Neighborhood models of minority opinion spreading

We study the effect of finite size population in Galam's model [Eur. Phys. J. B 25 (2002) 403] of minority opinion spreading and introduce neighborhood models that account for local spatial effects. For systems of different sizes N, the time to reach consensus is shown to scale as ln N in the original version, while the evolution is much slower in the new neighborhood models. The threshold value of the initial concentration of minority supporters for the defeat of the initial majority, which is independent of N in Galam's model, goes to zero with growing system size in the neighborhood models. This is a consequence of the existence of a critical size for the growth of a local domain of minority supporters

Contact Atomic Structure and Electron Transport Through Molecules

Using benzene sandwiched between two Au leads as a model system, we investigate from first principles the change in molecular conductance caused by different atomic structures around the metal-molecule contact. Our motivation is the variable situations that may arise in break junction experiments; our approach is a combined density functional theory and Green function technique. We focus on effects caused by (1) the presence of an additional Au atom at the contact and (2) possible changes in the molecule-lead separation. The effects of contact atomic relaxation and two different lead orientations are fully considered. We find that the presence of an additional Au atom at each of the two contacts will increase the equilibrium conductance by up to two orders of magnitude regardless of either the lead orientation or different group-VI anchoring atoms. This is due to a LUMO-like resonance peak near the Fermi energy. In the non-equilibrium properties, the resonance peak manifests itself in a large negative differential conductance. We find that the dependence of the equilibrium conductance on the molecule-lead separation can be quite subtle: either very weak or very strong depending on the separation regime.Comment: 8 pages, 6 figure

Electron Transport Through Molecules: Self-consistent and Non-self-consistent Approaches

A self-consistent method for calculating electron transport through a molecular device is proposed. It is based on density functional theory electronic structure calculations under periodic boundary conditions and implemented in the framework of the nonequilibrium Green function approach. To avoid the substantial computational cost in finding the I-V characteristic of large systems, we also develop an approximate but much more efficient non-self-consistent method. Here the change in effective potential in the device region caused by a bias is approximated by the main features of the voltage drop. As applications, the I-V curves of a carbon chain and an aluminum chain sandwiched between two aluminum electrodes are calculated -- two systems in which the voltage drops very differently. By comparing to the self-consistent results, we show that this non-self-consistent approach works well and can give quantitatively good results.Comment: 11 pages, 10 figure

Lyapunov Potential Description for Laser Dynamics

We describe the dynamical behavior of both class A and class B lasers in terms of a Lyapunov potential. For class A lasers we use the potential to analyze both deterministic and stochastic dynamics. In the stochastic case it is found that the phase of the electric field drifts with time in the steady state. For class B lasers, the potential obtained is valid in the absence of noise. In this case, a general expression relating the period of the relaxation oscillations to the potential is found. We have included in this expression the terms corresponding to the gain saturation and the mean value of the spontaneously emitted power, which were not considered previously. The validity of this expression is also discussed and a semi-empirical relation giving the period of the relaxation oscillations far from the stationary state is proposed and checked against numerical simulations.Comment: 13 pages (including 7 figures) LaTeX file. To appear in Phys Rev.A (June 1999

Vanishing Twist near Focus-Focus Points

We show that near a focus-focus point in a Liouville integrable Hamiltonian system with two degrees of freedom lines of locally constant rotation number in the image of the energy-momentum map are spirals determined by the eigenvalue of the equilibrium. From this representation of the rotation number we derive that the twist condition for the isoenergetic KAM condition vanishes on a curve in the image of the energy-momentum map that is transversal to the line of constant energy. In contrast to this we also show that the frequency map is non-degenerate for every point in a neighborhood of a focus-focus point.Comment: 13 page

Discretization-related issues in the KPZ equation: Consistency, Galilean-invariance violation, and fluctuation--dissipation relation

