Confinement induced instability of thin elastic film

A confined incompressible elastic film does not deform uniformly when subjected to adhesive interfacial stresses but with undulations which have a characteristic wavelength scaling linearly with the thickness of the film. In the classical peel geometry, undulations appear along the contact line below a critical film thickness or below a critical curvature of the plate. Perturbation analysis of the stress equilibrium equations shows that for a critically confined film the total excess energy indeed attains a minima for a finite amplitude of the perturbations which grow with further increase in the confinement.Comment: 11 pages, 6 figure

Long-term variations of turbulent transport coefficients in a solar-like convective dynamo simulation

The Sun, aside from its eleven year sunspot cycle is additionally subject to long term variation in its activity. In this work we analyse a solar-like convective dynamo simulation, containing approximately 60 magnetic cycles, exhibiting equatorward propagation of the magnetic field, multiple frequencies, and irregular variability, including a missed cycle and complex parity transitions between dipolar and quadrupolar modes. We compute the turbulent transport coefficients, describing the effects of the turbulent velocity field on the mean magnetic field, using the test-field method. The test-field analysis provides a plausible explanation of the missing cycle in terms of the reduction of $\alpha_{\phi\phi}$ in advance of the reduced surface activity, and enhanced downward turbulent pumping during the event to confine some of the magnetic field at the bottom of the convection zone, where local maximum of magnetic energy is observed during the event. At the same time, however, a quenching of the turbulent magnetic diffusivities is observed, albeit differently distributed in depth compared to the other transport coefficients. Therefore, dedicated mean-field modelling is required for verification.Comment: 11 pages, 12 figures, accepted by AN for 14th Potsdam Thinksho

The supernova-regulated ISM. II. The mean magnetic field

The origin and structure of the magnetic fields in the interstellar medium of spiral galaxies is investigated with 3D, non-ideal, compressible MHD simulations, including stratification in the galactic gravity field, differential rotation and radiative cooling. A rectangular domain, 1x1x2 kpc^{3} in size, spans both sides of the galactic mid-plane. Supernova explosions drive transonic turbulence. A seed magnetic field grows exponentially to reach a statistically steady state within 1.6 Gyr. Following Germano (1992) we use volume averaging with a Gaussian kernel to separate magnetic field into a mean field and fluctuations. Such averaging does not satisfy all Reynolds rules, yet allows a formulation of mean-field theory. The mean field thus obtained varies in both space and time. Growth rates differ for the mean-field and fluctuating field and there is clear scale separation between the two elements, whose integral scales are about 0.7 kpc and 0.3 kpc, respectively.Comment: 5 pages, 10 figures, submitted to Monthly Notices Letter

Assessing riveted connections to Eurocode 3

The focus of this paper is the assessment of wrought iron and early steel riveted connections in the future, with recommendations as to how different codes currently deal with the assessment and what may change if alternative codes are adopted. As British standards are being replaced by Eurocodes for design, it is inevitable that assessment codes of practice based on British standards will be replaced by those based on Eurocodes. This progression will ensure that future structures are designed and assessed using codes based on similar philosophies. However, this will also lead to older structures designed according to older codes based on different philosophies and constructed of materials not covered by the Eurocodes also being assessed according to Eurocode-based assessment codes. A similar situation already exists with structures being assessed using British standard-based assessment codes, which were written for the design of steel structures. This has resulted in the leading asset-owning organisations, such as Network Rail and Highways England, including guidance on adapting calculations to account for different material types

The supernova-regulated ISM. I. The multi-phase structure

We simulate the multi-phase interstellar medium randomly heated and stirred by supernovae, with gravity, differential rotation and other parameters of the solar neighbourhood. Here we describe in detail both numerical and physical aspects of the model, including injection of thermal and kinetic energy by SN explosions, radiative cooling, photoelectric heating and various transport processes. With 3D domain extending 1 kpc^2 horizontally and 2 kpc vertically, the model routinely spans gas number densities 10^-5 - 10^2 cm^-3, temperatures 10-10^8 K, local velocities up to 10^3 km s^-1 (with Mach number up to 25). The thermal structure of the modelled ISM is classified by inspection of the joint probability density of the gas number density and temperature. We confirm that most of the complexity can be captured in terms of just three phases, separated by temperature borderlines at about 10^3 K and 5x10^5 K. The probability distribution of gas density within each phase is approximately lognormal. We clarify the connection between the fractional volume of a phase and its various proxies, and derive an exact relation between the fractional volume and the filling factors defined in terms of the volume and probabilistic averages. These results are discussed in both observational and computational contexts. The correlation scale of the random flows is calculated from the velocity autocorrelation function; it is of order 100 pc and tends to grow with distance from the mid-plane. We use two distinct parameterizations of radiative cooling to show that the multi-phase structure of the gas is robust, as it does not depend significantly on this choice.Comment: 28 pages, 22 figures and 8 table

