The chebop system for automatic solution of differential equations

In MATLAB, it would be good to be able to solve a linear differential equation by typing u = L\f, where f, u, and L are representations of the right-hand side, the solution, and the differential operator with boundary conditions. Similarly it would be good to be able to exponentiate an operator with expm(L) or determine eigenvalues and eigenfunctions with eigs(L). A system is described in which such calculations are indeed possible, based on the previously developed chebfun system in object-oriented MATLAB. The algorithms involved amount to spectral collocation methods on Chebyshev grids of automatically determined resolution

Joint distribution of the first and second eigenvalues at the soft edge of unitary ensembles

The density function for the joint distribution of the first and second eigenvalues at the soft edge of unitary ensembles is found in terms of a Painlev\'e II transcendent and its associated isomonodromic system. As a corollary, the density function for the spacing between these two eigenvalues is similarly characterized.The particular solution of Painlev\'e II that arises is a double shifted B\"acklund transformation of the Hasting-McLeod solution, which applies in the case of the distribution of the largest eigenvalue at the soft edge. Our deductions are made by employing the hard-to-soft edge transitions to existing results for the joint distribution of the first and second eigenvalue at the hard edge \cite{FW_2007}. In addition recursions under $a \mapsto a+1$ of quantities specifying the latter are obtained. A Fredholm determinant type characterisation is used to provide accurate numerics for the distribution of the spacing between the two largest eigenvalues.Comment: 26 pages, 1 Figure, 2 Table

Slow to change? Individual fidelity to three-dimensional foraging habitats in southern elephant seals, Mirounga leonina

Long-term fidelity to foraging areas may have fitness benefits to individuals, particularly in unpredictable environments. However, such strategies may result in short-term energetic losses and delay responses to fast environmental changes. We used satellite tracking data and associated diving data to record the habitat use of nine individual southern elephant seals over 34 winter migrations. By assessing overlap in two- and three-dimensional home ranges we illustrate strong long-term (up to 7-year) fidelity to foraging habitat. Furthermore, a repeatability statistic and hierarchical clustering exercise provided evidence for individual specialization of foraging migration strategies.We discuss the possible influences of stable long-term foraging migration strategies on the adaptability of individual elephant seals to rapid environmental change. Our results further illustrate the need for more long-term longitudinal studies to quantify the influence of individual-level site familiarity, fidelity and specialization on population-level resource selection and population dynamics

Dynamical two electron states in a Hubbard-Davydov model

We study a model in which a Hubbard Hamiltonian is coupled to the dispersive phonons in a classical nonlinear lattice. Our calculations are restricted to the case where we have only two quasi-particles of opposite spins, and we investigate the dynamics when the second quasi-particle is added to a state corresponding to a minimal energy single quasi-particle state. Depending on the parameter values, we find a number of interesting regimes. In many of these, discrete breathers (DBs) play a prominent role with a localized lattice mode coupled to the quasiparticles. Simulations with a purely harmonic lattice show much weaker localization effects. Our results support the possibility that DBs are important in HTSC.Comment: 14 pages, 12 fig

Age and structure of the Shyok Suture in the Ladakh region of Northwestern India: Implications for slip on the Karakoram Fault System

A precise age for the collision of the Kohistan-Ladakh block with Eurasia along the Shyok suture zone (SSZ) is one key to understanding the accretionary history of Tibet and the tectonics of Eurasia during the India-Eurasia collision. Knowing the age of the SSZ also allows the suture to be used as a piercing line for calculating total offset along the Karakoram Fault, which effectively represents the SE border of the Tibetan Plateau and has played a major role in plateau evolution. We present a combined structural, geochemical, and geochronologic study of the SSZ as it is exposed in the Nubra region of India to test two competing hypotheses: that the SSZ is of Late Cretaceous or, alternatively, of Eocene age. Coarse-continental strata of the Saltoro Molasse, mapped in this area, contain detrital zircon populations suggestive of derivation from Eurasia despite the fact that the molasse itself is deposited unconformably onto Kohistan-Ladakh rocks, indicating that the molasse is postcollisional. The youngest population of detrital zircons in these rocks (approximately 92 Ma) and a U/Pb zircon date for a dike that cuts basal molasse outcrops (approximately 85 Ma) imply that deposition of the succession began in the Late Cretaceous. This establishes a minimum age for the SSZ and rules out the possibility of an Eocene collision between Kohistan-Ladakh and Eurasia. Our results support correlation of the SSZ with the Bangong suture zone in Tibet, which implies a total offset across the Karakoram Fault of approximately 130–190 km