In order to perform numerical simulations of the KPZ equation, in any dimensionality, a spatial discretization scheme must be prescribed. The known fact that the KPZ equation can be obtained as a result of a Hopf--Cole transformation applied to a diffusion equation (with \emph{multiplicative} noise) is shown here to strongly restrict the arbitrariness in the choice of spatial discretization schemes. On one hand, the discretization prescriptions for the Laplacian and the nonlinear (KPZ) term cannot be independently chosen. On the other hand, since the discretization is an operation performed on \emph{space} and the Hopf--Cole transformation is \emph{local} both in space and time, the former should be the same regardless of the field to which it is applied. It is shown that whereas some discretization schemes pass both consistency tests, known examples in the literature do not. The requirement of consistency for the discretization of Lyapunov functionals is argued to be a natural and safe starting point in choosing spatial discretization schemes. We also analyze the relation between real-space and pseudo-spectral discrete representations. In addition we discuss the relevance of the Galilean invariance violation in these consistent discretization schemes, and the alleged conflict of standard discretization with the fluctuation--dissipation theorem, peculiar of 1D.Comment: RevTex, 23pgs, 2 figures, submitted to Phys. Rev.

Selfsimilar Domain Growth, Localized Structures and Labyrinthine Patterns in Vectorial Kerr Resonators

We study domain growth in a nonlinear optical system useful to explore different scenarios that might occur in systems which do not relax to thermodynamic equilibrium. Domains correspond to equivalent states of different circular polarization of light. We describe three dynamical regimes: a coarsening regime in which dynamical scaling holds with a growth law dictated by curvature effects, a regime in which localized structures form, and a regime in which polarization domain walls are modulationally unstable and the system freezes in a labyrinthine pattern.Comment: 13 pages, 6 figure

Self-Pulsating Semiconductor Lasers: Theory and Experiment

We report detailed measurements of the pump-current dependency of the self-pulsating frequency of semiconductor CD lasers. A distinct kink in this dependence is found and explained using rate-equation model. The kink denotes a transition between a region where the self-pulsations are weakly sustained relaxation oscillations and a region where Q-switching takes place. Simulations show that spontaneous emission noise plays a crucial role for the cross-over.Comment: Revtex, 16 pages, 7 figure

Wound-up phase turbulence in the Complex Ginzburg-Landau equation

We consider phase turbulent regimes with nonzero winding number in the one-dimensional Complex Ginzburg-Landau equation. We find that phase turbulent states with winding number larger than a critical one are only transients and decay to states within a range of allowed winding numbers. The analogy with the Eckhaus instability for non-turbulent waves is stressed. The transition from phase to defect turbulence is interpreted as an ergodicity breaking transition which occurs when the range of allowed winding numbers vanishes. We explain the states reached at long times in terms of three basic states, namely quasiperiodic states, frozen turbulence states, and riding turbulence states. Justification and some insight into them is obtained from an analysis of a phase equation for nonzero winding number: rigidly moving solutions of this equation, which correspond to quasiperiodic and frozen turbulence states, are understood in terms of periodic and chaotic solutions of an associated system of ordinary differential equations. A short report of some of our results has been published in [Montagne et al., Phys. Rev. Lett. 77, 267 (1996)].Comment: 22 pages, 15 figures included. Uses subfigure.sty (included) and epsf.tex (not included). Related research in http://www.imedea.uib.es/Nonlinea

Winding number instability in the phase-turbulence regime of the Complex Ginzburg-Landau Equation

We give a statistical characterization of states with nonzero winding number in the Phase Turbulence (PT) regime of the one-dimensional Complex Ginzburg-Landau equation. We find that states with winding number larger than a critical one are unstable, in the sense that they decay to states with smaller winding number. The transition from Phase to Defect Turbulence is interpreted as an ergodicity breaking transition which occurs when the range of stable winding numbers vanishes. Asymptotically stable states which are not spatio-temporally chaotic are described within the PT regime of nonzero winding number.Comment: 4 pages,REVTeX, including 4 Figures. Latex (or postscript) version with figures available at http://formentor.uib.es/~montagne/textos/nupt