Convergence of linearized and adjoint approximations for discontinuous solutions of conservation laws. Part 2: adjoint approximations and extensions

This paper continues the convergence analysis in [M. Giles and S. Ulbrich, SIAM J. Numer. Anal., 48 (2010), pp. 882–904] of discrete approximations to the linearized and adjoint equations arising from an unsteady one-dimensional hyperbolic equation with a convex flux function. We consider a simple modified Lax–Friedrichs discretization on a uniform grid, and a key point is that the numerical smoothing increases the number of points across the nonlinear discontinuity as the grid is refined. It is proved that there is convergence in the discrete approximation of linearized output functionals even for Dirac initial perturbations and pointwise convergence almost everywhere for the solution of the adjoint discrete equations. In particular, the adjoint approximation converges to the correct uniform value in the region in which characteristics propagate into the discontinuity. Moreover, it is shown that the results of [M. Giles and S. Ulbrich, SIAM J. Numer. Anal., 48 (2010), pp. 882–904] and the present paper hold also for quite general nonlinear initial data which contain multiple shocks and for which shocks form at a later time and/or merge

Parastatistics of charged bosons partly localised by impurities

Coulomb repulsion is taken into account to derive the thermodynamics of charged bosons in a random external potential. A simple analytical form of the partition function is proposed for the case of non-overlapping localised states (i.e. a small amount of disorder). The density of localised bosons and the specific heat show a peculiar non-uniform temperature dependence below the Bose-Einstein condensation temperature. The superfluid - Bose-glass phase diagram is discussed. A new phase is predicted which is a Bose-glass at T=0 but a superfluid at finite T.Comment: 6 pages, Revtex, 6 figures (available on request from the authors

Document Archiving, Replication and Migration Container for Mobile Web Users

With the increasing use of mobile workstations for a wide variety of tasks and associated information needs, and with many variations of available networks, access to data becomes a prime consideration. This paper discusses issues of workstation mobility and proposes a solution wherein the data structures are accessed in an encapsulated form - through the Portable File System (PFS) wrapper. The paper discusses an implementation of the Portable File System, highlighting the architecture and commenting upon performance of an experimental system. Although investigations have been focused upon mobile access of WWW documents, this technique could be applied to any mobile data access situation.Comment: 5 page

A Note on the Importance of Weak Convergence Rates for SPDE Approximations in Multilevel Monte Carlo Schemes

It is a well-known rule of thumb that approximations of stochastic partial differential equations have essentially twice the order of weak convergence compared to the corresponding order of strong convergence. This is already known for many approximations of stochastic (ordinary) differential equations while it is recent research for stochastic partial differential equations. In this note it is shown how the availability of weak convergence results influences the number of samples in multilevel Monte Carlo schemes and therefore reduces the computational complexity of these schemes for a given accuracy of the approximations.Comment: 16 pages, 3 figures, updated to version published in the Proceedings of MCQMC1

Design considerations for attaining 200-knot test velocities at the aircraft landing loads and traction facility

Design studies are presented which consider the important parameters in providing 200 knot test velocities at the landing loads and traction facility. Two major components of this facility, the hydraulic jet catapult and the test carriage structure, are considered. Suitable factors are determined to correlate analytical data for characteristics of the hydraulic jet catapult with data measured from the existing catapult system. The resulting equations are used to calculate test velocities for a range of jet nozzle diameters and carriage masses with both the current 122 m and an increased 183 m catapult stroke. Using the catapult characteristics, a target design point is selected and a carriage structure is sized to meet the target point strength requirements

Gene-knockdown in the honey bee mite Varroa destructor by a non-invasive approach : studies on a glutathione S-transferase

Peer reviewedPublisher PD

A mathematical model for mechanically-induced deterioration of the binder in lithium-ion electrodes

This study is concerned with modeling detrimental deformations of the binder phase within lithium-ion batteries that occur during cell assembly and usage. A two-dimensional poroviscoelastic model for the mechanical behavior of porous electrodes is formulated and posed on a geometry corresponding to a thin rectangular electrode, with a regular square array of microscopic circular electrode particles, stuck to a rigid base formed by the current collector. Deformation is forced both by (i) electrolyte absorption driven binder swelling, and; (ii) cyclic growth and shrinkage of electrode particles as the battery is charged and discharged. The governing equations are upscaled in order to obtain macroscopic effective-medium equations. A solution to these equations is obtained, in the asymptotic limit that the height of the rectangular electrode is much smaller than its width, that shows the macroscopic deformation is one-dimensional. The confinement of macroscopic deformations to one dimension is used to obtain boundary conditions on the microscopic problem for the deformations in a 'unit cell' centered on a single electrode particle. The resulting microscale problem is solved using numerical (finite element) techniques. The two different forcing mechanisms are found to cause distinctly different patterns of deformation within the microstructure. Swelling of the binder induces stresses that tend to lead to binder delamination from the electrode particle surfaces in a direction parallel to the current collector, whilst cycling causes stresses that tend to lead to delamination orthogonal to that caused by swelling. The differences between the cycling-induced damage in both: (i) anodes and cathodes, and; (ii) fast and slow cycling are discussed. Finally, the model predictions are compared to microscopy images of nickel manganese cobalt oxide cathodes and a qualitative agreement is found.Comment: 25 pages, 11 figure

Transcriptome analysis of the synganglion from the honey bee mite, Varroa destructor and RNAi knockdown of neural peptide targets

Acknowledgements This work was funded by BBSRC-LINK grant # BB/J01009X/1 and Vita Europe Ltd. We are grateful to the Scottish Beekeepers Association, especially Mr Phil McAnespie in supporting this work at its inception. We acknowledge partial funding from a Genesis Faraday SPARK Award, part of a Scottish Government SEEKIT project for the early part of this work. We are grateful to Prof David Evans for his advice on Varroa destructor viruses.Peer reviewedPostprin

INCREASES IN COSTS AND RETURNS DUE TO INTENSIFYING RANGE FORAGE PRODUCTION SURVEYS: AN INFORMATION ECONOMIC ANALYSIS

The U.S. Congress and courts have directed federal natural resource agencies to use better information for management decisions than they have used in the past. It is also important for these agencies to improve the efficiency of resource use where possible. This information economics study estimates increased costs and revenues which can be directly imputed to improving the accuracy of range forage production surveys. It suggests that a high level of survey accuracy may often be justifiable.Crop Production/Industries, Research Methods/ Statistical Methods,