Faraday Rotation, Band Splitting, and One-Way Propagation of Plasmon Waves on a Nanoparticle Chain

We calculate the dispersion relations of plasmonic waves propagating along a chain of semiconducting or metallic nanoparticles in the presence of both a static magnetic field ${\bf B}$ and a liquid crystalline host. The dispersion relations are obtained using the quasistatic approximation and a dipole-dipole approximation to treat the interaction between surface plasmons on different nanoparticles. For a plasmons propagating along a particle chain in a nematic liquid crystalline host with both ${\bf B}$ and the director parallel to the chain, we find a small, but finite, Faraday rotation angle. For ${\bf B}$ perpendicular to the chain, but director still parallel to the chain, the field couples the longitudinal and one of the two transverse plasmonic branches. This coupling is shown to split the two branches at the zero field crossing by an amount proportional to $|{\bf B}|$. In a cholesteric liquid crystal host and an applied magnetic field parallel to the chain, the dispersion relations for left- and right-moving waves are found to be different. For some frequencies, the plasmonic wave propagates only in one of the two directions.Comment: 6 pages, 4 figures. arXiv admin note: substantial text overlap with arXiv:1502.0496

Tight-Binding Model for Adatoms on Graphene: Analytical Density of States, Spectral Function, and Induced Magnetic Moment

In the limit of low adatom concentration, we obtain exact analytic expressions for the local and total density of states (LDOS, TDOS) for a tight-binding model of adatoms on graphene. The model is not limited to nearest-neighbor hopping but can include hopping between carbon atoms at any separation. We also find an analytical expression for the spectral function $A({\bf k}, E)$ of an electron of Bloch vector ${\bf k}$ and energy E on the graphene lattice, to first order in the adatom concentration. We treat the electron-electron interaction by including a Hubbard term on the adatom, which we solve within a mean-field approximation. For finite Hubbard $U$, we find the spin-polarized LDOS, TDOS, and spectral function self-consistently. For any choice of parameters of the tight-binding model within mean field theory, we find a critical value of $U$ above which a moment develops on the adatom. For most choices of parameters, we find a substantial charge transfer from the adatom to the graphene host.Comment: 11 Pages, 6 figures, 1 tabl

Forecasting the viability of sea turtle eggs in a warming world

Animals living in tropical regions may be at increased risk from climate change because current temperatures at these locations already approach critical physiological thresholds. Relatively small temperature increases could cause animals to exceed these thresholds more often, resulting in substantial fitness costs or even death. Oviparous species could be especially vulnerable because the maximum thermal tolerances of incubating embryos is often lower than adult counterparts, and in many species mothers abandon the eggs after oviposition, rendering them immobile and thus unable to avoid extreme temperatures. As a consequence, the effects of climate change might become evident earlier and be more devastating for hatchling production in the tropics. Loggerhead sea turtles (Caretta caretta) have the widest nesting range of any living reptile, spanning temperate to tropical latitudes in both hemispheres. Currently, loggerhead sea turtle populations in the tropics produce nearly 30% fewer hatchlings per nest than temperate populations. Strong correlations between empirical hatching success and habitat quality allowed global predictions of the spatiotemporal impacts of climate change on this fitness trait. Under climate change, many sea turtle populations nesting in tropical environments are predicted to experience severe reductions in hatchling production, whereas hatching success in many temperate populations could remain unchanged or even increase with rising temperatures. Some populations could show very complex responses to climate change, with higher relative hatchling production as temperatures begin to increase, followed by declines as critical physiological thresholds are exceeded more frequently. Predicting when, where, and how climate change could impact the reproductive output of local populations is crucial for anticipating how a warming world will influence population size, growth, and stability

On cycle systems with specified weak chromatic number

AbstractA weak k-colouring of an m-cycle system is a colouring of the vertices of the system with k colours in such a way that no cycle of the system has all of its vertices receive the same colour. An m-cycle system is said to be weakly k-chromatic if it has a weak k-colouring but no weak (k−1)-colouring. In this paper we show that for all k⩾2 and m⩾3 with (k,m)≠(2,3) there is a weakly k-chromatic m-cycle system of order v for all sufficiently large admissible v

The Edge-Connectivity of Vertex-Transitive Hypergraphs

A graph or hypergraph is said to be vertex-transitive if its automorphism group acts transitively upon its vertices. A classic theorem of Mader asserts that every connected vertex-transitive graph is maximally edge-connected. We generalise this result to hypergraphs and show that every connected linear uniform vertex-transitive hypergraph is maximally edge-connected. We also show that if we relax either the linear or uniform conditions in this generalisation, then we can construct examples of vertex-transitive hypergraphs which are not maximally edge-connected.Comment: 8 page

Existential Closure in Line Graphs

A graph $G$ is $n$-existentially closed if, for all disjoint sets of vertices $A$ and $B$ with $|A\cup B|=n$, there is a vertex $z$ not in $A\cup B$ adjacent to each vertex of $A$ and to no vertex of $B$. In this paper, we investigate $n$-existentially closed line graphs. In particular, we present necessary conditions for the existence of such graphs as well as constructions for finding infinite families of such graphs. We also prove that there are exactly two $2$-existentially closed planar line graphs. We then consider the existential closure of the line graphs of hypergraphs and present constructions for $2$-existentially closed line graphs of hypergraphs.Comment: 13 pages, 2 figure