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Using a nonlocal second-order traffic flow model we present an approach to control the dynamics towards a steady state. The system is controlled by the leading vehicle driving at a prescribed velocity and also determines the steady state.…
In convex planar domains, given an initial vorticity with one sign, we study the regularity and geometric properties of the dynamically stable solutions to the Euler equations in the coadjoint orbit of the initial vorticity. These flows…
We propose a new way of thinking about one parameter persistence. We believe topological persistence is fundamentally not about decomposition theorems but a central role is played by a choice of metrics. Choosing a pseudometric between…
The dynamics of hexagon patterns in rotating systems are investigated within the framework of modified Swift-Hohenberg equations that can be considered as simple models for rotating convection with broken up-down symmetry, e.g.…
We study the meandering instability during growth of an isolated nanostructure, a crystalline cone, consisting of concentric circular steps. The onset of the instability is studied analytically within the framework of the standard…
Waves with constant vorticity and electrohydrodynamics flows are two topics in fluid dynamics that have attracted much attention from scientists for both the mathematical challenge and their industrial applications. The coupling of electric…
The general question of how a beam becomes unstable has been one of the fundamental research topics among beam and accelerator physicists for several decades. In this study, we revisited the general problem of linear beam stability in…
Based on the mean-field method applied either to the extended single-band Hubbard model or to the single-band Peierls-Hubbard Hamiltonian we study the stability of both site-centered and bond-centered charge domain walls. The difference in…
We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently…
The steady states of an isotone electric system are described by an isotone function with respect to the componentwise order. When there are steady states, we highlight a dominant steady state and we study its domain of attraction for the…
This research is focused on linear analysis of a plane-parallel flow stability in a transverse magnetic field (Hartmann flow) within a convective approximation. We derive and solve equations describing the perturbation growth. Perturbation…
We consider a continuum phase field model for crystal growth via molecular beam epitaxy, with the goal of determining stable numerical time integration methods for the dynamics. We parametrize a class of semi-implicit methods that are…
We consider the stability of position control of traveling waves in reaction-diffusion system as proposed in {[}J. L\"ober, H. Engel, arXiv:1304.2327{]}. Instead of analyzing the controlled reaction-diffusion system, stability is studied on…
Stability of solitons in parity-time (PT)-symmetric periodic potentials (optical lattices) is analyzed in both one- and two-dimensional systems. First we show analytically that when the strength of the gain-loss component in the PT lattice…
The stability of an expanding parton plasma is analyzed within quasi-particle models. The effective mass of the parton is calculated self-consistently from a gap equation which is either obtained from the Nambu Jona-Lasinio Lagrangian or…
We present analytic and numerical results for the evolution of currents on superconducting strings in the classical $U(1) \times U(1)$ model. We derive an energy functional for the currents and charges on these strings, establishing…
We study $\varepsilon$-stability in continuous logic. We first consider stability in a model, where we obtain a definability of types result with a better approximation than that in the literature. We also prove forking symmetry for…
The stability of heteroclinic cycles may be obtained from the value of the local stability index along each connection of the cycle. We establish a way of calculating the local stability index for quasi-simple cycles: cycles whose…
The linear stability of a stratified shear flow for smooth density profiles is studied. This work focuses on the nature of the stability boundaries of flows in which both Kelvin-Helmholtz and Holmboe instabilities are present. For a fixed…
We use numerical simulations and semi-analytical methods to investigate the stability and the interactions of nontopological stationary qball solutions. In the context of a simple model we map the parameter sectors of stability for a single…