Global error analysis and inertial manifold reduction

Four types of global error for initial value problems are considered in a common framework. They include classical forward error analysis and shadowing error analysis together with extensions of both to include rescaling of time. To determine the amplificatioh of the local error that bounds the global error we present a linear analysis similar in spirit to condition number estimation for linear systems of equations. We combine these ideas with techniques for dimension reduction of differential equations via a boundary value formulation of numerical inertial manifold reduction. These global error concepts are exercised to illustrate their utility on the Lorenz equations and inertial manifold reductions of the Kuramoto-Sivashinsky equation. (C) 2016 Elsevier B.V. All rights reserved

Gains and losses of coral skeletal porosity changes with ocean acidification acclimation

Ocean acidi\ufb01cation is predicted to impact ecosystems reliant on calcifying organisms, potentially reducing the socioeconomic bene\ufb01ts these habitats provide. Here we investigate the acclimation potential of stony corals living along a pH gradient caused by a Mediterranean CO2 vent that serves as a natural long-term experimental setting. We show that in response to reduced skeletal mineralization at lower pH, corals increase their skeletal macroporosity (features >10 micrometers) in order to maintain constant linear extension rate, an important criterion for reproductive output. At the nanoscale, the coral skeleton\u2019s structural features are not altered. However, higher skeletal porosity, and reduced bulk density and stiffness may contribute to reduce population density and increase damage susceptibility under low pH conditions. Based on these observations, the almost universally employed measure of coral biomineralization, the rate of linear extension, might not be a reliable metric for assessing coral health and resilience in a warming and acidifying ocean

Application of an Electric Impulse Technology tool for removing concrete or mineral surfaces and cutting concrete within existing structures

With the help of the Electric Impulse Technology, it is possible to remove concrete or mineral surfaces in existing building structures with low vibrations and emissions and to make openings by slotting and cutting. Very fast high-voltage impulses are generated and led to an electrode arrangement positioned on the material to be destroyed. A breakdown is generated in the material and thus the material is destroyed. On this basis, investigations into the removal of concrete as well as mineral structures are carried out and a machine concept for the use of the Electric Impulse Technology for operations in existing buildings is developed