Convergence of simple adaptive Galerkin schemes based on h − h/2 error estimators

We discuss several adaptive mesh-refinement strategies based on (h − h/2)-error estimation. This class of adaptivemethods is particularly popular in practise since it is problem independent and requires virtually no implementational overhead. We prove that, under the saturation assumption, these adaptive algorithms are convergent. Our framework applies not only to finite element methods, but also yields a first convergence proof for adaptive boundary element schemes. For a finite element model problem, we extend the proposed adaptive scheme and prove convergence even if the saturation assumption fails to hold in general

Born-Oppenheimer Approximation near Level Crossing

We consider the Born-Oppenheimer problem near conical intersection in two dimensions. For energies close to the crossing energy we describe the wave function near an isotropic crossing and show that it is related to generalized hypergeometric functions 0F3. This function is to a conical intersection what the Airy function is to a classical turning point. As an application we calculate the anomalous Zeeman shift of vibrational levels near a crossing.Comment: 8 pages, 1 figure, Lette

A review of data on abundance, trends in abundance, habitat use and diet of ice-breeding seals in the Southern Ocean

The development of models of marine ecosystems in the Southern Ocean is becoming increasingly important as a means of understanding and managing impacts such as exploitation and climate change. Collating data from disparate sources, and understanding biases or uncertainties inherent in those data, are important first steps for improving ecosystem models. This review focuses on seals that breed in ice habitats of the Southern Ocean (i.e. crabeater seal, Lobodon carcinophaga; Ross seal, Ommatophoca rossii; leopard seal, Hydrurga leptonyx; and Weddell seal, Leptonychotes weddellii). Data on populations (abundance and trends in abundance), distribution and habitat use (movement, key habitat and environmental features) and foraging (diet) are summarised, and potential biases and uncertainties inherent in those data are identified and discussed. Spatial and temporal gaps in knowledge of the populations, habitats and diet of each species are also identified

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

Coherent multi-flavour spin dynamics in a fermionic quantum gas

Microscopic spin interaction processes are fundamental for global static and dynamical magnetic properties of many-body systems. Quantum gases as pure and well isolated systems offer intriguing possibilities to study basic magnetic processes including non-equilibrium dynamics. Here, we report on the realization of a well-controlled fermionic spinor gas in an optical lattice with tunable effective spin ranging from 1/2 to 9/2. We observe long-lived intrinsic spin oscillations and investigate the transition from two-body to many-body dynamics. The latter results in a spin-interaction driven melting of a band insulator. Via an external magnetic field we control the system's dimensionality and tune the spin oscillations in and out of resonance. Our results open new routes to study quantum magnetism of fermionic particles beyond conventional spin 1/2 systems.Comment: 9 pages, 5 figure

Numerical study of the small dispersion limit of the Korteweg-de Vries equation and asymptotic solutions

We study numerically the small dispersion limit for the Korteweg-de Vries (KdV) equation $u_t+6uu_x+\epsilon^{2}u_{xxx}=0$ for $\epsilon\ll1$ and give a quantitative comparison of the numerical solution with various asymptotic formulae for small $\epsilon$ in the whole $(x,t)$-plane. The matching of the asymptotic solutions is studied numerically

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

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

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.