Unfolding the Sulcus

Sulci are localized furrows on the surface of soft materials that form by a compression-induced instability. We unfold this instability by breaking its natural scale and translation invariance, and compute a limiting bifurcation diagram for sulcfication showing that it is a scale-free, sub-critical {\em nonlinear} instability. In contrast with classical nucleation, sulcification is {\em continuous}, occurs in purely elastic continua and is structurally stable in the limit of vanishing surface energy. During loading, a sulcus nucleates at a point with an upper critical strain and an essential singularity in the linearized spectrum. On unloading, it quasi-statically shrinks to a point with a lower critical strain, explained by breaking of scale symmetry. At intermediate strains the system is linearly stable but nonlinearly unstable with {\em no} energy barrier. Simple experiments confirm the existence of these two critical strains.Comment: Main text with supporting appendix. Revised to agree with published version. New result in the Supplementary Informatio

Solution of a Model for the Oceanic Pycnocline Depth: Scaling of Overturning Strength and Meridional Pressure Difference

We present an analysis of the model by Gnanadesikan [1999] for the pycnocline depth in the ocean. An analytic solution for the overturning strength as a function of the meridional pressure difference is derived and used to discuss their mutual scaling. We show that scaling occurs only in two unphysical regimes of the model. In the absence of the Southern Ocean (SO) processes, i.e. for a northern overturning cell, the volume transport is proportional to the square root of the pressure difference. Linear scaling is seen when the overturning is restricted entirely to the SO, i.e. when no northern downwelling exists. For comparison, we present simulations with the coupled climate model CLIMBER-3$\alpha$ which show linear scaling over a large regime of pressure differences in the North Atlantic (NA). We conclude that the pycnocline model is not able to reproduce the linear scaling between its two central variables, pressure and volume transport.Comment: Geophysical Research Letters (2004), accepted. See also http://www.pik-potsdam.de/~ander

State of stress across UK regions

Knowledge of the in- situ stress field is a key constraint for a variety of sub surface activities and crucial for the safe and sustainable use of the sub surface. However is a lack of available stress magnitude data across the UK. This report assesses legacy stress magnitude data along with new analysis to characterise the UK onshore stress field. To investigate the UK onshore in-situ stress field, three regions were studied. The regions were selected based on the potential availability of information to characterise the stress field and their resource potential for unconventional shale resources, highlighted by Andrews et al. (2013). The study focused on: East Yorkshire and North Nottinghamshire, Cheshire and Lancashire and the Weald. The vertical stress across the UK varies between 23 and 26 MPakm-1 with higher values recorded in Cheshire and Scotland compared to East Yorkshire, North Nottinghamshire and the Weald. Pore pressure measurements from Cheshire, Lancashire, East Yorkshire and North Nottinghamshire are hydrostatic with a gradient of 10.19 MPakm-1. Leak off test and formation integrity test data has been used to estimate the gradient of minimum horizontal stress in Cheshire, Lancashire East Yorkshire and North Nottinghamshire. This estimates show that the minimum horizontal stress gradient is two MPakm-1 higher in Cheshire and Lancashire than East Yorkshire and North Nottinghamshire, which is similar to the differences in vertical stress gradients. Legacy maximum horizontal stress data has been compiled from a variety of techniques from the Coal Authority and peer review publications. This data shows that the maximum horizontal stress > vertical stress, When combined with the leak off test and formation integrity test data (which shows vertical stress > minimum horizontal stress) this indicates that the UK is predominately a strike slip faulting environment. Above 1200 m there are indications of reverse faulting though these are largely confined to igneous rocks in Cornwall, Leicestershire and Cumbria. The available information shows that there are similarities in the stress field across the UK though due to the geographic and stratigraphic constraints on the data more information would help to better characterise the stress field