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We study spatiotemporal pattern formation associated with the polarization degree of freedom of the electric field amplitude in a mean field model describing a Kerr medium in a cavity with flat mirrors and driven by a coherent plane-wave field. We consider linearly as well as elliptically polarized driving fields, and situations of self-focusing and self-defocusing. For the case of self-defocusing and a linearly polarized driving field, there is a stripe pattern orthogonally polarized to the driving field. Such a pattern changes into a hexagonal pattern for an elliptically polarized driving field. The range of driving intensities for which the pattern is formed shrinks to zero with increasing ellipticity. For the case of self-focusing, changing the driving field ellipticity leads from a linearly polarized hexagonal pattern (for linearly polarized driving) to a circularly polarized hexagonal pattern (for circularly polarized driving). Intermediate situations include a modified Hopf bifurcation at a finite wave number, leading to a time dependent pattern of deformed hexagons and a codimension 2 Turing-Hopf instability resulting in an elliptically polarized stationary hexagonal pattern. Our numerical observations of different spatiotemporal structures are described by appropriate model and amplitude equations., This work was supported by QSTRUCT ~Project No. ERB FMRX-CT96-0077!. Financial support from DGICYT ~Spain!, Project No. PB94- 1167, is also acknowledged. M.H. wants to acknowledge fi- nancial support from the FOMEC project 290, Dep. de Fı´sica FCEyN, Universidad Nacional de Mar del Plata, Argentina.

The mechanical behavior of thin films subjected to laser irradiation is described by a dynamical model that is based on coupled evolution equations for the deformation and vacancy density fields. Lattice vacancies are generated in a thin layer as a result of shallow absorption of electromagnetic laser radiation. The strain field associated with lattice dilatation due to vacancies is shown to couple with bending and stretching mechanical deformation fields. The dynamical model developed here is an extension of the work of Emel'yanov in two respects: (1) the coupling between the diffusion and mechanical deformation fields is rigorously developed with additional cross-field contributions; (2) new equations for reduced dynamics are derived from this model, and are used to analyze the physical conditions for the onset of a deformational instability. For a given material, the threshold for this instability is correlated mainly with laser power. We also show that, although the instability threshold and critical wavelengths are given by the linear part of the dynamics, the selection and type of deformation patterns induced by this instability require a nonlinear formulation. Both numerical and analytical analysis are performed here. According to the relative importance of nonlinearities arising from the defect or from the bending dynamics, square or hexagonal planforms are shown to be selected. Furthermore, it appears that one-dimensional gratings are always unstable in isotropic systems. The results for square patterns are consistent with experimental observations, while those for hexagonal and one-dimensional gratings show the importance of anisotropies on their final selection.

Evidence of noise-sustained patterns in nonlinear optical systems is given. They are found in passive optical cavities, filled by Kerr type nonlinear media, when the angle of incidence of the pump beam is not zero, in a regime of convective instability. These patterns arise as a macroscopic manifestation of dynamically amplified noise, with amplification factors of up to 105. We characterize the difference between noise-sustained and deterministic patterns in terms of statistical properties of the field spectral intensity., This work is supported by QSTRUCT (Project No. ERB FMRX-CT96-0077). Financial support from DGICYT (Spain) Project No. PB94-1167 is also acknowledged.

The coupling between surface deformation and defect dynamics may be at the origin of deformation patterns in thin films under laser irradiation. We analyze a simple model describing the dynamics of such systems in the case of focused laser irradiation. We show, through linear, nonlinear, and numerical analysis, how rose deformation patterns, with the petal number increasing with laser intensity, naturally arise in this model, in agreement with experimental observations.

The effect of mean flows on pattern stability in systems where oscillatory instabilities of the Hopf type interact with stationary ones is investigated. In particular, it is shown that pattern selection may be strongly modified when the absolute instability threshold of the trivial uniform steady state is rejected beyond the stationary instability. The effect of spatially distributed noise including the competition between noise sustained and dynamically sustained structures is also discussed.

