658 research outputs found
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
Jet Shapes and Jet Algorithms in SCET
Jet shapes are weighted sums over the four-momenta of the constituents of a
jet and reveal details of its internal structure, potentially allowing
discrimination of its partonic origin. In this work we make predictions for
quark and gluon jet shape distributions in N-jet final states in e+e-
collisions, defined with a cone or recombination algorithm, where we measure
some jet shape observable on a subset of these jets. Using the framework of
Soft-Collinear Effective Theory, we prove a factorization theorem for jet shape
distributions and demonstrate the consistent renormalization-group running of
the functions in the factorization theorem for any number of measured and
unmeasured jets, any number of quark and gluon jets, and any angular size R of
the jets, as long as R is much smaller than the angular separation between
jets. We calculate the jet and soft functions for angularity jet shapes \tau_a
to one-loop order (O(alpha_s)) and resum a subset of the large logarithms of
\tau_a needed for next-to-leading logarithmic (NLL) accuracy for both cone and
kT-type jets. We compare our predictions for the resummed \tau_a distribution
of a quark or a gluon jet produced in a 3-jet final state in e+e- annihilation
to the output of a Monte Carlo event generator and find that the dependence on
a and R is very similar.Comment: 62 pages plus 21 pages of Appendices, 13 figures, uses JHEP3.cls. v2:
corrections to finite parts of NLO jet functions, minor changes to plots,
clarified discussion of power corrections. v3: Journal version. Introductory
sections significantly reorganized for clarity, classification of logarithmic
accuracy clarified, results for non-Mercedes-Benz configurations adde
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
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