Related papers: Stable Multi-Level Monotonic Eroders
The sliding columnar phase is a new liquid-crystalline phase of matter composed of two-dimensional smectic lattices stacked one on top of the other. This phase is characterized by strong orientational but weak positional correlations…
The parametrically driven damped nonlinear Schr\"odinger equation serves as an amplitude equation for a variety of resonantly forced oscillatory systems on the plane. In this note, we consider its nodal soliton solutions. We show that…
A novel model of biological organisms is advanced, treating an organism as a self-consistent system subject to a pathogen flux. The principal novelty of the model is that it describes not some parts, but a biological organism as a whole.…
For a class of linear switched systems in continuous time a controllability condition implies that state feedbacks allow to achieve almost sure stabilization with arbitrary exponential decay rates. This is based on the Multiplicative…
In this paper, We study an one--dimensional morphogenesis model considered by C. Stinner et al. in (Math. Meth. Appl. Sci. 2012,35 (445-465). Under homogeneous boundary conditions, we prove the existence of nonconstant positive steady…
The meron-cluster algorithm was previously used to extensively study the physics associated with the spontaneous breaking of a discrete symmetry. We recently discovered that a larger class of models with spontaneous breaking of continuous…
The quantitative modeling and design of modern short-pulse fiber lasers cannot be performed with averaged models because of large variations in the pulse parameters within each round trip. Instead, lumped models obtained by concatenating…
We investigate the topological properties of invariant sets associated with the dynamics of scattering systems with three or more degrees of freedom. We show that the asymptotic separation of one degree of freedom from the rest in the…
Solitary wave and soliton solutions of nonlinear equations are well known for physicists. A soliton is a solitary wave with some outstanding features which make it reasonable to be studied seriously in nonlinear systems. In fact most of the…
The Euler equations on a three-dimensional periodic domain have a family of shear flow steady states. We show that the linearised system around these steady states decomposes into subsystems equivalent to the linearisation of shear flows in…
The decades-long search for a shape that tiles the plane only aperiodically under translations and rotations recently ended with the discovery of the `spectre' aperiodic monotile. In this setting we study the dimer model, in which dimers…
Unlike the well-known Mott's argument that extended and localized states should not coexist at the same energy in a generic random potential, we provide an example of a nearest-neighbor tight-binding disordered model which carries both…
This article offers a comprehensive survey of results obtained for solitons and complex nonlinear wave patterns supported by purely nonlinear lattices (NLs), which represent a spatially periodic modulation of the local strength and sign of…
A new class of deterministic dynamical systems, termed semipredictable dynamical systems, is presented. The spatiotemporal evolution of these systems have both predictable and unpredictable traits, as found in natural complex systems. We…
We consider linear stability of steady states of 1(1/2) and 3D Vlasov-Maxwell systems for collisionless plasmas. The linearized systems can be written as separable Hamiltonian systems with constraints. By using a general theory for…
We consider a simple analytically tractable model of metastability and ageing. In this model, a particle can jump left or right by two steps to an unoccupied site, but only if the the site in between is occupied. We show that the model is…
This is a study of two-dimensional steady periodic travelling waves on the surface of an infinitely deep irrotational ocean, when the top streamline is in contact with a membrane which has a nonlinear response to stretching and bending, and…
Surfaces eroded by ion-sputtering are sometimes observed to develop morphologies which are either ripple (periodic), or rough (non-periodic). We introduce a discrete stochastic model that allows us to interpret these experimental…
Periodic configurations of electrodes, in particular of microelectrodes, have been of interest since the advent of microfabrication. In this report, theory which is common to any periodic cell (or any cell that can be extended periodically)…
It is a classical result of Euler that the rotation of a torque-free three-dimensional rigid body about the short or the long axis is stable, whereas the rotation about the middle axis is unstable. This result is generalized to the case of…