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The quasistatic approximation is a useful but questionable simplification for analyzing step instabilities during the growth/evaporation of vicinal surfaces. Using this approximation, we characterized in Part I of this work the effect on…
We study an analytically tractable model with long-range interactions for which an out-of-equilibrium very long-lived coherent structure spontaneously appears. The dynamics of this model is indeed very peculiar: a bicluster forms at low…
This paper derives a density matrix of the steady-state statistical mechanics compatible with the steady-state thermodynamics proposed by Oono and Paniconi [Prog. Theor. Phys. Suppl. {\bf 130}, 29 (1998)]. To this end, we adopt three…
Given the significance of physical measures in understanding the complexity of dynamical systems as well as the noisy nature of real-world systems, investigating the stability of physical measures under noise perturbations is undoubtedly a…
Dufty, Lee, Lutsko, Montanero, and Santos have carried out stability analyses of steady stationary shear flows. Their approach is based on the compressible and heat conducting Navier-Stokes-Fourier model. It predicts the unstable…
The algebraic stability theorem for $\mathbb{R}$-persistence modules is a fundamental result in topological data analysis. We present a stability theorem for $n$-dimensional rectangle decomposable persistence modules up to a constant…
This article aims to investigate sufficient conditions for the stability of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic…
Accurate simulations of ice sheet dynamics, mantle convection, lava flow, and other highly viscous free-surface flows involve solving the coupled Stokes/free-surface equations. In this paper, we theoretically analyze the stability and…
Stochastic dynamical systems arise naturally across nearly all areas of science and engineering. Typically, a dynamical system model is based on some prior knowledge about the underlying dynamics of interest in which probabilistic features…
The scope of this contribution is to present an overview of the theory of structured deformations of continua, together with some applications. Structured deformations aim at being a unified theory in which elastic and plastic behaviours,…
This article is focused on two related topics within the study of partial differential equations (PDEs) that illustrate a beautiful connection between dynamics, topology, and analysis: stability and spatial dynamics. The first is a property…
In this paper, we provide an overview of the research conducted in the context of structural systems since the latest survey by Dion et al. in 2003. We systematically consider all the papers that cite this survey as well as the seminal work…
We study the stable behaviour of discrete dynamical systems where the map is convex and monotone with respect to the standard positive cone. The notion of tangential stability for fixed points and periodic points is introduced, which is…
This paper investigates the global stability and the global asymptotic stability independent of the sizes of the delays of linear time-varying Caputo fractional dynamic systems of real fractional order possessing internal point delays. The…
Reproducibility is imperative for any scientific discovery. More often than not, modern scientific findings rely on statistical analysis of high-dimensional data. At a minimum, reproducibility manifests itself in stability of statistical…
Determination of stability and instability of singular points in nonlinear dynamical systems is an important issue that has attracted considerable attention in different fields of engineering and science. So far, different well-defined…
Machine-learning technologies for learning dynamical systems from data play an important role in engineering design. This research focuses on learning continuous linear models from data. Stability, a key feature of dynamic systems, is…
We consider the motion described by the Navier-Stokes equations in a box with periodic boundary conditions. First we prove the existence of global strong two-dimensional solutions. Next we show the existence of global strong…
Estimation of structure, such as in variable selection, graphical modelling or cluster analysis is notoriously difficult, especially for high-dimensional data. We introduce stability selection. It is based on subsampling in combination with…
The Davey-Stewartson (DS) equations with a perturbation term are presented by taking a fluid system as an example on an uneven bottom. Stability of dromions, solutions of the DS equations with localized structures, against the perturbation…