We investigate a pattern-forming system close to a Hopf bifurcation with broken translational symmetry. In one-dimensional geometries, its evolution is governed by two coupled complex Ginzburg-Landau equations which describe the amplitude of the counterpropagating traveling waves that develop beyond the instability. The convective and absolute instabilities of the possible steady states are analyzed. In the regime of strong cross coupling, where traveling waves are favored by the dynamics, the results of previous analysis are recovered. In the weak cross-coupling regime, where standing waves are favored by the dynamics, traveling waves nevertheless appear, in the absence of noise, between the uniform steady state and the standing-wave patterns. In this regime, standing waves are sustained by spatially distributed external noise for all values of the bifurcation parameter beyond the Hopf bifurcation. Hence, the noise is not only able to sustain spatiotemporal patterns, but also to modify pattern selection processes in regimes of convective instability. In this weak coupling regime we also give a quantitative statistical characterization of the transition between deterministic and noise-sustained standing waves when varying the bifurcation parameter. We show that this transition occurs at a noise-shifted point and it is identified by an apparent divergence of a correlation time and the saturation of a correlation length to a value given by the system size., We acknowledge financial support from the DGICYT grant PB94-1167

Pattern selection and stability in viscoelastic convection are studied in the framework of amplitude equations derived in the vicinity of stationary and oscillatory instabilities. The oscillatory instability corresponds to a Hopf bifurcation with broken translational symmetry. When this instability is the first to appear with increasing Rayleigh number, such systems may be described by coupled one-dimensional complex Ginzburg-Landau equations for counterpropagating waves. The coefficients of these equations, as computed from the underlying Navier-Stokes equations, are such that the selected pattern corresponds to standing waves. The phase dynamics of these waves is derived and leads to coupled Kuramoto-Sivashinsky equations. Their stability range is also determined for different typical fluid parameters. \textcopyright{} 1996 The American Physical Society.

We investigate here the evolution of self-organized monolayer atomic clusters on atomically flat substrates during epitaxial deposition. A phase field-model is developed for the free energy of the system, which includes short-range as well as long-range interactions between deposited atom clusters mediated by the substrate, using the elastic theory of intrinsic surface stress. Natural self-organization of surface atomic clusters is shown to result from reaction-diffusion kinetics, where patterns are either dots or stripes, at low (high) and intermediate coverage, respectively. Cluster-cluster interactions slightly favor stripes. The length scale of natural self-organized structures is in the tens of nanometers range. Imposition of a substrate periodic strain field by subsurface interfacial dislocations is shown to dramatically change the self-organized pattern and its length scale. Qualitative agreements between model predictions and experimental observations on self-organized Ge quantum dots on Si substrate are demonstrated. © 2007 The American Physical Society.

We analyze the formation and selection of self-organized defect microstructure in irradiated materials within the framework of a kinetic model for point and clustered defects. We take explicitly into account the influence of glissile interstitial clusters on the stability and morphology of ordered microstructure. Under void growth conditions, we find that the anisotropic motion of interstitial clusters provides a key element for microstructure morphology selection. In particular, it results in the formation of the void lattice in parallel orientation with the underlying crystal structure, in agreement with experimental observations. We also find that bcc and fcc void lattices develop in bcc and fcc crystals, respectively, while in hcp crystals, voids form ordered arrays parallel to basal planes. It is also predicted that a fcc void lattice is unstable, explaining the experimental difficulty for void lattice formation in fcc crystals.

The effect of crystal structure on laser induced deformation patterns in thin films and surfaces is analyzed within the framework of a dynamical model for the coupled evolution of defect densities and deformation fields. In crystals with covalent bonding, such as Si and SiC, preferential bond breaking may occur, as a result of the relative orientation of the laser electric field and crystallographic axes. We extend here our theoretical framework to incorporate the effects of anisotropic defect diffusion, and the influence of film-substrate adhesion on deformation pattern selection and stability of thin films subjected to laser beams. We also compare theoretical predictions to experimental observations on single crystal silicon wafer surfaces. Furthermore, it is predicted that the laser induced damage threshold for SiC single crystals can be in excess of 200 J/cm 2 .

SCOPUS: ar.j, info:eu-repo/semantics/published

The formation of inhomogeneous distributions of vacancy loops in irradiated materials is discussed in the framework of a dynamical model based on the rate theory of radiation damage. Dislocation structures are associated with dynamical instabilities due to the competition between defect motion and interactions. The dependence of the critical wavelength of the microstructures on material variables, such as the displacement-damage rate, network-dislocation density, or temperature, is obtained. The postbifurcation analysis is performed in the weakly nonlinear regime, where the selection and stability properties of three-dimensional structures are investigated.

SCOPUS: ar.j, info:eu-repo/semantics/published

SCOPUS: ar.j, info:eu-repo/semantics/published

SCOPUS: ar.j, info:eu-repo/semantics/published

SCOPUS: ar.j, info:eu-repo/semantics/published

SCOPUS: ar.j, info:eu-repo/semantics/published

SCOPUS: ar.j, info:eu-repo/semantics/published

SCOPUS: ar.j, info:eu-repo/semantics/published

SCOPUS: ar.j, info:eu-repo/semantics/published

SCOPUS: ar.j, info:eu-repo/semantics/published