Related papers: Introduction to shape stability for a storage mode…
We provide a thorough study of stability of the 1-D continuity equation, which models many physical conservation laws. In our system-theoretic perspective, the velocity is considered to be an input. An additional input appears in the…
We are interested in developing a numerical method for capturing stationary sheaths, that a plasma forms in contact with a metallic wall. This work is based on a bi-species (ion/electron) Vlasov-Amp{\`e}re model proposed in [3]. The main…
We say that an algorithm is stable if small changes in the input result in small changes in the output. This kind of algorithm stability is particularly relevant when analyzing and visualizing time-varying data. Stability in general plays…
We study stability of a growth process generated by sequential adsorption of particles on a one-dimensional lattice torus, that is, the process formed by the numbers of adsorbed particles at lattice sites, called heights. Here the stability…
The aim of the article is to study the stability of a non-local kinetic model proposed by Loy and Preziosi (2019a). We split the population in two subgroups and perform a linear stability analysis. We show that pattern formation results…
In many contexts such as queuing theory, spatial statistics, geostatistics and meteorology, data are observed at irregular spatial positions. One model of this situation involves considering the observation points as generated by a Poisson…
Discrete stability extends the classical notion of stability to random elements in discrete spaces by defining a scaling operation in a randomised way: an integer is transformed into the corresponding binomial distribution. Similarly…
We study solutions to a one-phase singular perturbation problem that arises in combustion theory and that formally approximates the classical one-phase free boundary problem. We introduce a natural density condition on the transition layers…
We investigate a two-dimensional transmission model consisting of a wave equation and a Kirchhoff plate equation with dynamical boundary controls under geometric conditions. The two equations are coupled through transmission conditions…
A stable soliton configuration for a nucleon emerges when the nucleon stability and $\Sigma_N$ term discrepancy problems are studied semi-quantitatively within a local theory developed recently. The approach developed here goes beyond the…
Stability is a fundamental notion in dynamical systems and control theory that, traditionally understood, describes asymptotic behavior of solutions around an equilibrium point. This notion may be characterized abstractly as continuity of a…
Parametric projections let analysts embed new points in real time, but input variations from measurement noise or data drift can produce unpredictable shifts in the 2D layout. Whether and where a projection is locally stable remains largely…
The stability of stationary solutions of first-order systems of PDE's are considered. They may include some singular geometric terms, leading to discontinuous flux and non-conservative products. Based on several examples in Fluid Mechanics,…
Stability is a key property of both forward models and inverse problems, and depends on the norms considered in the relevant function spaces. For instance, stability estimates for hyperbolic partial differential equations are often based on…
A classical model of fluid dynamics is considered which describes the shape evolution of a viscous liquid droplet on a homogeneous substrate. All equilibria are characterized and their stability is analyzed by a geometric reduction…
We give a geometric account of the relative motion or the shape dynamics of $N$ point vortices on the sphere exploiting the $\mathsf{SO}(3)$-symmetry of the system. The main idea is to bypass the technical difficulty of the…
We consider a generalized version in continuous time of the parking problem of Knuth. Files arrive following a Poisson point process and are stored on a hardware identified with the real line. We specify the distribution of the space of…
The long-time behavior is one of the most fundamental properties of dynamical systems. Poincar\'e studied the Poisson stability to capture the property of whether points return arbitrarily near the initial positions. Birkhoff studied the…
Variational stability, in the sense of local good behavior of optimal values and solutions in problems of optimization under shifts in parameters, is important not only for validating model robustness in practical applications but also for…
We prove homological stability for sequences of "oriented configuration spaces" as the number of points in the configuration goes to infinity. These are spaces of configurations of n points in a connected manifold M of dimension at least 2…