Evolutionary Convergence to Ideal Free Dispersal Strategies and Coexistence

We study a two species competition model in which the species have the same population dynamics but different dispersal strategies and show how these dispersal strategies evolve. We introduce a general dispersal strategy which can result in the ideal free distributions of both competing species at equilibrium and generalize the result of Averill et al. (2011). We further investigate the convergent stability of this ideal free dispersal strategy by varying random dispersal rates, advection rates, or both of these two parameters simultaneously. For monotone resource functions, our analysis reveals that among two similar dispersal strategies, selection generally prefers the strategy which is closer to the ideal free dispersal strategy. For nonmonotone resource functions, our findings suggest that there may exist some dispersal strategies which are not ideal free, but could be locally evolutionarily stable and/or convergent stable, and allow for the coexistence of more than one species

Near-infrared photoluminescence enhancement in Ge/CdS and Ge/ZnS core/shell nanocrystals: Utilizing IV/II-VI semiconductor epitaxy

Ge nanocrystals have a large Bohr radius and a small, size-tunable band gap that may engender direct character via strain or doping. Colloidal Ge nanocrystals are particularly interesting in the development of near-infrared materials for applications in bioimaging, telecommunications and energy conversion. Epitaxial growth of a passivating shell is a common strategy employed in the synthesis of highly luminescent II-VI, III-V and IV-VI semiconductor quantum dots. Here, we use relatively unexplored IV/II-VI epitaxy as a way to enhance the photoluminescence and improve the optical stability of colloidal Ge nanocrystals. Selected on the basis of their relatively small lattice mismatch compared with crystalline Ge, we explore the growth of epitaxial CdS and ZnS shells using the successive ion layer adsorption and reaction method. Powder X-ray diffraction and electron microscopy techniques, including energy dispersive X-ray spectroscopy and selected area electron diffraction, clearly show the controllable growth of as many as 20 epitaxial monolayers of CdS atop Ge cores. In contrast, Ge etching and/or replacement by ZnS result in relatively small Ge/ZnS nanocrystals. The presence of an epitaxial II-VI shell greatly enhances the near-infrared photoluminescence and improves the photoluminescence stability of Ge. Ge/II-VI nanocrystals are reproducibly 1-3 orders of magnitude brighter than the brightest Ge cores. Ge/4.9CdS core/shells show the highest photoluminescence quantum yield and longest radiative recombination lifetime. Thiol ligand exchange easily results in near-infrared active, water-soluble Ge/II-VI nanocrystals. We expect this synthetic IV/II-VI epitaxial approach will lead to further studies into the optoelectronic behavior and practical applications of Si and Ge-based nanomaterials

Evolutionary Convergence to Ideal Free Dispersal Strategies and Coexistence

We study a two species competition model in which the species have the same population dynamics but different dispersal strategies and show how these dispersal strategies evolve. We introduce a general dispersal strategy which can result in the ideal free distributions of both competing species at equilibrium and generalize the result of Averill et al. (2011). We further investigate the convergent stability of this ideal free dispersal strategy by varying random dispersal rates, advection rates, or both of these two parameters simultaneously. For monotone resource functions, our analysis reveals that among two similar dispersal strategies, selection generally prefers the strategy which is closer to the ideal free dispersal strategy. For nonmonotone resource functions, our findings suggest that there may exist some dispersal strategies which are not ideal free, but could be locally evolutionarily stable and/or convergent stable, and allow for the coexistence of more than one species

Transient chaos in fractional Bloch equations

AbstractThe Bloch equation provides the fundamental description of nuclear magnetic resonance (NMR) and relaxation (T1 and T2). This equation is the basis for both NMR spectroscopy and magnetic resonance imaging (MRI). The fractional-order Bloch equation is a generalization of the integer-order equation that interrelates the precession of the x, y and z components of magnetization with time- and space-dependent relaxation. In this paper we examine transient chaos in a non-linear version of the Bloch equation that includes both fractional derivatives and a model of radiation damping. Recent studies of spin turbulence in the integer-order Bloch equation suggest that perturbations of the magnetization may involve a fading power law form of system memory, which is concisely embedded in the order of the fractional derivative. Numerical analysis of this system shows different patterns in the stability behavior for α near 1.00. In general, when α is near 1.00, the system is chaotic, while for 0.98 ≥α≥ 0.94, the system shows transient chaos. As the value of α decreases further, the duration of the transient chaos diminishes and periodic sinusoidal oscillations emerge. These results are consistent with studies of the stability of both the integer and the fractional-order Bloch equation. They provide a more complete model of the dynamic behavior of the NMR system when non-linear feedback of magnetization via radiation damping is present