Postbuckling of a Circular Plate - Comparing Different Solutions

Azisymmetric problems have been often investigated in the past. Since the problem is one-dimensional, the boundary problem is suitable for analytical investigations and acts as a benchmark for numerical methods. The postbuckling of an elastic circular plate under azisymmetric loading is investigated. An analytical description is given. Solutions by means of the perturbation method and the finite element method (axisymmetric shell element) are introduced. Numerical results are presented

Remarks on Raasch’s Hook

Finite Element’s designers have always been seeking for benchmarks to judge the capability and potentiality of a numerical method. Considering shell elements many benchmark tests have been established over the years. The Raasch challenge problem, a clamped curved hook with a tip in-plane shear load, acts as a very interesting benchmark of shell elements. The structure consists of two cylindrical shells with different curvatures. In this paper the problem is also modelled as a curved beam with a rectangular cross-section. The beam model is investigated analytically. Thus an analytical expression for the tip deflection can be obtained. Further on numerical calculations with 4-node-shell elements based on a director theory are carried out and verify the elements applicability

Non-global Structure of the O({\alpha}_s^2) Dijet Soft Function

High energy scattering processes involving jets generically involve matrix elements of light- like Wilson lines, known as soft functions. These describe the structure of soft contributions to observables and encode color and kinematic correlations between jets. We compute the dijet soft function to O({\alpha}_s^2) as a function of the two jet invariant masses, focusing on terms not determined by its renormalization group evolution that have a non-separable dependence on these masses. Our results include non-global single and double logarithms, and analytic results for the full set of non-logarithmic contributions as well. Using a recent result for the thrust constant, we present the complete O({\alpha}_s^2) soft function for dijet production in both position and momentum space.Comment: 55 pages, 8 figures. v2: extended discussion of double logs in the hard regime. v3: minor typos corrected, version published in JHEP. v4: typos in Eq. (3.33), (3.39), (3.43) corrected; this does not affect the main result, numerical results, or conclusion

Pattern formation and selection in quasi-static fracture

Fracture in quasi-statically driven systems is studied by means of a discrete spring-block model. Developed from close comparison with desiccation experiments, it describes crack formation induced by friction on a substrate. The model produces cellular, hierarchical patterns of cracks, characterized by a mean fragment size linear in the layer thickness, in agreement with experiments. The selection of a stationary fragment size is explained by exploiting the correlations prior to cracking. A scaling behavior associated with the thickness and substrate coupling, derived and confirmed by simulations, suggests why patterns have similar morphology despite their disparity in scales.Comment: 4 pages, RevTeX, two-column, 5 PS figures include

Pure Samples of Quark and Gluon Jets at the LHC

Having pure samples of quark and gluon jets would greatly facilitate the study of jet properties and substructure, with many potential standard model and new physics applications. To this end, we consider multijet and jets+X samples, to determine the purity that can be achieved by simple kinematic cuts leaving reasonable production cross sections. We find, for example, that at the 7 TeV LHC, the pp {\to} {\gamma}+2jets sample can provide 98% pure quark jets with 200 GeV of transverse momentum and a cross section of 5 pb. To get 10 pb of 200 GeV jets with 90% gluon purity, the pp {\to} 3jets sample can be used. b+2jets is also useful for gluons, but only if the b-tagging is very efficient.Comment: 19 pages, 16 figures; v2 section on formally defining quark and gluon jets has been adde

Vortex line topology during vortex tube reconnection

This paper addresses reconnection of vortex tubes, with particular focus on the topology of the vortex lines (field lines of the vorticity). This analysis of vortex line topology reveals previously undiscovered features of the reconnection process, such as the generation of many small flux rings, formed when reconnection occurs in multiple locations in the vortex sheet between the tubes. Consideration of three-dimensional reconnection principles leads to a robust measurement of the reconnection rate, even once instabilities break the symmetry. It also allows us to identify internal reconnection of vortex lines within the individual vortex tubes. Finally, the introduction of a third vortex tube is shown to render the vortex reconnection process fully three-dimensional, leading to a fundamental change in the topological structure of the process. An additional interesting feature is the generation of vorticity null points.Comment: Accepted for publication in Physical Review Fluid

Stable propagation of an ordered array of cracks during directional drying

We study the appearance and evolution of an array of parallel cracks in a thin slab of material that is directionally dried, and show that the cracks penetrate the material uniformly if the drying front is sufficiently sharp. We also show that cracks have a tendency to become evenly spaced during the penetration. The typical distance between cracks is mainly governed by the typical distance of the pattern at the surface, and it is not modified during the penetration. Our results agree with recent experimental work, and can be extended to three dimensions to describe the properties of columnar polygonal patterns observed in some geological formations.Comment: 8 pages, 4 figures, to appear in PR

Development and geometry of isotropic and directional shrinkage crack patterns

We have studied shrinkage crack patterns which form when a thin layer of an alumina/water slurry dries. Both isotropic and directional drying were studied. The dynamics of the pattern formation process and the geometric properties of the isotropic crack patterns are similar to what is expected from recent models, assuming weak disorder. There is some evidence for a gradual increase in disorder as the drying layer become thinner, but no sudden transition, in contrast to what has been seen in previous experiments. The morphology of the crack patterns is influenced by drying gradients and front propagation effects, with sharp gradients having a strong orienting and ordering effect.Comment: 8 pages, 11 figures, 8 in jpg format, 3 in postscript. See also http://mobydick.physics.utoronto.ca/mud.htm

An update on retinal prostheses

Retinal prostheses are designed to restore a basic sense of sight to people with profound vision loss. They require a relatively intact posterior visual pathway (optic nerve, lateral geniculate nucleus and visual cortex). Retinal implants are options for people with severe stages of retinal degenerative disease such as retinitis pigmentosa and age-related macular degeneration. There have now been three regulatory-approved retinal prostheses. Over five hundred patients have been implanted globally over the past 15 years. Devices generally provide an improved ability to localize high-contrast objects, navigate, and perform basic orientation tasks. Adverse events have included conjunctival erosion, retinal detachment, loss of light perception, and the need for revision surgery, but are rare. There are also specific device risks, including overstimulation (which could cause damage to the retina) or delamination of implanted components, but these are very unlikely. Current challenges include how to improve visual acuity, enlarge the field-of-view, and reduce a complex visual scene to its most salient components through image processing. This review encompasses the work of over 40 individual research groups who have built devices, developed stimulation strategies, or investigated the basic physiology underpinning retinal prostheses. Current technologies are summarized, along with future challenges that face the field