Stability Analysis of Galerkin/Runge-Kutta Navier-Stokes Discretisations on Unstructured Grids

This paper presents a timestep stability analysis for a class of discretisations applied to the linearised form of the Navier-Stokes equations on a 3D domain with periodic boundary conditions. Using a suitable definition of the `perturbation energy' it is shown that the energy is monotonically decreasing for both the original p.d.e. and the semi-discrete system of o.d.e.'s arising from a Galerkin discretisation on a tetrahedral grid. Using recent theoretical results concerning algebraic and generalised stability, sufficient stability limits are obtained for both global and local timesteps for fully discrete algorithms using Runge-Kutta time integration

Structural, EPR, photo and thermoluminescence properties of ZnO:Fe nanoparticles

Zn (1-x)Fe (x)O (1+0.5x) (x = 0.5-5 mol) nanoparticles were synthesized by a low temperature solution combustion route. The structural characterization of these nanoparticles by PXRD, SEM and TEM confirmed the phase purity of the samples and indicated a reduction in the particle size with increase in Fe content. A small increase in micro strain in the Fe doped nanocrystals is observed from W-H plots. EPR spectrum exhibits an intense resonance signal with effective g values at g â 2.0 with a sextet hyperfine structure (hfs) besides a weak signal at g â 4.13. The signal at g â 2.0 with a sextet hyperfine structure might be due to manganese impurity where as the resonance signal at g â 4.13 is due to iron. The optical band gap E g was found to decrease with increase of Fe content. Raman spectra exhibit two non-polar optical phonon (E 2) modes at low and high frequencies at 100 and 435 cm -1 in Fe doped samples. These modes broaden and disappear with increase of Fe dopant concentration. TL measurements of γ-irradiated (1-5 kGy) samples show a main glow peak at 368°C at a warming rate of 6.7°Cs -1. The thermal activation parameters were estimated from Glow peak shape method. The average activation energy was found to be in the range 0.34-2.81 eV. © 2012 Elsevier B.V. All rights reserved

Virus shapes and buckling transitions in spherical shells

We show that the icosahedral packings of protein capsomeres proposed by Caspar and Klug for spherical viruses become unstable to faceting for sufficiently large virus size, in analogy with the buckling instability of disclinations in two-dimensional crystals. Our model, based on the nonlinear physics of thin elastic shells, produces excellent one parameter fits in real space to the full three-dimensional shape of large spherical viruses. The faceted shape depends only on the dimensionless Foppl-von Karman number \gamma=YR^2/\kappa, where Y is the two-dimensional Young's modulus of the protein shell, \kappa is its bending rigidity and R is the mean virus radius. The shape can be parameterized more quantitatively in terms of a spherical harmonic expansion. We also investigate elastic shell theory for extremely large \gamma, 10^3 < \gamma < 10^8, and find results applicable to icosahedral shapes of large vesicles studied with freeze fracture and electron microscopy.Comment: 11 pages, 12 figure

B-cell activating factor (BAFF) plasma level at the time of chronic GvHD diagnosis is a potential predictor of non-relapse mortality

Biological markers for risk stratification of chronic GvHD (cGvHD) could improve the care of patients undergoing allogeneic hematopoietic stem cell transplantation. Increased plasma levels of B-cell activating factor (BAFF), chemokine (C-X-C motif) ligand 9 (CXCL9) and elafin have been associated with the diagnosis, but not with outcome in patients with cGvHD. We evaluated the association between levels of these soluble proteins, measured by ELISA at the time of cGvHD diagnosis and before the initiation of therapy, with non-relapse-mortality (NRM). Based on the log-transformed values, factor levels were divided into tertiles defined respectively as low, intermediate, and high levels. On univariable analysis, BAFF levels were significantly associated with NRM, whereas CXCL9 and elafin levels were not. Both low (⩽2.3 ng/mL, hazard ratio (HR)=5.8, P=0.03) and high (>5.7 ng/mL, HR=5.4, P=0.03) BAFF levels were associated with a significantly higher NRM compared with intermediate BAFF level. The significant effect of high or low BAFF levels persisted in multivariable analysis. A subset of cGvHD patients had persistently low BAFF levels. In conclusion, our data show that BAFF levels at the time of cGvHD diagnosis are associated with NRM, and also are potentially useful for risk stratification. These results warrant confirmation in larger studies

The interfascicular matrix enables fascicle sliding and recovery in tendon, and behaves more elastically in energy storing tendons