Habitat-based density models of pack-ice seal distribution in the southern Weddell Sea, Antarctica

Climate variability and changes in sea ice dynamics have caused several ice-obligate or krill-dependent populations of marine predators to decline, eliciting concern about their demographic persistence and the indirect ecological consequences that predator depletions may have on marine ecosystems. Pack-ice seals are dominant ice-obligate predators in the Antarctic marine ecosystem, but there is considerable uncertainty about their abundance and population trends. We modelled the density and distribution of pack-ice seals as a function of environmental covariates in the southern Weddell Sea, Antarctica. Our density surface modelling approach used data from aerial surveys of pack-ice seals collected in the 2013/14 austral summer. Crabeater seals Lobo don carcinophaga, the most numerous pack-ice seal we observed, occurred at the highest densities in areas with extensive sea ice near the continental shelf break, but were almost absent in areas of similar sea ice concentration in the southern extent of the Weddell Sea. The highest densities of Weddell seals Leptonychotes weddelli, which were less abundant than crabeater seals within the pack-ice habitat, were predicted to occur over the continental shelf, near the shelf break. The distribution of both seal species broadly corresponded with the distribution and relative abundance of their main prey (Antarctic krill Euphausia superba and Antarctic silverfish Pleuragramma antarctica) obtained from concurrent ecosystem surveys. Ross seals Ommatophoca rossii and leopard seals Hydrurga leptonyx were not detected at all and are apparently rare within the southern Weddell Sea. These results can contribute to biodiversity assessments in the context of marine protected area planning in this region of the Southern Ocean

The 1+1-dimensional Kardar-Parisi-Zhang equation and its universality class

We explain the exact solution of the 1+1 dimensional Kardar-Parisi-Zhang equation with sharp wedge initial conditions. Thereby it is confirmed that the continuum model belongs to the KPZ universality class, not only as regards to scaling exponents but also as regards to the full probability distribution of the height in the long time limit.Comment: Proceedings StatPhys 2

Isotope effects and possible pairing mechanism in optimally doped cuprate superconductors

We have studied the oxygen-isotope effects on T_{c} and in-plane penetration depth \lambda_{ab}(0) in an optimally doped 3-layer cuprate Bi_{1.6}Pb_{0.4}Sr_{2}Ca_{2}Cu_{3}O_{10+y} (T_{c} \sim 107 K). We find a small oxygen-isotope effect on T_{c} (\alpha_{O} = 0.019), and a substantial effect on \lambda_{ab} (0) (\Delta \lambda_{ab} (0)/\lambda_{ab} (0) = 2.5\pm0.5%). The present results along with the previously observed isotope effects in single-layer and double-layer cuprates indicate that the isotope exponent \alpha_{O} in optimally doped cuprates is small while the isotope effect on the in-plane effective supercarrier mass is substantial and nearly independent of the number of the CuO_{2} layers. A plausible pairing mechanism is proposed to explain the isotope effects, high-T_{c} superconductivity and tunneling spectra in a consistent way.Comment: 5 pages, 4 figure

Endpoint distribution of directed polymers in 1+1 dimensions

We give an explicit formula for the joint density of the max and argmax of the Airy$_2$ process minus a parabola. The argmax has a universal distribution which governs the rescaled endpoint for large time or temperature of directed polymers in 1+1 dimensions.Comment: Expanded introductio

Isotope effects in underdoped cuprate superconductors: a quantum phenomenon

We show that the unusual doping dependence of the isotope effects on transition temperature and zero temperature in - plane penetration depth naturally follows from the doping driven 3D-2D crossover, the 2D quantum superconductor to insulator transition (QSI) in the underdoped limit and the change of the relative doping concentration upon isotope substitution. Close to the QSI transition both, the isotope coefficient of transition temperature and penetration depth approach the coefficient of the relative dopant concentration, and its divergence sets the scale. These predictions are fully consistent with the experimental data and imply that close to the underdoped limit the unusual isotope effect on transition temperature and penetration depth uncovers critical phenomena associated with the quantum superconductor to insulator transition in two dimensions.Comment: 6 pages, 3 figure