The modulational stability of the nonlinear Schrödinger (NLS) equation is examined in the case with a quadratic external potential. This study is motivated by recent experimental studies in the context of matter waves in Bose-Einstein condensates (BECs). The theoretical analysis invokes a lens-type transformation that converts the Gross-Pitaevskii into a regular NLS equation with an additional growth term. This analysis suggests the particular interest of a specific time-varying potential (∼ (t + t ⋆ ) −2 ). We examine both this potential, as well as the time independent one numerically and conclude by suggesting experiments for the production of solitonic wave-trains in BEC.

Despite the growing awareness that larval competition can influence adult mosquito life history traits including susceptibility to pathogens, the net effect of larval competition on human risk of exposure to mosquito-borne pathogens remains poorly understood. We examined how intraspecific larval competition affects dengue-2 virus (DENV-2) extrinsic incubation period and vectorial capacity of its natural vector Aedes albopictus. Adult Ae. albopictus from low and high-larval density conditions were orally challenged with DENV-2 and then assayed for virus infection and dissemination rates following a 6, 9, or 12-day incubation period using real-time quantitative reverse transcription PCR. We then modeled the effect of larval competition on vectorial capacity using parameter estimates obtained from peer-reviewed field and laboratory studies. Larval competition resulted in significantly longer development times, lower emergence rates, and smaller adults, but did not significantly affect the extrinsic incubation period of DENV-2 in Ae. albopictus. Our vectorial capacity models suggest that the effect of larval competition on adult mosquito longevity likely has a greater influence on vectorial capacity relative to any competition-induced changes in vector competence. Furthermore, we found that large increases in the viral dissemination rate may be necessary to compensate for small competition-induced reductions in daily survivorship. Our results indicate that mosquito populations that experience stress from larval competition are likely to have a reduced vectorial capacity, even when susceptibility to pathogens is enhanced.

Using a time-dependent linear (Rabi) coupling between the components of a weakly interacting multicomponent Bose-Einstein condensate (BEC), we propose a protocol for transferring the wavefunction of one component to the other. This "Rabi switch" can be generated in a binary BEC mixture by an electromagnetic field between the two components, typically two hyperfine states. When the wavefunction to be transfered is -at a given time -a stationary state of the multicomponent Hamiltonian, then, after a time delay (depending on the Rabi frequency), it is possible to have the same wavefunction on the other condensate. The Rabi switch can be used to transfer also moving bright matter-wave solitons, as well as vortices and vortex lattices in two-dimensional condensates. The efficiency of the proposed switch is shown to be 100 % when inter-species and intra-species interaction strengths are equal. The deviations from equal interaction strengths are analyzed within a two-mode model and the dependence of the efficiency on the interaction strengths and on the presence of external potentials is examined in both 1D and 2D settings.

In this paper, we study the competition of linear and nonlinear lattices and its effects on the stability and dynamics of bright solitary waves. We consider both lattices in a perturbative framework, whereby the technique of Hamiltonian perturbation theory can be used to obtain information about the existence of solutions, and the same approach, as well as eigenvalue count considerations, can be used to obtained detailed conditions about their linear stability. We find that the analytical results are in very good agreement with our numerical findings and can also be used to predict features of the dynamical evolution of such solutions.

Few insects exhibit the striking colour pattern radiation found in bumble bees (Bombus), which have diversified globally into a wide range of colours and patterns. Their potent sting is often advertised by conspicuous bands of contrasting colour commonly mimicked by scores of harmless (Batesian mimics) and noxious species (Müllerian co-mimics). Despite extensive documentation of colour pattern diversification, next to nothing is known about the genetic regulation of pattern formation in bumble bees, hindering progress toward a more general model of the evolution of colour pattern mimicry. A critical first step in understanding the colour pattern genotype is an unambiguous understanding of the phenotype under selection, which has not been objectively defined in bumble bees. Here, we quantitatively define the principal colour pattern elements that comprise the phenotype array across all species. Matrix analysis of meticulously scored colour patterns of ∼95% of described species indicates there are 12 discrete primary 'ground plan' elements in common among all species, many of which correspond to segmentation patterning. Additional secondary elements characterize individual species and geographical variants. The boundaries of these elements appear to correspond to expression patterns of Hox genes in Drosophila and Apis but also suggest novel post-Hox specialization of abdominal patterning. Our findings provide the first foundation for exploring candidate genes regulating adaptive pattern variation in bumble bees and broaden the framework for understanding common genetic mechanisms of pattern evolution in insects.