25 research outputs found
A Bogomol`nyi equation for intersecting domain walls
We argue that the Wess-Zumino model with quartic superpotential admits static
solutions in which three domain walls intersect at a junction. We derive an
energy bound for such junctions and show that configurations saturating it
preserve 1/4 supersymmetry.Comment: 4 pages revtex. No figures. Revised version to appear in Physical
Review Letters includes discussion of the supersymmetry algebr
One-dimensional symmetry and Liouville type results for the fourth order Allen-Cahn equation in R
In this paper, we prove an analogue of Gibbons' conjecture for the extended
fourth order Allen-Cahn equation in R N , as well as Liouville type results for
some solutions converging to the same value at infinity in a given direction.
We also prove a priori bounds and further one-dimensional symmetry and rigidity
results for semilinear fourth order elliptic equations with more general
nonlinearities
Spontaneous angular momentum generation of two-dimensional fluid flow in an elliptic geometry
Spontaneous spin-up, i.e. the significant increase of the total angular momentum of a flow that initially has no net angular momentum, is very characteristic for decaying two-dimensional turbulence in square domains bounded by rigid no-slip walls. In contrast, spontaneous spin-up is virtually absent for such flows in a circular domain with a no-slip boundary. In order to acquire understanding of this strikingly different behavior observed on the square and the circle we consider a set of elliptic geometries with a gradual increase of the eccentricity. It is shown that a variation of the eccentricity can be used as a control parameter to tune the relative contribution of the pressure and viscous stresses in the angular momentum balance. Direct numerical simulations demonstrate that the magnitude of the torque can be related to the relative contribution of the pressure. As a consequence, the number of spin-up events in an ensemble of slightly different initial conditions strongly depends on the eccentricity.For small eccentricities strong and rapid spin-up events are observed occasionally, whereas the majority of the runs does not show significant spin-up. Small differences in the initial condition can result in a completely different evolution of the flow and appearance of the end-state of the decay process. For sufficiently large eccentricities all the runs in the ensemble demonstrate strong and rapid spin-up, which is consistent with the flow development on the square. It is verified that the number of spin-up events for a given eccentricity does not depend on the Reynolds number of the flow. This observation is consistent with the conjecture that it is the pressure on the domain boundaries thatdrives the spin-up processes
Hysteresis for ferromagnetism: asymptotics of some two-scale Landau-Lifshitz model
International audienceWe study a two-scale version of the Landau-Lifshitz system of ferromagnetism, introduced by Starynkevitch to modelize hysteresis: the response of the magnetization is fast compared to a slowly varying applied magnetic field. Taking the exchange term into account, in space dimension 3, we prove that, under some natural stability assumption on the equilibria of the system, the strong solutions follow the dynamics of these equilibria. We also give explicit examples of relevant equilibria and exterior magnetic fields, when the ferromagnetic medium occupies some ellipsoidal domain