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 L₂ Libration Point Satellite with θ-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 θ-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 $2\pi/j,$ $j\in\mathbb{N},$ 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 $L^2$ 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