Emergence of patterns in driven and in autonomous spatiotemporal systems

The relationship between a driven extended system and an autonomous spatiotemporal system is investigated in the context of coupled map lattice models. Specifically, a locally coupled map lattice subjected to an external drive is compared to a coupled map system with similar local couplings plus a global interaction. It is shown that, under some conditions, the emergent patterns in both systems are analogous. Based on the knowledge of the dynamical responses of the driven lattice, we present a method that allows the prediction of parameter values for the emergence of ordered spatiotemporal patterns in a class of coupled map systems having local coupling and general forms of global interactions.Comment: 7 pages, 3 figs, submitted to PRE (2002

Electronic structure and dynamics of optically excited single-wall carbon nanotubes

We have studied the electronic structure and charge-carrier dynamics of individual single-wall carbon nanotubes (SWNTs) and nanotube ropes using optical and electron-spectroscopic techniques. The electronic structure of semiconducting SWNTs in the band-gap region is analyzed using near-infrared absorption spectroscopy. A semi-empirical expression for $E_{11}^{\rm S}$ transition energies, based on tight-binding calculations is found to give striking agreement with experimental data. Time-resolved PL from dispersed SWNT-micelles shows a decay with a time constant of about 15 ps. Using time-resolved photoemission we also find that the electron-phonon ({\it e-ph}) coupling in metallic tubes is characterized by a very small {\it e-ph} mass-enhancement of 0.0004. Ultrafast electron-electron scattering of photo-excited carriers in nanotube ropes is finally found to lead to internal thermalization of the electronic system within about 200 fs.Comment: 10 pages, 10 figures, submitted to Applied Physics

Close encounters of a rotating star with planets in parabolic orbits of varying inclination and the formation of Hot Jupiters

(abbreviated) We extend the theory of close encounters of a planet on a parabolic orbit with a star to include the effects of tides induced on the central rotating star. Orbits with arbitrary inclination to the stellar rotation axis are considered. We obtain results both from an analytic treatment and numerical one that are in satisfactory agreement. These results are applied to the initial phase of the tidal circularisation problem. We find that both tides induced in the star and planet can lead to a significant decrease of the orbital semi-major axis for orbits having periastron distances smaller than 5-6 stellar radii (corresponding to periods $\sim 4-5$ days after the circularisation has been completed) with tides in the star being much stronger for retrograde orbits compared to prograde orbits. We use the simple Skumanich law for the stellar rotation with its rotational period equal to one month at the age of 5Gyr. The strength of tidal interactions is characterised by circularisation time scale, $t_{ev}$ defined as a time scale of evolution of the planet's semi-major axis due to tides considered as a function of orbital period $P_{obs}$ after the process of tidal circularisation has been completed. We find that the ratio of the initial circularisation time scales corresponding to prograde and retrograde orbits is of order 1.5-2 for a planet of one Jupiter mass and $P_{obs}\sim$ four days. It grows with the mass of the planet, being of order five for a five Jupiter mass planet with the same $P_{orb}$. Thus, the effect of stellar rotation may provide a bias in the formation of planetary systems having planets on close orbits around their host stars, as a consequence of planet-planet scattering, favouring systems with retrograde orbits. The results may also be applied to the problem of tidal capture of stars in young stellar clusters.Comment: to be published in Celestial Mechanics and Dynamical Astronom

Superconductivity near the vibrational mode instability in MgCNi3

To understand the role of electron-phonon interaction in superconducting MgCNi$_{3}$ we have performed density functional based linear response calculations of its lattice dynamical properties. A large coupling constant $\lambda$= 1.51 is predicted and contributing phonons are identified as displacements of Ni atoms towards octahedral interstitials of the perovskite lattice. Instabilities found for some vibrational modes emphasize the role of anharmonic effects in resolving experimental controversies.Comment: 4 pages, 4 eps figures, replaces the older versio

