Large N Effects and Renormalization of the Long-Range Coulomb Interaction in Carbon Nanotubes

We develop a dimensional regularization approach to deal with the low-energy effects of the long-range Coulomb interaction in 1D electron systems. The method allows us to avoid the infrared singularities arising from the long-range Coulomb interaction at D = 1, providing at the same time insight about the fixed-points of the theory. We show that the effect of increasing the number N of subbands at the Fermi level is opposite to that of approaching the bare Coulomb interaction in the limit D --> 1. Then, we devise a double scaling limit, in which the large N effects are able to tame the singularities due to the long-range interaction. Thus, regular expressions can be obtained for all observables right at D = 1, bearing also a dependence o the doping level of the system. Our results imply a variation with N in the value of the exponent for the tunneling density of states, which is in fair agreement with that observed in different transport experiments involving carbon nanotubes. As the doping level is increased in nanotubes of large radius and multi-walled nanotubes, we predict a significant reduction of order N^{-1/2} in the critical exponent of the tunneling density of states.Comment: 16 pages, 5 figures, PACS codes: 73.40, 11.10.

Crossover from Luttinger liquid to Coulomb blockade regime in carbon nanotubes

We develop a theoretical approach to the low-energy properties of 1D electron systems aimed to encompass the mixed features of Luttinger liquid and Coulomb blockade behavior observed in the crossover between the two regimes. For this aim we extend the Luttinger liquid description by incorporating the effects of a discrete single-particle spectrum. The intermediate regime is characterized by a power-law behavior of the conductance, but with an exponent oscillating with the gate voltage, in agreement with recent experimental observations. Our construction also accounts naturally for the existence of a crossover in the zero-bias conductance, mediating between two temperature ranges where the power-law behavior is preserved but with different exponent.Comment: 5 pages, 3 figure

Suppression of electron-electron repulsion and superconductivity in Ultra Small Carbon Nanotubes

Recently, ultra-small-diameter Single Wall Nano Tubes with diameter of $\sim 0.4 nm$ have been produced and many unusual properties were observed, such as superconductivity, leading to a transition temperature $T_c\sim 15^oK$, much larger than that observed in the bundles of larger diameter tubes. By a comparison between two different approaches, we discuss the issue whether a superconducting behavior in these carbon nanotubes can arise by a purely electronic mechanism. The first approach is based on the Luttinger Model while the second one, which emphasizes the role of the lattice and short range interaction, is developed starting from the Hubbard Hamiltonian. By using the latter model we predict a transition temperature of the same order of magnitude as the measured one.Comment: 7 pages, 3 figures, to appear in J. Phys.-Cond. Ma

Refraction of a Gaussian Seaway

Refraction of a Longuet-Higgins Gaussian sea by random ocean currents creates persistent local variations in average energy and wave action. These variations take the form of lumps or streaks, and they explicitly survive dispersion over wavelength and incoming wave propagation direction. Thus, the uniform sampling assumed in the venerable Longuet-Higgins theory does not apply following refraction by random currents. Proper handling of the non-uniform sampling results in greatly increased probability of freak wave formation. The present theory represents a synthesis of Longuet-Higgins Gaussian seas and the refraction model of White and Fornberg, which considered the effect of currents on a plane wave incident seaway. Using the linearized equations for deep ocean waves, we obtain quantitative predictions for the increased probability of freak wave formation when the refractive effects are taken into account. The crest height or wave height distribution depends primarily on the ``freak index", gamma, which measures the strength of refraction relative to the angular spread of the incoming sea. Dramatic effects are obtained in the tail of this distribution even for the modest values of the freak index that are expected to occur commonly in nature. Extensive comparisons are made between the analytical description and numerical simulations.Comment: 18 pages, 10 figure

Modulational instability and wave amplification in finite water depth

The modulational instability of a uniform wave train to side band perturbations is one of the most plausible mechanisms for the generation of rogue waves in deep water. In a condition of finite water depth, however, the interaction with the sea floor generates a wave-induced current that subtracts energy from the wave field and consequently attenuates the instability mechanism. As a result, a plane wave remains stable under the influence of collinear side bands for relative depths <i>kh</i> &leq; 1.36 (where <i>k</i> is the wavenumber of the plane wave and <i>h</i> is the water depth), but it can still destabilise due to oblique perturbations. Using direct numerical simulations of the Euler equations, it is here demonstrated that oblique side bands are capable of triggering modulational instability and eventually leading to the formation of rogue waves also for <i>kh</i> &leq; 1.36. Results, nonetheless, indicate that modulational instability cannot sustain a substantial wave growth for <i>kh</i> < 0.8

