Elasticity effects on the stability of growing films

It is shown how the combination of atomic deposition and nonlinear diffusion may lead, below a critical temperature, to the growth of nonuniform layers on a substrate. The dynamics of such a system is of the Cahn-Hilliard type, supplemented by reaction terms representing adsorption-desorption processes. The instability of uniform layers leads to the formation of nanostructures which correspond to regular spatial variations of substrate coverage. Since coverage inhomogeneities generate internal stresses, the coupling between coverage evolution and film elasticity fields is also considered, for film thickness below the critical thickness for misfit dislocation nucleation. It is shown that this coupling is destabilizing and favors nanostructure formation. It also favors square planforms which could compete, and even dominate over the haxagonal or stripe nanostructures induced by coverage dynamics alon

Convective and Absolute Instabilities in the Subcritical Ginzburg-Landau Equation

We study the nature of the instability of the homogeneous steady states of the subcritical Ginzburg-Landau equation in the presence of group velocity. The shift of the absolute instability threshold of the trivial steady state, induced by the destabilizing cubic nonlinearities, is confirmed by the numerical analysis of the evolution of its perturbations. It is also shown that the dynamics of these perturbations is such that finite size effects may suppress the transition from convective to absolute instability. Finally, we analyze the instability of the subcritical middle branch of steady states, and show, analytically and numerically, that this branch may be convectively unstable for sufficiently high values of the group velocity.Comment: 13 pages, 10 figures (fig1.ps, fig2.eps, fig3.ps, fog4a.ps, fig 4b.ps, fig5.ps, fig6.eps, fig7a.ps, fig7b.ps, fig8.p

Patterns arising from the interaction between scalar and vectorial instabilities in two-photon resonant Kerr cavities

We study pattern formation associated with the polarization degree of freedom of the electric field amplitude in a mean field model describing a nonlinear Kerr medium close to a two-photon resonance, placed inside a ring cavity with flat mirrors and driven by a coherent $\hat x$-polarized plane-wave field. In the self-focusing case, for negative detunings the pattern arises naturally from a codimension two bifurcation. For a critical value of the field intensity there are two wave numbers that become unstable simultaneously, corresponding to two Turing-like instabilities. Considered alone, one of the instabilities would originate a linearly polarized hexagonal pattern whereas the other instability is of pure vectorial origin and would give rise to an elliptically polarized stripe pattern. We show that the competition between the two wavenumbers can originate different structures, being the detuning a natural selection parameter.Comment: 21 pages, 6 figures. http://www.imedea.uib.es/PhysDep

Theory for the spatiotemporal dynamics of domain walls close to a nonequilibrium Ising-Bloch transition

© 2015 American Physical Society. We derive a generic model for the interaction of domain walls close to a nonequilibrium-Bloch transition. The universal scenario predicted by the model includes stationary Ising and Bloch localized structures (dissipative solitons), as well as drifting and oscillating Bloch structures. Our theory also explains the behavior of Bloch walls during a collision. The results are confirmed by numerical simulations of the Ginzburg-Landau equation forced at twice its natural frequency and are in agreement with previous observations in several physical systems.Peer Reviewe

Wave-unlocking transition in resonantly coupled complex Ginzburg-Landau equations

We study the effect of spatial frequency forcing on standing-wave solutions of coupled complex Ginzburg-Landau equations. The model considered describes several situations of nonlinear counterpropagating waves and also of the dynamics of polarized light waves. We show that forcing introduces spatial modulations on standing waves which remain frequency locked with a forcing-independent frequency. For forcing above a threshold the modulated standing waves unlock, bifurcating into a temporally periodic state. Below the threshold the system presents a kind of excitability.Financial support from DGICYT Projects PB94-1167 and PB94-1172 is acknowledged.Peer Reviewe

Magnetization and spin-spin energy diffusion in the XY model: a diagrammatic approach

It is shown that the diagrammatic cluster expansion technique for equilibrium averages of spin operators may be straightforwardly extended to the calculation of time-dependent correlation functions of spin operators. We use this technique to calculate exactly the first two non-vanishing moments of the spin-spin and energy-energy correlation functions of the XY model with arbitrary couplings, in the long-wavelength, infinite temperature limit appropriate for spin diffusion. These moments are then used to estimate the magnetization and spin-spin energy diffusion coefficients of the model using a phenomenological theory of Redfield. Qualitative agreement is obtained with recent experiments measuring diffusion of dipolar energy in calcium fluoride.Comment: 28 pages, 15 embedded .eps figures, Elsevier preprint forma

Numerical Solution of the Walgraef-Aifantis Model for Simulation of Dislocation Dynamics in Materials Subjected to Cyclic Loading

Abstract. Strain localization and dislocation pattern formation are typical features of plastic deformation in metals and alloys. Glide and climb dislocation motion along with accompanying production/annihilation processes of dislocations lead to the occurrence of instabilities of initially uniform dislocation distributions. These instabilities result into the development of various types of dislocation micro-structures, such as dislocation cells, slip and kink bands, persistent slip bands, labyrinth structures, etc., depending on the externally applied loading and the intrinsic lattice constraints. The Walgraef-Aifantis (WA) (Walgraef and Aifanits, J. Appl. Phys., 58, 668, 1985) model is an example of a reaction-diffusion model of coupled nonlinear equations which describe 0 formation of forest (immobile) and gliding (mobile) dislocation densities in the presence of cyclic loading. This paper discuss two versions of the WA model, the first one comprising linear diffusion of the density of mobile dislocations and the second one, with nonlinear diffusion of said variable. Subsequently, the paper focus on a finite difference, second order in time Cranck-Nicholson semi-implicit scheme, with internal iterations at each time step and a spatial splitting using the Stabilizing, Correction (Christov and Pontes, Mathematical and Computer 0, 35, 87, 2002) for solving the model evolution equations in two dimensions. The discussion on the WA model and on the numerical scheme was already presented on a conference paper by the authors (Pontes et al., AIP Conference Proceedings, Vol. 1301 pp. 511-519, 2010. The first results of four simulations, one with linear diffusion of the mobile dislocations and three with nonlinear diffusion are presented. Several phenomena were observed in the numerical simulations, like the increase of the fundamental wavelength of the structure, the increase of the walls height and the decrease of its thickness

Polarization coupling and pattern selection in a type-II optical parametric oscillator

We study the role of a direct intracavity polarization coupling in the dynamics of transverse pattern formation in type-II optical parametric oscillators. Transverse intensity patterns are predicted from a stability analysis, numerically observed, and described in terms of amplitude equations. Standing wave intensity patterns for the two polarization components of the field arise from the nonlinear competition between two concentric rings of unstable modes in the far field. Close to threshold a wavelength is selected leading to standing waves with the same wavelength for the two polarization components. Far from threshold the competition stabilizes patterns in which two different wavelengths coexist.Comment: 14 figure