Statistics of transverse mode turn-on dynamics in VCSEL's

The turn-on process of a multimode VCSEL is investigated from a statistical point of view. Special attention is paid to quantities such as time jitter and bit error rate. The single-mode performance of VCSEL¿s during current modulation is compared to that of edge-emitting lasers.

Frequency dynamics of gain-switched injection-locked semiconductor lasers

The frequency dynamics of gain-switched singlemode semiconductor lasers subject to optical injection is investigated. The requirements for low time jitter and reduced frequency chirp operation are studied as a function of the frequency mismatch between the master and slave lasers. Suppression of the power overshoot, typical during gain-switched operation, can be achieved for selected frequency detunings.

Gauge-invariant actions from constraint Hamiltonian dynamics

Dirac's constraint Hamiltonian formalism is used to construct a gauge-invariant action for the massive spin-one and -two fields.

Effects of external noise on the Swift-Hohenberg Equation

The Swift-Hohenberg equation is studied in the presence of a multiplicative noise. This stochastic equation could describe a situation in which a noise has been superimposed on the temperature gradient between the two plates of a Rayleigh-Bnard cell. A linear stability analysis and numerical simulations show that, in constrast to the additive-noise case, convective structures appear in a regime in which a deterministic analysis predicts a homogeneous solution.

Dynamics of turing patterns under spatiotemporal forcing

We study, both theoretically and experimentally, the dynamical response of Turing patterns to a spatiotemporal forcing in the form of a traveling-wave modulation of a control parameter. We show that from strictly spatial resonance, it is possible to induce new, generic dynamical behaviors, including temporally modulated traveling waves and localized traveling solitonlike solutions. The latter make contact with the soliton solutions of Coullet [Phys. Rev. Lett. 56, 724 (1986)] and generalize them. The stability diagram for the different propagating modes in the Lengyel-Epstein model is determined numerically. Direct observations of the predicted solutions in experiments carried out with light modulations in the photosensitive chlorine dioxide-iodine-malonic acid reaction are also reported.

Dynamics of domain walls in pattern formation under traveling-wave forcing

We study dynamics of domain walls in pattern forming systems that are externally forced by a moving space-periodic modulation close to 2:1 spatial resonance. The motion of the forcing induces nongradient dynamics, while the wave number mismatch breaks explicitly the chiral symmetry of the domain walls. The combination of both effects yields an imperfect nonequilibrium Ising-Bloch bifurcation, where all kinks (including the Ising-like one) drift. Kink velocities and interactions are studied within the generic amplitude equation. For nonzero mismatch, a transition to traveling bound kink-antikink pairs and chaotic wave trains occurs.

Probing elastic anisotropy from defect dynamics in Langmuir monolayers

We study the dynamics of annihilation of point defects in Langmuir monolayers. The absence of hydrodynamic effects allows us to quantitatively relate the asymmetry in defect mobility to the elastic anisotropy of the material, which in turn can be varied through the control of the surface pressure applied to the monolayer. Using the proposed theoretical analysis, we are able to obtain rather elusive equilibrium properties out of relatively simple dynamical measurements. In particular, we measure the elastic constants and their pressure dependence.

Defect dynamics in viscous fingering

We study the dynamics of Staffman-Taylor fingering in terms of topological defects of the flow field. The defects are created and/or annihilated at the interface. The route towards the single-finger steady state is characterized by a detailed mechanism for defect annihilation. For small viscosity contrast this mechanism is impeded, and creation of new defects leads the system away from a single-finger solution. Strong evidence for a drastic reduction of the basin of attraction of the Saffman-Taylor finger is presented.

Phase separation dynamics under stirring

Phase separation dynamics in the presence of externally imposed stirring is studied. The stirring is assumed independent of the concentration and it is generated with a well-defined energy spectrum. The domain growth process is either favored or frozen depending on the intensity and correlation length of this advective flow. This behavior is explained by analytical arguments.

External Fluctuations in Front Propagation

We study the effects of external noise in a one-dimensional model of front propagation. Noise is introduced through the fluctuations of a control parameter leading to a multiplicative stochastic partial differential equation. Analytical and numerical results for the front shape and velocity are presented. The linear-marginal-stability theory is found to increase its range of validity in the presence of external noise. As a consequence noise can stabilize fronts not allowed by the deterministic equation.

Evaporation and coarsening dynamics with open boundaries

We present a study of the evaporation dynamics of a substance undergoing a coarsening process. The system is modeled by the Cahn-Hilliard equation with absorbing boundaries. We have found that the dynamics, although of a diffusive nature, is much slower than the usual one without coarsening. Analytical and simulation results are in reasonable agreement.

Effects of small surface tension in Hele-Shaw multifinger dynamics: an analytical and numerical study

We study the singular effects of vanishingly small surface tension on the dynamics of finger competition in the Saffman-Taylor problem, using the asymptotic techniques described by Tanveer [Philos. Trans. R. Soc. London, Ser. A 343, 155 (1993)] and Siegel and Tanveer [Phys. Rev. Lett. 76, 419 (1996)], as well as direct numerical computation, following the numerical scheme of Hou, Lowengrub, and Shelley [J. Comput. Phys. 114, 312 (1994)]. We demonstrate the dramatic effects of small surface tension on the late time evolution of two-finger configurations with respect to exact (nonsingular) zero-surface-tension solutions. The effect is present even when the relevant zero-surface-tension solution has asymptotic behavior consistent with selection theory. Such singular effects, therefore, cannot be traced back to steady state selection theory, and imply a drastic global change in the structure of phase-space flow. They can be interpreted in the framework of a recently introduced dynamical solvability scenario according to which surface tension unfolds the structurally unstable flow, restoring the hyperbolicity of multifinger fixed points.

External fluctuations in a pattern-forming instability

The effect of external fluctuations on the formation of spatial patterns is analyzed by means of a stochastic Swift-Hohenberg model with multiplicative space-correlated noise. Numerical simulations in two dimensions show a shift of the bifurcation point controlled by the intensity of the multiplicative noise. This shift takes place in the ordering direction (i.e., produces patterns), but its magnitude decreases with that of the noise correlation length. Analytical arguments are presented to explain these facts.

Dynamics of the two-dimensional gonihedric spin model

In this paper, we study dynamical aspects of the two-dimensional (2D) gonihedric spin model using both numerical and analytical methods. This spin model has vanishing microscopic surface tension and it actually describes an ensemble of loops living on a 2D surface. The self-avoidance of loops is parametrized by a parameter ¿. The ¿=0 model can be mapped to one of the six-vertex models discussed by Baxter, and it does not have critical behavior. We have found that allowing for ¿¿0 does not lead to critical behavior either. Finite-size effects are rather severe, and in order to understand these effects, a finite-volume calculation for non-self-avoiding loops is presented. This model, like his 3D counterpart, exhibits very slow dynamics, but a careful analysis of dynamical observables reveals nonglassy evolution (unlike its 3D counterpart). We find, also in this ¿=0 case, the law that governs the long-time, low-temperature evolution of the system, through a dual description in terms of defects. A power, rather than logarithmic, law for the approach to equilibrium has been found.