Related papers: Degenerate Dynamical Systems
This paper addresses the stability of a class of parabolic equations in non-cylindrical domains. We investigate the $L^\infty$-stability of systems for both nondegenerate and degenerate cases. Unlike in cylindrical domains, solutions to…
The interplay between dissipation and internal interactions in quantum many-body systems gives rise to a wealth of novel phenomena. Here we investigate spin-1/2 chains with uniform local couplings to a Markovian environment using the…
Dynamics of cylindrical and spherical relativistic domain walls is investigated with the help of a new method based on Taylor expansion of the scalar field in a vicinity of the core of the wall. Internal oscillatory modes for the domain…
In [30] different statistical behavior of dynamical orbits without syndetic center are considered. In present paper we continue this project and consider different statistical behavior of dynamical orbits with nonempty syndetic center: Two…
Transitions between different topologically ordered phases have been studied by artificially creating boundaries between these gapped phases and thus studying their effects relating to condensation and tunneling of particles from one phase…
Domain walls (DWs) can be produced when a discrete symmetry is spontaneously broken, and long-lived DWs can dominate the energy density of the universe. In this work, we explore the possibility that a "domain wall dominant (DWD)" phase…
This letter investigates the molecular dynamics of inelastic disks without external forcing. By introducing a new observation frame with a rescaled time, we observe the virtual steady states converted from asymptotic energy dissipation…
In this paper we study the dynamics of a general non-autonomous dynamical system generated by a family of continuous self maps on a compact space $X$. We derive necessary and sufficient conditions for the system to exhibit complex dynamical…
We develop a no-go theorem for two-dimensional bosonic systems with crystal symmetries: if there is a half-integer spin at a rotation center, where the point-group symmetry is $\mathbb D_{2,4,6}$, such a system must have a ground-state…
Using Monte Carlo simulation, we study a fluid of two-dimensional hard rods inside a small circular cavity bounded by a hard wall, from the dilute regime to the high-density, layering regime. Both planar and homeotropic anchoring of the…
We analyze the morphological transition of a one-dimensional system described by a scalar field, where a flat state looses its stability. This scalar field may for example account for the position of a crystal growth front, an order…
Decomposition of state spaces into dynamically different components is helpful for the understanding of dynamical behaviors of complex systems. A Conley type decomposition theorem is proved for nonautonomous dynamical systems defined on a…
The spatiotemporal structure formation problem is investigated in the region far above the transverse ferromagnetic resonance instability. The investigations are based on the dissipative Landau-Lifshitz equation and have been performed on a…
We consider evolution of a passive scalar (concentration of pollutants or temperature) in a chaotic (turbulent) flow. A universal asymptotic behavior of the passive scalar decay (homogenization) related to peripheral regions (near walls) is…
Spiral waves are investigated in chemical systems whose underlying spatially-homogeneous dynamics is governed by a deterministic chaotic attractor. We show how the local periodic behavior in the vicinity of a spiral defect is transformed to…
The dynamics of a domain wall in magnetostrictive materials is investigated. The domain wall is modeled by a d-dimensional interface moving in a d+1-dimensional environment. Long-range demagnetization effects and quenched disorder are…
The late-time cosmological dynamics of disformal gravity are investigated using dynamical systems methods. It is shown that in the general case there are no stable attractors that screen fifth-forces locally and simultaneously describe a…
The crossing of a transition state in a multidimensional reactive system is mediated by invariant geometric objects in phase space: An invariant hyper-sphere that represents the transition state itself and invariant hyper-cylinders that…
Since closed lines of {\it accidental} electronic degeneracies were demonstrated to be possible, even frequent, by Herring in 1937, no further developments arose for eight decades. The earliest report of such a nodal loop in a real material…
Enslaved phase-separation fronts that move with a speed just smaller than that of a free front will leave in their wake a morphology of alternating domains that are roughly aligned with the front. However, these alternating domains will…