Critical slowing down in random anisotropy magnets

We study the purely relaxational critical dynamics with non-conserved order parameter (model A critical dynamics) for three-dimensional magnets with disorder in a form of the random anisotropy axis. For the random axis anisotropic distribution, the static asymptotic critical behaviour coincides with that of random site Ising systems. Therefore the asymptotic critical dynamics is governed by the dynamical exponent of the random Ising model. However, the disorder influences considerably the dynamical behaviour in the non-asymptotic regime. We perform a field-theoretical renormalization group analysis within the minimal subtraction scheme in two-loop approximation to investigate asymptotic and effective critical dynamics of random anisotropy systems. The results demonstrate the non-monotonic behaviour of the dynamical effective critical exponent $z_{\rm eff}$.Comment: 11 pages, 4 figures, style file include

Total destruction of invariant tori for the generalized Frenkel-Kontorova model

We consider generalized Frenkel-Kontorova models on higher dimensional lattices. We show that the invariant tori which are parameterized by continuous hull functions can be destroyed by small perturbations in the $C^r$ topology with $r<1$

Hyperbolic outer billiards : a first example

We present the first example of a hyperbolic outer billiard. More precisely we construct a one parameter family of examples which in some sense correspond to the Bunimovich billiards.Comment: 11 pages, 8 figures, to appear in Nonlinearit

Sensitivity of mixing layers to three-dimensional forcing

It is well known that turbulent mixing layers are dominated by large scale, fairly coherent structures, and that these structures are related to the stability characteristics of the flow. These facts have led researchers to attempt controlling such flows by selectively forcing certain unstable modes, which can in addition have the effect of suppressing other modes. Much of the work on controlling the mixing layer has relied on forcing 2-D instabilities. The results of forcing 3-D instabilities are addressed. The objectives of the work are twofold: to understand how a mixing layer responds to 3-D perturbations, and to test the validity of an amplitude expansion in predicting the mixing layer development. The amplitude expansion could be very useful in understanding and predicting the 3-D response of the flow to a variety of initial conditions

Dynamics of coherent structures in a plane mixing layer

An incompressible, time developing 3-D mixing layer with idealized initial conditions was simulated numerically. Consistent with the suggestions from experimental measurements, the braid region between the dominant spanwise vortices or rolls develops longitudinal vortices or ribs, which are aligned upstream and downstream of a roll and produce spanwise distortion of the rolls. The process by which this distortion occurs is explained by studying a variety of quantities of dynamic importance (e.g., production of enstrophy, vortex stretching). Other quantities of interest (dissipation, helicity density) are also computed and discussed. The currently available simulation only allows the study of the early evolution (before pairing) of the mixing layer. New simulations in progress will relieve this restriction