6,735 research outputs found
Monopoles from Rational Maps
The moduli space of charge k SU(2) BPS monopoles is diffeomorphic to the
moduli space of degree k rational maps between Riemann spheres. In this note we
describe a numerical algorithm to compute the monopole fields and energy
density from the rational map. The results for some symmetric examples are
presented.Comment: 8 pages, 2 figures. To appear in Phys. Lett.
Instanton Moduli and Topological Soliton Dynamics
It has been proposed by Atiyah and Manton that the dynamics of Skyrmions may
be approximated by motion on a finite dimensional manifold obtained from the
moduli space of SU(2) Yang-Mills instantons. Motivated by this work we describe
how similar results exist for other soliton and instanton systems. We describe
in detail two examples for the approximation of the infinite dimensional
dynamics of sine-Gordon solitons by finite dimensional dynamics on a manifold
obtained from instanton moduli. In the first example we use the moduli space of
CP1 instantons and in the second example we use the moduli space of SU(2)
Yang-Mills instantons. The metric and potential functions on these manifolds
are constructed and the resulting dynamics is compared with the explicit exact
soliton solutions of the sine-Gordon theory.Comment: uuencoded tex file, 27 pages including 4 figures, requires phyzzx
macro. DAMTP 94-5
Non-Bogomolny SU(N) BPS Monopoles
For N>2 we present static monopole solutions of the second order SU(N) BPS
Yang-Mills-Higgs equations which are not solutions of the first order Bogomolny
equations. These spherically symmetric solutions may be interpreted as monopole
anti-monopole configurations and their construction involves harmonic maps into
complex projective spaces.Comment: 14 pages, 1 figur
Kink Chains from Instantons on a Torus
We describe how the procedure of calculating approximate solitons from
instanton holonomies may be extended to the case of soliton crystals. It is
shown how sine-Gordon kink chains may be obtained from CP1 instantons on a
torus. These kink chains turn out to be remarkably accurate approximations to
the true solutions. Some remarks on the relevance of this work to Skyrme
crystals are also made.Comment: latex 17 pages, DAMTP 94-7
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Image Transformations and Printing of Plaster Layers in Spiral Growth Manufacturing
Spiral growth manufacturing (SGM) is a high speed rapid manufacturing technique in
which objects are built up, layer by layer, by simultaneously depositing, levelling and selectively
consolidating thin powder layers onto a rotating build platform. The size and position of the
jetted droplets are mapped by the position and greyscale level of pixels within an 8 bit greyscale
bitmap image. This paper reports on the development of software in which mathematical
algorithms apply geometric transformations to images in preparation for printing onto a rotating
substrate. In support of this work, dimensional accuracy measurements of printed images and
methods to correct radial print density variations are reported. The accuracy of printed images
were found to be within ±0.2mm of their predicted size. The experimental work is briefly
extended to the direct printing of plaster layers, formed by mixing two reactive ink solutions.Mechanical Engineerin
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Spiral Growth Manufacturing (SGM) – A Continuous Additive Manufacturing Technology for Processing Metal Powder by Selective Laser Melting
Spiral growth manufacturing is a new innovative powder based rapid manufacturing
technique. The innovation exists in the methodology in which powder layers are deposited.
Unlike other pre-placed powder systems, the deposited layers move relative to the location at
which they are processed. This is made possible by a rotating build drum into which powder is
deposited, in spiralled layers, from a stationary hopper. With this configuration powder can be
continuously deposited and levelled and simultaneously processed, eliminating delays in the
build cycle. Stainless steel and cobalt-chrome powder is selectively melted using a 100W flash
lamp pumped Nd:YAG laser. This paper reports on factors affecting build rate and on build
strategies for creating a number of axis-symmetric thin and thick walled cylinders. Experimental
results suggest that build rate for thin walled structures bonded to a substrate will ultimately be
governed by tangential movements of the powder particles when frictional forces are not
sufficient to accelerate the particles along a curved path, provided that enough laser power is
available for melting. Even melt pool balling, which is evident when melting one layer at high
speeds, diminishes in multiple layer builds due to re-melting and infilling.Mechanical Engineerin
Solitons, Links and Knots
Using numerical simulations of the full nonlinear equations of motion we
investigate topological solitons of a modified O(3) sigma model in three space
dimensions, in which the solitons are stabilized by the Hopf charge. We find
that for solitons up to charge five the solutions have the structure of closed
strings, which become increasingly twisted as the charge increases. However,
for higher charge the solutions are more exotic and comprise linked loops and
knots. We discuss the structure and formation of these solitons and demonstrate
that the key property responsible for producing such a rich variety of solitons
is that of string reconnection.Comment: 24 pages plus 14 figures in GIF forma
Automated Reasoning and Presentation Support for Formalizing Mathematics in Mizar
This paper presents a combination of several automated reasoning and proof
presentation tools with the Mizar system for formalization of mathematics. The
combination forms an online service called MizAR, similar to the SystemOnTPTP
service for first-order automated reasoning. The main differences to
SystemOnTPTP are the use of the Mizar language that is oriented towards human
mathematicians (rather than the pure first-order logic used in SystemOnTPTP),
and setting the service in the context of the large Mizar Mathematical Library
of previous theorems,definitions, and proofs (rather than the isolated problems
that are solved in SystemOnTPTP). These differences poses new challenges and
new opportunities for automated reasoning and for proof presentation tools.
This paper describes the overall structure of MizAR, and presents the automated
reasoning systems and proof presentation tools that are combined to make MizAR
a useful mathematical service.Comment: To appear in 10th International Conference on. Artificial
Intelligence and Symbolic Computation AISC 201
Multi-soliton dynamics in the Skyrme model
We exhibit the dynamical scattering of multi-solitons in the Skyrme model for
configurations with charge two, three and four. First, we construct maximally
attractive configurations from a simple profile function and the product
ansatz. Then using a sophisticated numerical algorithm, initially
well-separated skyrmions in approximately symmetric configurations are shown to
scatter through the known minimum energy configurations. These scattering
events illustrate a number of similarities to BPS monopole configurations of
the same charge. A simple modification of the dynamics to a dissipative regime,
allows us to compute the minimal energy skyrmions for baryon numbers one to
four to within a few percent.Comment: latex, 10 pages, plus 5 figures (as gif files
The moduli space metric for tetrahedrally symmetric 4-monopoles
The metric on the moduli space of SU(2) charge four BPS monopoles with tetrahedral symmetry is calculated using numerical methods. In the asymptotic region, in which the four monopoles are located on the vertices of a large tetrahedron, the metric is in excellent agreement with the point particle metric. We find that the four monopoles are accelerated through the cubic monopole configuration and compute the time advance. Numerical evidence is presented for a remarkable equivalence between a proper distance in the 4-monopole moduli space and a related proper distance in the point particle moduli space
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