69,325 research outputs found
Labyrinthine pathways towards supercycle attractors in unimodal maps
We uncover previously unknown properties of the family of periodic
superstable cycles in unimodal maps characterized each by a Lyapunov exponent
that diverges to minus infinity. Amongst the main novel properties are the
following: i) The basins of attraction for the phases of the cycles develop
fractal boundaries of increasing complexity as the period-doubling structure
advances towards the transition to chaos. ii) The fractal boundaries, formed by
the preimages of the repellor, display hierarchical structures organized
according to exponential clusterings that manifest in the dynamics as
sensitivity to the final state and transient chaos. iii) There is a functional
composition renormalization group (RG) fixed-point map associated to the family
of supercycles. iv) This map is given in closed form by the same kind of
-exponential function found for both the pitchfork and tangent bifurcation
attractors. v) There is a final stage ultra-fast dynamics towards the attractor
with a sensitivity to initial conditions that decreases as an exponential of an
exponential of time.Comment: 8 pages, 13 figure
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An Investigation into the Effect of the Shell on SALM Processed Parts
Shell Assisted Layer Manufacturing (SALM) is a novel process for rapid prototyping/
tooling/ manufacture (RP/RT/RM) which is presently undergoing feasibility studies. SALM is
based on layered manufacturing technology (LMT). Initially it develops the shell (boundaries)
of a selected layer using a technique similar to fused deposition modelling (FDM). The
developed shell is filled with a UV curable resin and is exposed to UV radiation for curing.
This procedure is repeated until the complete part is built. This paper compares and contrasts
properties of parts made using two options available with the SALM technique: building the
part using a soluble shell (FDM support structure material, finally dissolved to recover the
part); or using a polymer material such as ABS that is bonded with the resin whilst making
the part.Mechanical Engineerin
Gluon and Ghost Dynamics from Lattice QCD
The two point gluon and ghost correlation functions and the three gluon
vertex are investigated, in the Landau gauge, using lattice simulations. For
the two point functions, we discuss the approach to the continuum limit looking
at the dependence on the lattice spacing and volume. The analytical structure
of the propagators is also investigated by computing the corresponding spectral
functions using an implementation of the Tikhonov regularisation to solve the
integral equation. For the three point function we report results when the
momentum of one of the gluon lines is set to zero and discuss its implications.Comment: Proceedings of Light Cone 2016, held in Lisbon, September 2016. Minor
changes in text. To appear in Few B Sy
A monopole solution from noncommutative multi-instantons
We extend the relation between instanton and monopole solutions of the
selfduality equations in SU(2) gauge theory to noncommutative space-times.
Using this approach and starting from a noncommutative multi-instanton solution
we construct a U(2) monopole configuration which lives in 3 dimensional
ordinary space. This configuration resembles the Wu-Yang monopole and satisfies
the selfduality (Bogomol'nyi) equations for a U(2) Yang-Mills-Higgs system.Comment: 19 pages; title and abstract changed, brane interpretation corrected.
Version to appear in JHE
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