , for reconstructing unknown parameters in…
On the nudging approach to continuous data assimilation in the limit of infinite error feedback gain
Elizabeth Carlson, Aseel Farhat, Vincent R. Martinez +1
This article studies the intimate relationship between two filtering algorithms for continuous data assimilation, the synchronization filter and the nudging filter, in the paradigm…
Determining Modes, State Reconstruction, and Intertwinement: A Synchronization Framework
Elizabeth Carlson, Aseel Farhat, Vincent R. Martinez +1
This article studies the interrelation between the determining modes property in the two-dimensional (2D) Navier-Stokes equations (NSE) of incompressible fluids and the reconstruct…
Remarks on the stabilization of large-scale growth in the 2D Kuramoto-Sivashinsky equation
Adam Larios, Vincent R. Martinez
In this article, some elementary observations are made regarding the behavior of solutions to the two-dimensional curl-free Burgers equation which suggest the distinguished role pl…