A note on the 1-prevalence of continuous images with full Hausdorff dimension

We consider the Banach space consisting of real-valued continuous functions on an arbitrary compact metric space. It is known that for a prevalent (in the sense of Hunt, Sauer and Yorke) set of functions the Hausdorff dimension of the image is as large as possible, namely 1. We extend this result by showing that `prevalent' can be replaced by `1-prevalent', i.e. it is possible to \emph{witness} this prevalence using a measure supported on a one dimensional subspace. Such one dimensional measures are called \emph{probes} and their existence indicates that the structure and nature of the prevalence is simpler than if a more complicated `infinite dimensional' witnessing measure has to be used.Comment: 8 page

The Hausdorff dimension of graphs of prevalent continuous functions

We prove that the Hausdorff dimension of the graph of a prevalent continuous function is 2. We also indicate how our results can be extended to the space of continuous functions on $[0,1]^d$ for $d \in \mathbb{N}$ and use this to obtain results on the `horizon problem' for fractal surfaces. We begin with a survey of previous results on the dimension of a generic continuous function

Structural Phases of Bounded Three-Dimensional Screened Coulomb Clusters (Finite Yukawa System)

The formation of three-dimensional (3D) dust clusters within a complex plasma modeled as a spatially confined Yukawa system is simulated using the box_tree code. Similar to unscreened Coulomb clusters, the occurrence of concentric shells with characteristic occupation numbers was observed. Both the occupation numbers and radii were found to depend on the Debye length. Ground and low energy meta-stable states of the shielded 3D Coulomb clusters were determined for 4<N<20. The structure and energy of the clusters in different states was analyzed for various Debye lengths. Structural phase transitions, including inter-shell structural phase transitions and intra-shell structural phase transitions, were observed for varying Debye length and the critical value for transitions calculated

Structural transitions of monoolein bicontinuous cubic phase induced by inclusion of protein lysozyme solutions

Inclusion of protein lysozyme molecules in lipidic monoolein cubic phase induces a transition from a $\rm Pn\bar{3}m$ structure to $\rm Im\bar{3}m$ one. Small-angle X-ray scattering (SAXS) method with high intensity synchrotron radiation enabled us to follow closely the transition depending on the conditions of lysozyme solutions. We showed that concentrated lysozyme solutions induced the appearance of the $\rm Im\bar{3}m$ structure coexisting with the $\rm Pn\bar{3}m$ structure. From the relation between the lattice parameters of these two structures it was shown that they were related by the Bonnet transformation of underlying triply periodic minimal surfaces. We found that the transition also occurred at lower lysozyme concentration when NaCl induced attraction between lysozyme molecules. The origin of the transition was considered as a frustration in the cubic phase where lysozyme molecules were highly confined. A simple estimation of the frustration was given, which took into account of the translational entropy of lysozyme molecules. At the highest concentration of lysozyme and NaCl the $\rm Im\bar{3}m$ structure was found to disappear and left only the $\rm Pn\bar{3}m$ structure. This was probably either due to the crystallization or phase separation of lysozyme solutions ongoing microscopically, which absorbed lysozyme molecules from channels of the cubic phase and thus removed the frustration.Comment: 8 pages, 5 figure

On the interpretation of results from small punch creep tests

The small punch creep testing method is highly complex and involves interactions between a number of non-linear processes. The deformed shapes that are produced from such tests are related to the punch and specimen dimensions and to the elastic, plastic, and creep behaviour of the test material, under contact and large deformation conditions, at elevated temperature. Owing to its complex nature, it is difficult to interpret the small punch test creep data in relation to the corresponding uniaxial creep behaviour of the material. One of the aims of this paper is to identify the important characteristics of the creep deformation resulting from ‘localized’ deformations and from the ‘overall’ deformation of the specimen. Following this, the results of approximate analytical and detailed finite element analyses of small punch tests are investigated. It is shown that the regions of the uniaxial creep test curves dominated by primary, secondary, and tertiary creep are not those that are immediately apparent from the displacement versus time records produced during a small punch test. On the basis of the interpretation of the finite element results presented, a method based on a reference stress approach is proposed for interpreting the results of small punch test experimental data. Future work planned for the interpretation of small punch tests data is briefly addressed