Accommodative facility: Assessment of variables limiting performance

Evaluation of available normative data and protocols for accommodative facility testing in school aged children shows a lack of agreement among authors, and many studies failed to include or consider the unique conditions under which this age group must be tested. This study was designed to assess variables which have been implicated in previous research as having an impact upon testing in children, and ultimately limits their usefulness. Specifically, these variables are linguistic/cognitive processing (visual-verbal automaticity), and the motor response act of turning the lens flipper. The purpose of this study was to determine the potential impact these two variables have upon the measurement of relative accommodative response time during lens rock facility testing with school children. Methods include presentation of a new testing paradigm and a unique target (Modified Landolt C). Forty-nine fourth graders and twenty-two first graders participated in a within- subjects design where each subject\u27s response time was measured for each of five separate test conditions. These conditions were designed to assess both the impact and effect the above variables may have upon performance during accommodative facility testing at these two grade levels. Results indicate: (1) Use of a flipper slows performance at both first and fourth grade levels; (2) There was no significant difference in performance either when the examiner or the subject was manipulating the flipper. This was true for both our samples of first and fourth graders. Therefore, motor dexterity is not an issue in performance; (3) Although visual-verbal response time plays a significant role in lens rock performance, relative accommodative response is a major limiting variable with each grade level; and (4) Relative accommodative response time may improve between first and fourth grade

Triggering rogue waves in opposing currents

We show that rogue waves can be triggered naturally when a stable wave train enters a region of an opposing current flow. We demonstrate that the maximum amplitude of the rogue wave depends on the ratio between the current velocity, $U_0$, and the wave group velocity, $c_g$. We also reveal that an opposing current can force the development of rogue waves in random wave fields, resulting in a substantial change of the statistical properties of the surface elevation. The present results can be directly adopted in any field of physics in which the focusing Nonlinear Schrodinger equation with non constant coefficient is applicable. In particular, nonlinear optics laboratory experiments are natural candidates for verifying experimentally our results.Comment: 5 pages, 5 figure

Dynamics of a Black Bear Population within a Desert Metapopulation

Understanding metapopulation dynamics in large carnivores with naturally fragmented populations is difficult because of the large temporal and spatial context of such dynamics. We coupled a long-term database of visitor sighting records with an intensive 3-year telemetry study to describe population dynamics of recolonization by black bears (Ursus americanus) of Big Bend National Park in Texas during 1988–2002. This population, which occurs within a metapopulation in western Texas and northern Mexico, increased from a single pair of known breeding-age animals in 1988 to 29 bears (including 6 females of breeding age) in March 2000 (λ = 1.25/year). A migration and dispersal event in August–December 2000 reduced the population to 2 adult females and as few as 5–7 individuals. One-way movement distances from the study area during this event averaged 76 km for females (n = 7) and 92 km for males (n = 4), and 3 animals conducted migrations of at least 154, 178, and 214 km, respectively. Our observations exemplify the importance of stochastic events on demographics of small populations and highlight the potential scale of bear movement among montane islands of southwestern North America. They also provide insight into the use of dispersal data in parameterizing metapopulation models for large carnivores

Influence of dimensionality on superconductivity in carbon nanotubes

We investigate the electronic instabilities in carbon nanotubes (CNs), looking for the break-down of the one dimensional Luttinger liquid regime due to the strong screening of the long-range part of the Coulomb repulsion. We show that such a breakdown is realized both in ultra-small single wall CNs and multi wall CNs, while a purely electronic mechanism could explain the superconductivity (SC) observed recently in ultra-small (diameter $\sim 0.4 nm$) single wall CNs ($T_c\sim 15 ^{o}K$) and entirely end-bonded multi-walled ones ($T_c\sim 12 ^{o}K$). We show that both the doping and the screening of long-range part of the electron-electron repulsion, needed to allow the SC phase, are related to the intrinsically 3D nature of the environment where the CNs operate.Comment: 5 pages, 3 figures, PACS: 71.10.Pm,74.50.+r,71.20.Tx, to appear in J. Phys. Cond. Ma