A simple nonlinear model of a generic axisymmetric wave energy converter

The aim of this work is to develop a simple nonlinear model of a wave energy converter (WEC) for capturing power from ocean waves and converting it into electrical power. A generic axisymmetric device is considered, which consists of a vertical circular cylinder surrounded by a circular annulus. The nonlinear system of equations of motion of this generic WEC are derived; these include the nonlinear term arising from viscous drag due to boundary layer separation. The expressions for radiation damping and added mass are determined by dimensional analysis. These equations are then solved numerically and the results are displayed graphically in a number of figures. Consideration of these graphs leads to conclusions that should be taken into account by the design engineer

A simple nonlinear model of a generic axisymmetric wave energy converter

The aim of this work is to develop a simple nonlinear model of a wave energy converter (WEC) for capturing power from ocean waves and converting it into electrical power. A generic axisymmetric device is considered, which consists of a vertical circular cylinder surrounded by a circular annulus. The nonlinear system of equations of motion of this generic WEC are derived; these include the nonlinear term arising from viscous drag due to boundary layer separation. The expressions for radiation damping and added mass are determined by dimensional analysis. These equations are then solved numerically and the results are displayed graphically in a number of figures. Consideration of these graphs leads to conclusions that should be taken into account by the design engineer

Second order parameter-uniform convergence for a finite difference method for a partially singularly perturbed linear parabolic system

A linear system of $n$ second order differential equations of parabolic reaction-diffusion type with initial and boundary conditions is considered. The first $k$ equations are singularly perturbed. Each of the leading terms of the first $m$ equations, $mleq k$, is multiplied by a small positive parameter and these parameters are assumed to be distinct. The leading terms of the next $k-m$ equations are multiplied by the same perturbation parameter $varepsilon_m$. Since the components of the solution exhibit overlapping layers, Shishkin piecewise-uniform meshes are introduced, which are used in conjunction with a classical finite difference discretisation, to construct a numerical method for solving this problem. It is proved that in the maximum norm the numerical approximations obtained with this method are first order convergent in time and essentially second order convergent in the space variable, uniformly with respect to all of the parameters

Second order parameter-uniform convergence for a finite difference method for a partially singularly perturbed linear parabolic system

A linear system of $n$ second order differential equations of parabolic reaction-diffusion type with initial and boundary conditions is considered. The first $k$ equations are singularly perturbed. Each of the leading terms of the first $m$ equations, $mleq k$, is multiplied by a small positive parameter and these parameters are assumed to be distinct. The leading terms of the next $k-m$ equations are multiplied by the same perturbation parameter $varepsilon_m$. Since the components of the solution exhibit overlapping layers, Shishkin piecewise-uniform meshes are introduced, which are used in conjunction with a classical finite difference discretisation, to construct a numerical method for solving this problem. It is proved that in the maximum norm the numerical approximations obtained with this method are first order convergent in time and essentially second order convergent in the space variable, uniformly with respect to all of the parameters

A parameter uniform fitted mesh method for a weakly coupled system of two singularly perturbed convection-diffusion equations

In this paper, a boundary value problem for a singularly perturbed linear system of two second order ordinary differential equations of convection-diffusion type is considered on the interval [0, 1]. The components of the solution of this system exhibit boundary layers at 0. A numerical method composed of an upwind finite difference scheme applied on a piecewise uniform Shishkin mesh is suggested to solve the problem. The method is proved to be first order convergent in the maximum norm uniformly in the perturbation parameters. Numerical examples are provided in support of the theory

Second order parameter-uniform numerical method for a partially singularly perturbed linear system of reaction-diusion type

A partially singularly perturbed linear system of second order ordinary differential equations of reaction-diffusion type with given boundary conditions is considered. The leading terms of first $m$ equations are multiplied by small positive singular perturbation parameters which are assumed to be distinct. The rest of the equations are not singularly perturbed. The first $m$ components of the solution exhibit overlapping layers and the remaining $n-m$ components have less-severe overlapping layers. Shishkin piecewise-uniform meshes are used in conjunction with a classical finite difference discretisation, to construct a numerical method for solving this problem. It is proved that the numerical approximation obtained by this method is essentially second order convergent uniformly with respect to all the parameters. Numerical illustrations are presented in support of the theory

A parameter uniform almost first order convergent numerical method for non-linear system of singularly perturbed differential equations

In this paper an initial value problem for a non-linear system of two singularly perturbed first order differential equations is considered on the interval (0,1]. The components of the solution of this system exhibit initial layers at 0. A numerical method composed of a classical finite difference scheme on a piecewise uniform Shishkin mesh is suggested. This method is proved to be almost first order convergent in the maximum norm uniformly in the perturbation parameters

Identification of the lipopolysaccharide modifications controlled by the Salmonella PmrA/PmrB system mediating resistance to Fe(III) and Al(III)

Iron is an essential metal but can be toxic in excess. While several homeostatic mechanisms prevent oxygen-dependent killing promoted by Fe(II), little is known about how cells cope with Fe(III), which kills by oxygen-independent means. Several Gram-negative bacterial species harbour a regulatory system – termed PmrA/PmrB – that is activated by and required for resistance to Fe(III). We now report the identification of the PmrA-regulated determinants mediating resistance to Fe(III) and Al(III) in Salmonella enterica serovar Typhimurium. We establish that these determinants remodel two regions of the lipopolysaccharide, decreasing the negative charge of this major constituent of the outer membrane. Remodelling entails the covalent modification of the two phosphates in the lipid A region with phosphoethanolamine and 4-aminoarabinose, which has been previously implicated in resistance to polymyxin B, as well as dephosphorylation of the Hep(II) phosphate in the core region by the PmrG protein. A mutant lacking the PmrA-regulated Fe(III) resistance genes bound more Fe(III) than the wild-type strain and was defective for survival in soil, suggesting that these PmrA-regulated lipopolysaccharide modifications aid Salmonella's survival and spread in non-host environments

Building a refinement checker for Z

In previous work we have described how refinements can be checked using a temporal logic based model-checker, and how we have built a model-checker for Z by providing a translation of Z into the SAL input language. In this paper we draw these two strands of work together and discuss how we have implemented refinement checking in our Z2SAL toolset. The net effect of this work is that the SAL toolset can be used to check refinements between Z specifications supplied as input files written in the LaTeX mark-up. Two examples are used to illustrate the approach and compare it with a manual translation and refinement check.Comment: In Proceedings Refine 2011, arXiv:1106.348

Demonstration of the temporal matter-wave Talbot effect for trapped matter waves

We demonstrate the temporal Talbot effect for trapped matter waves using ultracold atoms in an optical lattice. We investigate the phase evolution of an array of essentially non-interacting matter waves and observe matter-wave collapse and revival in the form of a Talbot interference pattern. By using long expansion times, we image momentum space with sub-recoil resolution, allowing us to observe fractional Talbot fringes up to 10th order.Comment: 17 pages, 7 figure