The spectral properties and singularities of monodromy-free Schroedinger operators

The main object of study is the theory of Schrödinger operators with meromorphic potentials, having trivial monodromy in the complex domain. In the first part we study the spectral properties of a class of such operators related to the classical Whittaker-Hill equation (-d^2/dx^2+Acos2x+Bcos4x)ψ=λψ. The equation, for special choices of A and B, is known to have the remarkable property that half of the gaps eventually become closed (semifinite-gap operator). Using the Darboux transformation we construct new trigonometric examples of semifinite-gap operators with real, smooth potentials. A similar technique applied to the Lamé operator gives smooth, real, finite-gap potentials in terms of classical Jacobi elliptic functions. In the second part we study the singular locus of monodromy-free potentials in the complex domain. A particular case is given by the zeros of Wronskians of Hermite polynomials, which are studied in detail. We introduce a class of partitions (doubled partitions) for which we observe a direct qualitative relationship between the pattern of zeros and the shape of the corresponding Young diagram. For the Wronskians W(H_n,H_{n+k}) we give an asymptotic formula for the curve on which zeros lie as n → ∞. We also give some empirical formulas for asymptotic behaviour of zeros of Wronskians of 3 and 4 Hermite polynomials. In the last chapter we apply the theory of monodromy-free operators to produce new vortex equilibria in the periodic case and in the presence of background flow

Whittaker-Hill equation and semifinite-gap Schroedinger operators

A periodic one-dimensional Schroedinger operator is called semifinite-gap if every second gap in its spectrum is eventually closed. We construct explicit examples of semifinite-gap Schroedinger operators in trigonometric functions by applying Darboux transformations to the Whittaker-Hill equation. We give a criterion of the regularity of the corresponding potentials and investigate the spectral properties of the new operators.Comment: Revised versio

Thermosensitive polymer-grafted iron oxide nanoparticles studied by in situ dynamic light backscattering under magnetic hyperthermia

© 2015 IOP Publishing Ltd. Thermometry at the nanoscale is an emerging area fostered by intensive research on nanoparticles (NPs) that are capable of converting electromagnetic waves into heat. Recent results suggest that stationary gradients can be maintained between the surface of NPs and the bulk solvent, a phenomenon sometimes referred to as \u27cold hyperthermia\u27. However, the measurement of such highly localized temperatures is particularly challenging. We describe here a new approach to probing the temperature at the surface of iron oxide NPs and enhancing the understanding of this phenomenon. This approach involves the grafting of thermosensitive polymer chains to the NP surface followed by the measurement of macroscopic properties of the resulting NP suspension and comparison to a calibration curve built up by macroscopic heating. Superparamagnetic iron oxide NPs were prepared by the coprecipitation of ferrous and ferric salts and functionalized with amines, then azides using a sol-gel route followed by a dehydrative coupling reaction. Thermosensitive poly[2-(dimethylamino)ethyl methacrylate] (PDMAEMA) with an alkyne end-group was synthesized by controlled radical polymerization and was grafted using a copper assisted azide-alkyne cycloaddition reaction. Measurement of the colloidal properties by dynamic light scattering (DLS) indicated that the thermosensitive NPs exhibited changes in their Zeta potential and hydrodynamic diameter as a function of pH and temperature due to the grafted PDMAEMA chains. These changes were accompanied by changes in the relaxivities of the NPs, suggesting application as thermosensitive contrast agents for magnetic resonance imaging (MRI). In addition, a new fibre-based backscattering setup enabled positioning of the DLS remote-head as close as possible to the coil of a magnetic heating inductor to afford in situ probing of the backscattered light intensity, hydrodynamic diameter, and temperature. This approach provides a promising platform for estimating the response of magnetic NPs to application of a radiofrequency magnetic field or for understanding the behaviour of other thermogenic NPs

Human Impacts on Forest Biodiversity in Protected Walnut-Fruit Forests in Kyrgyzstan

We used a spatially explicit model of forest dynamics, supported by empirical field data and socioeconomic data, to examine the impacts of human disturbances on a protected forest landscape in Kyrgyzstan. Local use of 27 fruit and nut species was recorded and modeled. Results indicated that in the presence of fuelwood cutting with or without grazing, species of high socioeconomic impor- tance such as Juglans regia, Malus spp., and Armeniaca vulgaris were largely eliminated from the landscape after 50–150 yr. In the absence of disturbance or in the presence of grazing only, decline of these species occurred at a much lower rate, owing to competi- tive interactions between tree species. This suggests that the current intensity of fuelwood harvesting is not sustainable. Conversely, cur- rent grazing intensities were found to have relatively little impact on forest structure and composition, and could potentially play a positive role in supporting regeneration of tree species. These results indicate that both positive and negative impacts on biodiversity can arise from human populations living within a protected area. Potentially, these could be reconciled through the development of participatory approaches to conservation management within this reserve, to ensure the maintenance of its high conservation value while meeting human needs

Climate driven life histories: the case of the Mediterranean Storm petrel

Seabirds are affected by changes in the marine ecosystem. The influence of climatic factors on marine food webs can be reflected in long-term seabird population changes. We modelled the survival and recruitment of the Mediterranean storm petrel (Hydrobates pelagicus melitensis) using a 21-year mark-recapture dataset involving almost 5000 birds. We demonstrated a strong influence of prebreeding climatic conditions on recruitment age and of rainfall and breeding period conditions on juvenile survival. The results suggest that the juvenile survival rate of the Mediterranean subspecies may not be negatively affected by the predicted features of climate change, i.e., warmer summers and lower rainfall. Based on considerations of winter conditions in different parts of the Mediterranean, we were able to draw inferences about the wintering areas of the species for the first time

Comparison of the bifurcation scenarios predicted by the single-mode and multimode semiconductor laser rate equations

We present a detailed comparison of the bifurcation scenarios predicted by single-mode and multimode semiconductor laser rate equation models under large amplitude injection current modulation. The influence of the gain model on the predicted dynamics is investigated. Calculations of the dependence of the time averaged longitudinal mode intensities on modulation frequency are compared with experiments performed on an AlxGa1-xAs Fabry-Pérot semiconductor laser.K. A. Corbett and M. W. Hamilto