Nonlinear r-Modes in Neutron Stars: Instability of an unstable mode

We study the dynamical evolution of a large amplitude r-mode by numerical simulations. R-modes in neutron stars are unstable growing modes, driven by gravitational radiation reaction. In these simulations, r-modes of amplitude unity or above are destroyed by a catastrophic decay: A large amplitude r-mode gradually leaks energy into other fluid modes, which in turn act nonlinearly with the r-mode, leading to the onset of the rapid decay. As a result the r-mode suddenly breaks down into a differentially rotating configuration. The catastrophic decay does not appear to be related to shock waves at the star's surface. The limit it imposes on the r-mode amplitude is significantly smaller than that suggested by previous fully nonlinear numerical simulations.Comment: Published in Phys. Rev. D Rapid Comm. 66, 041303(R) (2002

Scattering mechanism in a step-modulated subwavelength metal slit: a multi-mode multi-reflection analysis

In this paper, the scattering/transmission inside a step-modulated subwavelength metal slit is investigated in detail. We firstly investigate the scattering in a junction structure by two types of structural changes. The variation of transmission and reflection coefficients depending on structural parameters are analyzed. Then a multi-mode multi-reflection model based on ray theory is proposed to illustrate the transmission in the step-modulated slit explicitly. The key parts of this model are the multi-mode excitation and the superposition procedure of the scatterings from all possible modes, which represent the interference and energy transfer happened at interfaces. The method we use is an improved modal expansion method (MEM), which is a more practical and efficient version compared with the previous one [Opt. Express 19, 10073 (2011)]. In addition, some commonly used methods, FDTD, scattering matrix method, and improved characteristic impedance method, are compared with MEM to highlight the preciseness of these methods.Comment: 25 pages, 9 figure

Casimir Effect of Graviton and the Entropy Bound

In this note we calculate the Casimir effect of free thermal gravitons in Einstein universe and discuss how it changes the entropy bound condition proposed recently by Verlinde [hep-th/0008140] as a higher dimensional generalization of Cardy's formula for conformal field theories (CFT). We find that the graviton's Casimir effect is necessary in order not to violate Verlinde's bound for weakly coupled CFT. We also comment on the implication of this new Cardy's formula to the thermodynamics of black $p$-brane.Comment: 10 pages; v2. a typo correcte

Theory of Melting and the Optical Properties of Gold/DNA Nanocomposites

We describe a simple model for the melting and optical properties of a DNA/gold nanoparticle aggregate. The optical properties at fixed wavelength change dramatically at the melting transition, which is found to be higher and narrower in temperature for larger particles, and much sharper than that of an isolated DNA link. All these features are in agreement with available experiments. The aggregate is modeled as a cluster of gold nanoparticles on a periodic lattice connected by DNA bonds, and the extinction coefficient is computed using the discrete dipole approximation. Melting takes place as an increasing number of these bonds break with increasing temperature. The melting temperature corresponds approximately to the bond percolation threshold.Comment: 5 pages, 4 figure. To be published in Phys. Rev.

Magnetic and pair correlations of the Hubbard model with next-nearest-neighbor hopping

A combination of analytical approaches and quantum Monte Carlo simulations is used to study both magnetic and pairing correlations for a version of the Hubbard model that includes second-neighbor hopping $t^{\prime }=-0.35t$ as a model for high-temperature superconductors. Magnetic properties are analyzed using the Two-Particle Self-Consistent approach. The maximum in magnetic susceptibility as a function of doping appears both at finite $$ and at $t^{\prime }=0$ but for two totally different physical reasons. When $t^{\prime }=0$, it is induced by antiferromagnetic correlations while at $t^{\prime }=-0.35t$ it is a band structure effect amplified by interactions. Finally, pairing fluctuations are compared with $$-matrix results to disentangle the effects of van Hove singularity and of nesting on superconducting correlations. The addition of antiferromagnetic fluctuations increases slightly the $d$-wave superconducting correlations despite the presence of a van Hove singularity which tends to decrease them in the repulsive model. Some aspects of the phase diagram and some subtleties of finite-size scaling in Monte Carlo simulations, such as inverted finite-size dependence, are also discussed.Comment: Revtex, 8 pages + 15 uuencoded postcript figure