Conditional linearizability criteria for a system of third-order ordinary differential equations

We provide linearizability criteria for a class of systems of third-order ordinary differential equations (ODEs) that is cubically semi-linear in the first derivative, by differentiating a system of second-order quadratically semi-linear ODEs and using the original system to replace the second derivative. The procedure developed splits into two cases, those where the coefficients are constant and those where they are variables. Both cases are discussed and examples given

Current carrying capacity of carbon nanotubes

The current carrying capacity of ballistic electrons in carbon nanotubes that are coupled to ideal contacts is analyzed. At small applied voltages, where electrons are injected only into crossing subbands, the differential conductance is $4e^2/h$. At applied voltages larger than $\Delta E_{NC}/2e$ ($\Delta E_{NC}$ is the energy level spacing of first non crossing subbands), electrons are injected into non crossing subbands. The contribution of these electrons to current is determined by the competing processes of Bragg reflection and Zener type inter subband tunneling. In small diameter nanotubes, Bragg reflection dominates, and the maximum differential conductance is comparable to $4e^2/h$. Inter subband Zener tunneling can be non negligible as the nanotube diameter increases because $\Delta E_{NC}$ is inversely proportional to the diameter. As a result, with increasing nanotube diameter, the differential conductance becomes larger than $4e^2/h$, though not comparable to the large number of subbands into which electrons are injected from the contacts. These results may be relevant to recent experiments in large diameter multi-wall nanotubes that observed conductances larger than $4e^2/h$.Comment: 12 pages, 4 figure

Correlates of elevational specialisation in Southeast Asian tropical birds

The understanding of elevational selectivity in extremely rich tropical biotas is critical to the study of accelerating human-mediated environmental changes (e.g., deforestation and global climate warming). This paper explores the characteristics of Southeast Asian birds that are altitudinal specialists (i.e., lowland specialists and montane specialists) by assessing the relative importance of various species traits (e.g., breeding phenology and clutch size) in determining the altitudinal specialisation of these tropical birds. After controlling for phylogeny, we found that habitat specificity, breeding phenology, and clutch size were significant correlates of lowland specialisation. The most parsimonious model predicting lowland specialisation included the first of these only. Breeding phenology was the significant phylogeny-independent correlate of montane specialisation. Thus, species were confined to altitudinal niches by different constraints. By analysing the altitudinal distribution of Southeast Asian birds, we provide insights on why altitudinal confinement exists in lowland and montane specialists. Understanding such constraints may be important for the conservation of tropical birds

Selectively tunable optical Stark effect of anisotropic excitons in atomically thin ReS2

The optical Stark effect is a coherent light-matter interaction describing the modification of quantum states by non-resonant light illumination in atoms, solids and nanostructures. Researchers have strived to utilize this effect to control exciton states, aiming to realize ultra-high-speed optical switches and modulators. However, most studies have focused on the optical Stark effect of only the lowest exciton state due to lack of energy selectivity, resulting in low degree-of-freedom devices. Here, by applying a linearly polarized laser pulse to few-layer ReS2, where reduced symmetry leads to strong in-plane anisotropy of excitons, we control the optical Stark shift of two energetically separated exciton states. Especially, we selectively tune the Stark effect of an individual state with varying light polarization. This is possible because each state has a completely distinct dependence on light polarization due to different excitonic transition dipole moments. Our finding provides a methodology for energy-selective control of exciton states.111612Ysciescopu