Correlation Effects in Carbon Nanotubes

We consider the effects of Coulomb interactions on single-wall carbon nanotubes using an on-site Hubbard interaction, u. For the (N,N) armchair tubes the low energy theory is shown to be identical to a 2-chain Hubbard model at half-filling, with an effective interaction u_N = u/N. Umklapp scattering leads to gaps in the spectrum of charge and spin excitations which are exponentially small for large N. Above the gaps the intrinsic nanotube resistivity due to these scattering processes is linear in temperature, as observed experimentally. The presence of "d-wave" superconductivity in the 2-chain Hubbard model away from half-filling suggests that doped armchair nanotubes might exhibit superconductity with a purely electronic mechanism.Comment: 4 pages (REVTeX), 5 postscript figures included automatically using epsf.sty. Complete postscript version also available at http://www.itp.ucsb.edu/~balents/papers.htm

Social encounter networks : characterizing Great Britain

A major goal of infectious disease epidemiology is to understand and predict the spread of infections within human populations, with the intention of better informing decisions regarding control and intervention. However, the development of fully mechanistic models of transmission requires a quantitative understanding of social interactions and collective properties of social networks. We performed a cross-sectional study of the social contacts on given days for more than 5000 respondents in England, Scotland and Wales, through postal and online survey methods. The survey was designed to elicit detailed and previously unreported measures of the immediate social network of participants relevant to infection spread. Here, we describe individual-level contact patterns, focusing on the range of heterogeneity observed and discuss the correlations between contact patterns and other socio-demographic factors. We find that the distribution of the number of contacts approximates a power-law distribution, but postulate that total contact time (which has a shorter-tailed distribution) is more epidemiologically relevant. We observe that children, public-sector and healthcare workers have the highest number of total contact hours and are therefore most likely to catch and transmit infectious disease. Our study also quantifies the transitive connections made between an individual's contacts (or clustering); this is a key structural characteristic of social networks with important implications for disease transmission and control efficacy. Respondents' networks exhibit high levels of clustering, which varies across social settings and increases with duration, frequency of contact and distance from home. Finally, we discuss the implications of these findings for the transmission and control of pathogens spread through close contact

Measuring and Comparing Quantum Yield in Two Species of Marine Diatoms Subjected to Constant and Fluctuating Light Conditions

A small-scale study was conducted to determine the effects of light fluctuations on the photosynthetic efficiency of marine phytoplankton. Two species, Phaeodactylum tricornutum and Chaetoceros gracile were grown in specialized photobioreactors on a 12-hour:12-hour light:dark cycle. The cultures were diluted 50% daily to attain a specific growth rate of 0.70 d-1. To simulate vertical mixing in high turbidity habitats under various wind conditions, dense cultures were subjected to fluctuating light treatments with frequencies ranging from 0.10 Hz to 2.00 Hz. Parallel experiments subjected the cultures to static light conditions with equal total daily light doses as those of the cultures in fluctuating light. Aside from the light parameters, all growth conditions remained the same for each paired experiment. Quantum yield was measured using two methods: 14C fixation at the end of the light period to determine maximum quantum yield (Φmax), and increase in depth-integrated particulate organic carbon during the day to determine daily averaged quantum yield (Φave). Photosynthetic efficiency of Photosystem II photocenters was also determined using two types of variable fluorescence: FIRe (ΦFIRe) and dual pulse amplitude modulated fluorescence (ΦPBR). These analyses were performed under both nutrient-replete and nutrient-stressed conditions. Results have shown that, when subjected to fluctuating light, the Φmax for C. gracile tended to increase for fluctuating light treatments up to a frequency of 2.00 Hz. However, no benefit of fluctuating light was evident in measures of Φave for this strain. Results of ΦFIRe did not appear to be different for the various light treatments for C. gracile, although the measurements of ΦPBR were greater when acclimated to static light and to light fluctuating 0.50 Hz and 1.00 Hz than when acclimated to the other light treatments. Every quantum yield parameter determined for P. tricornutum when subjected to fluctuating light was lower, relative to static light values. These experiments help give insight into the photosynthetic efficiency of these two strains and how they respond to various fluctuating light treatments. With this information, these, and other strains, can be manipulated to maximize their production and can be utilized on larger scales for pharmaceutical, biomedical, aquaculture, and biofuels applications

Measuring Fractional Charge in Carbon Nanotubes

The Luttinger model of the one-dimensional Fermi gas is the cornerstone of modern understanding of interacting electrons in one dimension. In fact, the enormous class of systems whose universal behavior is adiabatically connected to it are now deemed Luttinger liquids. Recently, it has been shown that metallic single-walled carbon nanotubes are almost perfectly described by the Luttinger Hamiltonian. Indeed, strongly non-Fermi liquid behavior has been observed in a variety of DC transport experiments, in very good agreement with theoretical predictions. Here, we describe how fractional quasiparticle charge, a fundamental property of Luttinger liquids, can be observed in impurity-induced shot noise.Comment: 6 pages, 2 figure

Charge accumulation on a Luttinger liquid

The average charge Q on a quantum wire, modeled as a single-channel Luttinger liquid, connected to metallic leads and coupled to a gate is studied theoretically. We find that the behavior of the charge as the gate voltage V_G varies depends strongly on experimentally adjustable parameters (length, contact transmission, temperature,...). When the intrinsic backscattering at the contacts is weak (i.e. the conductance is close to 2e^2/h at high temperature), we predict that this behavior should be described by a universal function. For short such wires, the charge increases roughly linearly with V_G, with small oscillations due to quantum interference between electrons scattered at the contacts. For longer wires at low temperature, Coulomb blockade behavior sets in, and the charge increases in steps. In both limits $\partial Q/\partial V_G$, which should characterize the linear response conductance, exhibits periodic peaks in V_G. We show that due to Coulomb interactions the period in the former limit is twice that of the latter, and describe the evolution of the peaks through this crossover. The study can be generalized to multi-channel Luttinger liquids, and may explain qualitatively the recent observation by Liang et al (Phys. Rev. Lett. 88, 126801) of a four-electron periodicity for electron addition in single-walled carbon nanotubes.Comment: 10 pages, 9 figure

Adaptive Complex Contagions and Threshold Dynamical Systems

A broad range of nonlinear processes over networks are governed by threshold dynamics. So far, existing mathematical theory characterizing the behavior of such systems has largely been concerned with the case where the thresholds are static. In this paper we extend current theory of finite dynamical systems to cover dynamic thresholds. Three classes of parallel and sequential dynamic threshold systems are introduced and analyzed. Our main result, which is a complete characterization of their attractor structures, show that sequential systems may only have fixed points as limit sets whereas parallel systems may only have period orbits of size at most two as limit sets. The attractor states are characterized for general graphs and enumerated in the special case of paths and cycle graphs; a computational algorithm is outlined for determining the number of fixed points over a tree. We expect our results to be relevant for modeling a broad class of biological, behavioral and socio-technical systems where adaptive behavior is central.Comment: Submitted for publicatio