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

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

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

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

Airy processes and variational problems

We review the Airy processes; their formulation and how they are conjectured to govern the large time, large distance spatial fluctuations of one dimensional random growth models. We also describe formulas which express the probabilities that they lie below a given curve as Fredholm determinants of certain boundary value operators, and the several applications of these formulas to variational problems involving Airy processes that arise in physical problems, as well as to their local behaviour.Comment: Minor corrections. 41 pages, 4 figures. To appear as chapter in "PASI Proceedings: Topics in percolative and disordered systems

On the construction of high-order force gradient algorithms for integration of motion in classical and quantum systems

A consequent approach is proposed to construct symplectic force-gradient algorithms of arbitrarily high orders in the time step for precise integration of motion in classical and quantum mechanics simulations. Within this approach the basic algorithms are first derived up to the eighth order by direct decompositions of exponential propagators and further collected using an advanced composition scheme to obtain the algorithms of higher orders. Contrary to the scheme by Chin and Kidwell [Phys. Rev. E 62, 8746 (2000)], where high-order algorithms are introduced by standard iterations of a force-gradient integrator of order four, the present method allows to reduce the total number of expensive force and its gradient evaluations to a minimum. At the same time, the precision of the integration increases significantly, especially with increasing the order of the generated schemes. The algorithms are tested in molecular dynamics and celestial mechanics simulations. It is shown, in particular, that the efficiency of the new fourth-order-based algorithms is better approximately in factors 5 to 1000 for orders 4 to 12, respectively. The results corresponding to sixth- and eighth-order-based composition schemes are also presented up to the sixteenth order. For orders 14 and 16, such highly precise schemes, at considerably smaller computational costs, allow to reduce unphysical deviations in the total energy up in 100 000 times with respect to those of the standard fourth-order-based iteration approach.Comment: 23 pages, 2 figures; submitted to Phys. Rev.

Eliashberg-type equations for correlated superconductors

The derivation of the Eliashberg -- type equations for a superconductor with strong correlations and electron--phonon interaction has been presented. The proper account of short range Coulomb interactions results in a strongly anisotropic equations. Possible symmetries of the order parameter include s, p and d wave. We found the carrier concentration dependence of the coupling constants corresponding to these symmetries. At low hole doping the d-wave component is the largest one.Comment: RevTeX, 18 pages, 5 ps figures added at the end of source file, to be published in Phys.Rev. B, contact: [email protected]

Late Maastrichtian carbon isotope stratigraphy and cyclostratigraphy of the Newfoundland Margin (Site U1403, IODP Expedition 342)

Earth’s climate during the Maastrichtian (latest Cretaceous) was punctuated by brief warming and cooling episodes, accompanied by perturbations of the global carbon cycle. Superimposed on a long-term cooling trend, the middle Maastrichtian is characterized by deep-sea warming and relatively high values of stable carbon-isotope ratios, followed by strong climatic variability towards the end of the Cretaceous. A lack of knowledge on the timing of climatic change inhibits our understanding of underlying causal mechanisms. We present an integrated stratigraphy from Integrated Ocean Drilling Program (IODP) Site U1403, providing an expanded deep ocean record from the North Atlantic (Expedition 342, Newfoundland Margin). Distinct sedimentary cyclicity suggests that orbital forcing played a major role in depositional processes, which is confirmed by statistical analyses of high resolution elemental data obtained by X-ray fluorescence (XRF) core scanning. Astronomical calibration reveals that the investigated interval encompasses seven 405-kyr cycles (Ma4051 to Ma4057) and spans the 2.8 Myr directly preceding the Cretaceous/Paleocene (K/Pg) boundary. A high-resolution carbon-isotope record from bulk carbonates allows us to identify global trends in the late Maastrichtian carbon cycle. Low-amplitude variations (up to 0.4‰) in carbon isotopes at Site U1403 match similar scale variability in records from Tethyan and Pacific open-ocean sites. Comparison between Site U1403 and the hemipelagic restricted basin of the Zumaia section (northern Spain), with its own well-established independent cyclostratigraphic framework, is more complex. Whereas the pre-K/Pg oscillations and the negative values of the Mid-Maastrichtian Event (MME) can be readily discerned in both the Zumaia and U1403 records, patterns diverge during a ~ 1 Myr period in the late Maastrichtian (67.8–66.8 Ma), with Site U1403 more reliably reflecting global carbon cycling. Our new carbon isotope record and cyclostratigraphy offer promise for Site U1403 to serve as a future reference section for high-resolution studies of late Maastrichtian paleoclimatic change