Nitrous Oxide Emissions

End of project reportNitrous oxide (N2O) is one of the three most important greenhouse gases (GHG). Nitrous oxide emissions currently account for approximately one third of GHG emissions from agriculture in Ireland. Emissions of N2O arise naturally from soil sources and from the application of nitrogen (N) in the form of N fertilizers and N in dung and urine deposition by grazing animals at pasture. Nitrous oxide emission measurements were conducted at three different scales. Firstly, a large-scale field experiment was undertaken to compare emission rates from a pasture receiving three different rates of N fertilizer application and to identify the effects of controlling variables over a two-year period. Variation in emission rates was large both within and between years. Two contrasting climatic years were identified. The cooler and wetter conditions in year 1 gave rise to considerably lower emission levels than the warmer and drier year 2. However, in both years, peak emissions were associated with fertilizer N applications coincident with rainfall events in the summer months. A small-plot study was conducted to identify the individual and combined effects of fertilizer, dung and urine applications to grassland. Treatment effects were however, difficult to obtain due to the overriding effects of environmental variables. Thirdly, through the use of a small-scale mini-lysimeter study, the diurnal nature of N2O emission rates was identified for two distinct periods during the year. The occurrence of a diurnal pattern has important implications for the identification of a measurement period during the day which is representative of the true daily flux. The research presented aims to identify the nature and magnitude of N2O emissions and the factors which affect emission rates from a grassland in Ireland. Further work is required to integrate the effects of different soil types and contrasting climatic regimes across soil types on N2O emissions.Environmental Protection Agenc

Cyclic thermomechanical testing of 316 stainless steel

Materials used for components such as power plant steam pipes, gas turbines discs and die forming machinery can be subject to combinations of extreme loading and temperature conditions. In addition, the materials can contain or develop cracks. Once a crack has initiated, the conditions under which the components operate can cause these cracks to propagate. This paper is concerned with the experimental testing of 316 stainless steel, corner cracked samples under thermomechanical fatigue conditions, and the measurement of the crack propagation during testing using alternating current potential difference readings. Fracture mechanics (Paris Law) methods have been used in the processing of the experimental data

Detection of human influence on a new, validated 1500-Year temperature reconstruction

Climate records over the last millennium place the twentieth-century warming in a longer historical context. Reconstructions of millennial temperatures show a wide range of variability, raising questions about the reliability of currently available reconstruction techniques and the uniqueness of late-twentieth-century warming. A calibration method is suggested that avoids the loss of low-frequency variance. A new reconstruction using this method shows substantial variability over the last 1500 yr. This record is consistent with independent temperature change estimates from borehole geothermal records, compared over the same spatial and temporal domain. The record is also broadly consistent with other recent reconstructions that attempt to fully recover low-frequency climate variability in their central estimate. High variability in reconstructions does not hamper the detection of greenhouse gas-induced climate change, since a substantial fraction of the variance in these reconstructions from the beginning of the analysis in the late thirteenth century to the end of the records can be attributed to external forcing. Results from a detection and attribution analysis show that greenhouse warming is detectable in all analyzed high-variance reconstructions (with the possible exception of one ending in 1925), and that about a third of the warming in the first half of the twentieth century can be attributed to anthropogenic greenhouse gas emissions. The estimated magnitude of the anthropogenic signal is consistent with most of the warming in the second half of the twentieth century being anthropogenic

Experimental investigation of the mechanical stiffness of periodic framework-patterned elastomers

Recent advances in the cataloguing of three-dimensional nets mean a systematic search for framework structures with specific properties is now feasible. Theoretical arguments about the elastic deformation of frameworks suggest characteristics of mechanically isotropic networks. We explore these concepts on both isotropic and anisotropic networks by manufacturing porous elastomers with three different periodic net geometries. The blocks of patterned elastomers are subjected to a range of mechanical tests to determine the dependence of elastic moduli on geometric and topological parameters. We report results from axial compression experiments, three-dimensional X-ray computed tomography imaging and image-based finite-element simulations of elastic properties of framework-patterned elastomers