348 research outputs found
Characterisation of damage mechanisms in oxide ceramics indented at dynamic and quasi-static strain rates
Ceramic materials are known to display rate dependent behaviour under impact. Tests to establish the strain-rate dependent variations in damage mechanisms have been carried out on debased alumina, an alumina-zirconia composite, and 3Y-TZP. Materials were indented dynamically and quasi-statically using identical sharp hardened steel projectiles while recording the load profile. Characteristics typical of both sharp and blunt indentation types were observed using scanning electron microscopy and piezospectroscopic mapping. At dynamic strain rates both the depth of the indentation and the residual stress in the material were lower than for quasi-static tests. This was attributed to temperature-induced softening of the projectile. Unusual behaviour was observed in the 3Y-TZP samples due to the reversible transformation from tetragonal to monoclinic crystal structures during mechanical loading. These effects and the observed superior mechanical strength against impact suggest that zirconia or zirconia-composite materials may have advantages over debased alumina for application as ceramic armour materials
New hyper-Kaehler manifolds by fixing monopoles
The construction of new hyper-Kaehler manifolds by taking the infinite
monopole mass limit of certain Bogomol'nyi-Prasad-Sommerfield monopole moduli
spaces is considered. The one-parameter family of hyperkaehler manifolds due to
Dancer is shown to be an example of such manifolds. A new family of fixed
monopole spaces is constructed. They are the moduli spaces of four SU(4)
monopoles, in the infinite mass limit of two of the monopoles. These manifolds
are shown to be nonsingular when the fixed monopole positions are distinct.Comment: Version in Phys. Rev. D. 11 pp, RevTeX, 14 Postscript diagram
SU(3) monopoles and their fields
Some aspects of the fields of charge two SU(3) monopoles with minimal
symmetry breaking are discussed. A certain class of solutions look like SU(2)
monopoles embedded in SU(3) with a transition region or ``cloud'' surrounding
the monopoles. For large cloud size the relative moduli space metric splits as
a direct product AH\times R^4 where AH is the Atiyah-Hitchin metric for SU(2)
monopoles and R^4 has the flat metric. Thus the cloud is parametrised by R^4
which corresponds to its radius and SO(3) orientation. We solve for the
long-range fields in this region, and examine the energy density and rotational
moments of inertia. The moduli space metric for these monopoles, given by
Dancer, is also expressed in a more explicit form.Comment: 17 pages, 3 figures, latex, version appearing in Phys. Rev.
Stationkeeping of an Lâ Libration Point Satellite with Ξ-D Technique
A new method for L2 libration-point orbit stationkeeping is proposed in this paper using continuous thrust. The circular restricted three-body problem with Sun and Earth as the two primaries is considered. The unstable orbit about the L2 libration-point requires stationkeeping maneuvers to maintain the nominal path. In this study, an approach, called the Ξ-D technique, based on optimal control theory gives a closed-form suboptimal feedback solution to solve this nonlinear control problem. In this approach the Hamiltonian-Jacobi-Bellman (HJB) equation is solved approximately by adding some perturbations to the cost function. The controller is designed such that the actual trajectory tracks a predetermined reference orbit with good accuracy. Numerical results employing this method demonstrate the potential of this method
On the structure of the set of bifurcation points of periodic solutions for multiparameter Hamiltonian systems
This paper deals with periodic solutions of the Hamilton equation with many
parameters. Theorems on global bifurcation of solutions with periods
from a stationary point are proved. The Hessian matrix of the
Hamiltonian at the stationary point can be singular. However, it is assumed
that the local topological degree of the gradient of the Hamiltonian at the
stationary point is nonzero. It is shown that (global) bifurcation points of
solutions with given periods can be identified with zeros of appropriate
continuous functions on the space of parameters. Explicit formulae for such
functions are given in the case when the Hessian matrix of the Hamiltonian at
the stationary point is block-diagonal. Symmetry breaking results concerning
bifurcation of solutions with different minimal periods are obtained. A
geometric description of the set of bifurcation points is given. Examples of
constructive application of the theorems proved to analytical and numerical
investigation and visualization of the set of all bifurcation points in given
domain are provided.
This paper is based on a part of the author's thesis [W. Radzki, ``Branching
points of periodic solutions of autonomous Hamiltonian systems'' (Polish), PhD
thesis, Nicolaus Copernicus University, Faculty of Mathematics and Computer
Science, Toru\'{n}, 2005].Comment: 35 pages, 4 figures, PDFLaTe
Inversion symmetric 3-monopoles and the Atiyah-Hitchin manifold
We consider 3-monopoles symmetric under inversion symmetry. We show that the
moduli space of these monopoles is an Atiyah-Hitchin submanifold of the
3-monopole moduli space. This allows what is known about 2-monopole dynamics to
be translated into results about the dynamics of 3-monopoles. Using a numerical
ADHMN construction we compute the monopole energy density at various points on
two interesting geodesics. The first is a geodesic over the two-dimensional
rounded cone submanifold corresponding to right angle scattering and the second
is a closed geodesic for three orbiting monopoles.Comment: latex, 22 pages, 2 figures. To appear in Nonlinearit
A note on monopole moduli spaces
We discuss the structure of the framed moduli space of Bogomolny monopoles
for arbitrary symmetry breaking and extend the definition of its stratification
to the case of arbitrary compact Lie groups. We show that each stratum is a
union of submanifolds for which we conjecture that the natural metric is
hyperKahler. The dimensions of the strata and of these submanifolds are
calculated, and it is found that for the latter, the dimension is always a
multiple of four.Comment: 17 pages, LaTe
Calibrated Sub-Bundles in Non-Compact Manifolds of Special Holonomy
This paper is a continuation of math.DG/0408005. We first construct special
Lagrangian submanifolds of the Ricci-flat Stenzel metric (of holonomy SU(n)) on
the cotangent bundle of S^n by looking at the conormal bundle of appropriate
submanifolds of S^n. We find that the condition for the conormal bundle to be
special Lagrangian is the same as that discovered by Harvey-Lawson for
submanifolds in R^n in their pioneering paper. We also construct calibrated
submanifolds in complete metrics with special holonomy G_2 and Spin(7)
discovered by Bryant and Salamon on the total spaces of appropriate bundles
over self-dual Einstein four manifolds. The submanifolds are constructed as
certain subbundles over immersed surfaces. We show that this construction
requires the surface to be minimal in the associative and Cayley cases, and to
be (properly oriented) real isotropic in the coassociative case. We also make
some remarks about using these constructions as a possible local model for the
intersection of compact calibrated submanifolds in a compact manifold with
special holonomy.Comment: 20 pages; for Revised Version: Minor cosmetic changes, some
paragraphs rewritten for improved clarit
Scattering of massless and massive monopoles in an SU(N) theory
We use the moduli space approximation to study the time evolution of
magnetically charged configurations in a theory with an SU(N+2) gauge symmetry
spontaneously broken to U(1) x SU(N) x U(1). We focus on configurations
containing two massive and N-1 massless monopoles. The latter do not appear as
distinct objects, but instead coalesce into a cloud of non-Abelian field. We
find that at large times the cloud and the massless particles are decoupled,
with separately conserved energies. The interaction between them occurs through
a scattering process in which the cloud, acting very much like a thin shell,
contracts and eventually bounces off the cores of the massive monopoles. The
strength of the interaction, as measured, e.g., by the amount of energy
transfer, tends to be greatest if the shell is small at the time that it
overlaps the massive cores. We also discuss the corresponding behavior for the
case of the SU(3) multimonopole solutions studied by Dancer.Comment: 32 pages, 7 figure
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