Postbuckling behaviour of beams with discrete nonlinear restraints

A beam with nonlinearly ‐ elastic lateral restraints attached at discrete points along its span is investigated via analytical and numerical methods. Previous results for the critical moment and the deflected shape based on an eigenvalue analysis of a similar beam with linearly ‐ elastic restraints are discussed, along with a validation of these results against an equivalent finite element model and results from numerical continuation. A beam with nonlinearly ‐ elastic restraints is then analysed with treatments for both quadratic and cubic restraint force–displacement relationships being provided. After formulation of the potential energy functionals, the governing differential equations of the system are derived via the calculus of variations and appropriate boundary conditions are applied. The equations are then solved using the numerical continuation software AUTO ‐ 07p for a standard I ‐ section beam. The variation in elastic critical buckling moment with the linear component of the restraint stiffness is tracked via a two ‐ parameter numerical continuation, allowing determination of the stiffness values at which the critical buckling modes changes qualitatively. Using these stiffness values, subsequent analyses are conducted to examine the influence of the nonlinear component of the restraint stiffness, from which post ‐ buckling equilibrium paths and deformation modes are extracted. The results of these analyses are then compared with an equivalent Rayleigh–Ritz formulation whereby the displacement components are represented by Fourier series. Equilibrium equations are derived by minimizing the potential energy functional with respect to the amplitudes of the constituent harmonics of the Fourier series. The amplitudes are solved for in the post ‐ buckling range by AUTO ‐ O7p and equilibrium paths are produced and compared to the equivalent solutions of the differential equations, with good agreement observed

NMR evidence of strong-correlated superconductivity in LiFeAs: tuning toward an SDW ordering

In this letter, we reported the results of NMR study on LiFeAs single crystals. We find a strong evidence of the low temperature spin fluctuations; by changing sample preparation conditions, the system can be tuned toward an spin-density-wave (SDW) quantum-critical point. The detection of an interstitial Li(2) ion, possibly locating in the tetrahedral hole, suggests that the off-stoichiometry and/or lattice defect can probably account for the absence of the SDW ordering in LiFeAs. These facts show that LiFeAs is a strongly correlated system and the superconductivity is likely originated from the SDW fluctuations.Comment: 5 pages, s figure

Kondo correlation and spin-flip scattering in spin-dependent transport through a quantum dot coupled to ferromagnetic leads

We investigate the linear and nonlinear dc transport through an interacting quantum dot connected to two ferromagnetic electrodes around Kondo regime with spin-flip scattering in the dot. Using a slave-boson mean field approach for the Anderson Hamiltonian having finite on-site Coulomb repulsion, we find that a spin-flip scattering always depresses the Kondo correlation at arbitrary polarization strength in both parallel and antiparallel alignment of the lead magnetization and that it effectively reinforces the tunneling related conductance in the antiparallel configuration. For systems deep in the Kondo regime, the zero-bias single Kondo peak in the differential conductance is split into two peaks by the intradot spin-flip scattering; while for systems somewhat further from the Kondo center, the spin-flip process in the dot may turn the zero-bias anomaly into a three-peak structure.Comment: 4 pages, 2 figure

Measuring the equation of state of trapped ultracold bosonic systems in an optical lattice with in-situ density imaging

We analyze quantitatively how imaging techniques with single-site resolution allow to measure thermodynamical properties that cannot be inferred from time-of-light images for the trapped Bose-Hubbard model. If the normal state extends over a sufficiently large range, the chemical potential and the temperature can be extracted from a single shot, provided the sample is in thermodynamic equilibrium. When the normal state is too narrow, temperature is low but can still be extracted using the fluctuation-dissipation theorem over the entire trap range as long as the local density approximation remains valid, as was recently suggested by Qi Zhou and Tin-Lun Ho [arXiv:0908.3015]. However, for typical present-day experiments, the number of samples needed is of the order of 1000 in order to get the temperature at least $10 \%$ accurate, but it is possible to reduce the variance by 2 orders of magnitude if the density-density correlation length is short, which is the case for the Bose-Hubbard model. Our results provide further evidence that cold gases in an optical lattices can be viewed as quantum analog computers.Comment: 8 pages, 10 figure

A Class of Coupled KdV systems and Their Bi-Hamiltonian Formulations

A Hamiltonian pair with arbitrary constants is proposed and thus a sort of hereditary operators is resulted. All the corresponding systems of evolution equations possess local bi-Hamiltonian formulation and a special choice of the systems leads to the KdV hierarchy. Illustrative examples are given.Comment: 8 pages, late

Visualising and quantifying 'excess deaths' in Scotland compared with the rest of the UK and the rest of Western Europe

BACKGROUND: Scotland has higher mortality rates than the rest of Western Europe (rWE), with more cardiovascular disease and cancer among older adults; and alcohol-related and drug-related deaths, suicide and violence among younger adults. METHODS: We obtained sex, age-specific and year-specific all-cause mortality rates for Scotland and other populations, and explored differences in mortality both visually and numerically. RESULTS: Scotland's age-specific mortality was higher than the rest of the UK (rUK) since 1950, and has increased. Between the 1950s and 2000s, 'excess deaths' by age 80 per 100 000 population associated with living in Scotland grew from 4341 to 7203 compared with rUK, and from 4132 to 8828 compared with rWE. UK-wide mortality risk compared with rWE also increased, from 240 'excess deaths' in the 1950s to 2320 in the 2000s. Cohorts born in the 1940s and 1950s throughout the UK including Scotland had lower mortality risk than comparable rWE populations, especially for males. Mortality rates were higher in Scotland than rUK and rWE among younger adults from the 1990s onwards suggesting an age-period interaction. CONCLUSIONS: Worsening mortality among young adults in the past 30 years reversed a relative advantage evident for those born between 1950 and 1960. Compared with rWE, Scotland and rUK have followed similar trends but Scotland has started from a worse position and had worse working age-period effects in the 1990s and 2000s