While the predominant function of all tendons is to transfer force from muscle to bone and position the limbs, some tendons additionally function as energy stores, reducing the cost of locomotion. Energy storing tendons experience extremely high strains and need to be able to recoil efficiently for maximum energy storage and return. In the equine forelimb, the energy storing superficial digital flexor tendon (SDFT) has much higher failure strains than the positional common digital extensor tendon (CDET). However, we have previously shown that this is not due to differences in the properties of the SDFT and CDET fascicles (the largest tendon subunits). Instead, there is a greater capacity for interfascicular sliding in the SDFT which facilitates the greater extensions in this particular tendon (Thorpe et al., 2012). In the current study, we exposed fascicles and interfascicular matrix (IFM) from the SDFT and CDET to cyclic loading followed by a test to failure. The results show that IFM mechanical behaviour is not a result of irreversible deformation, but the IFM is able to withstand cyclic loading, and is more elastic in the SDFT than in the CDET. We also assessed the effect of ageing on IFM properties, demonstrating that the IFM is less able to resist repetitive loading as it ages, becoming stiffer with increasing age in the SDFT. These results provide further indications that the IFM is important for efficient function in energy storing tendons, and age-related alterations to the IFM may compromise function and predispose older tendons to injury

Neutron matter at zero temperature with auxiliary field diffusion Monte Carlo

The recently developed auxiliary field diffusion Monte Carlo method is applied to compute the equation of state and the compressibility of neutron matter. By combining diffusion Monte Carlo for the spatial degrees of freedom and auxiliary field Monte Carlo to separate the spin-isospin operators, quantum Monte Carlo can be used to simulate the ground state of many nucleon systems (A\alt 100). We use a path constraint to control the fermion sign problem. We have made simulations for realistic interactions, which include tensor and spin--orbit two--body potentials as well as three-nucleon forces. The Argonne $v_8'$ and $v_6'$ two nucleon potentials plus the Urbana or Illinois three-nucleon potentials have been used in our calculations. We compare with fermion hypernetted chain results. We report results of a Periodic Box--FHNC calculation, which is also used to estimate the finite size corrections to our quantum Monte Carlo simulations. Our AFDMC results for $v_6$ models of pure neutron matter are in reasonably good agreement with equivalent Correlated Basis Function (CBF) calculations, providing energies per particle which are slightly lower than the CBF ones. However, the inclusion of the spin--orbit force leads to quite different results particularly at relatively high densities. The resulting equation of state from AFDMC calculations is harder than the one from previous Fermi hypernetted chain studies commonly used to determine the neutron star structure.Comment: 15 pages, 15 tables and 5 figure

Quenching of Weak Interactions in Nucleon Matter

We have calculated the one-body Fermi and Gamow-Teller charge-current, and vector and axial-vector neutral-current nuclear matrix elements in nucleon matter at densities of 0.08, 0.16 and 0.24 fm$^{-3}$ and proton fractions ranging from 0.2 to 0.5. The correlated states for nucleon matter are obtained by operating on Fermi-gas states by a symmetrized product of pair correlation operators determined from variational calculations with the Argonne v18 and Urbana IX two- and three-nucleon interactions. The squares of the charge current matrix elements are found to be quenched by 20 to 25 % by the short-range correlations in nucleon matter. Most of the quenching is due to spin-isospin correlations induced by the pion exchange interactions which change the isospins and spins of the nucleons. A large part of it can be related to the probability for a spin up proton quasi-particle to be a bare spin up/down proton/neutron. We also calculate the matrix elements of the nuclear Hamiltonian in the same correlated basis. These provide relatively mild effective interactions which give the variational energies in the Hartree-Fock approximation. The calculated two-nucleon effective interaction describes the spin-isospin susceptibilities of nuclear and neutron matter fairly accurately. However $\geq$ 3-body terms are necessary to reproduce the compressibility. All presented results use the simple 2-body cluster approximation to calculate the correlated basis matrix elements.Comment: submitted to PR

Approximation of Parametric Derivatives by the Empirical Interpolation Method

We introduce a general a priori convergence result for the approximation of parametric derivatives of parametrized functions. We consider the best approximations to parametric derivatives in a sequence of approximation spaces generated by a general approximation scheme, and we show that these approximations are convergent provided that the best approximation to the function itself is convergent. We also provide estimates for the convergence rates. We present numerical results with spaces generated by a particular approximation scheme—the Empirical Interpolation Method—to confirm the validity of the general theory