320 research outputs found
Preparation, microstructure and microwave dielectric properties of sprayed PFA/barium titanate composite films
Frequency dependence of the dielectric properties of polymer-ferroelectric composites at different bands of microwave frequencies was investigated in this work. Perfluoroalkoxy (PFA)/barium titanate (BaTiO3) nanocomposite films were prepared by spray deposition. The spraying process was scaled up to fabricate large area (max. 160 mm Ă 160 mm) uniform composite sheets out of which a controlled bonding process was introduced to form composite blocks. The microstructure of the composite films was examined by SEM with a microtome sample preparation method to evaluate the effectiveness of the spraying process at producing uniform particle distributions. The dielectric properties of the composite films with various BaTiO3 loadings were characterised by an Impedance Analyzer at frequencies between 10 Hz and 1 MHz and Vector Network Analyzer at 12â18 GHz respectively. The Lichtenecker mixing rule was incorporated to fit the measured dielectric constant data, which gives estimates of dielectric constant of the BaTiO3 nanometer sized particles to be 895 and 571 at 10 kHz and 15 GHz respectively. In comparison, the composite effective dielectric constant was approximately reduced by 25% at 10 kHz than that at 15 GHz
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.
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
Metrics with Prescribed Ricci Curvature near the Boundary of a Manifold
Suppose is a manifold with boundary. Choose a point . We
investigate the prescribed Ricci curvature equation \Ric(G)=T in a
neighborhood of under natural boundary conditions. The unknown here is
a Riemannian metric. The letter in the right-hand side denotes a
(0,2)-tensor. Our main theorems address the questions of the existence and the
uniqueness of solutions. We explain, among other things, how these theorems may
be used to study rotationally symmetric metrics near the boundary of a solid
torus . The paper concludes with a brief discussion of the Einstein
equation on .Comment: 13 page
A nonlocal eigenvalue problem and the stability of spikes for reaction-diffusion systems with fractional reaction rates
We consider a nonlocal eigenvalue problem which arises in the study of stability of spike solutions for reaction-diffusion systems with
fractional reaction rates such as the Sel'kov model, the
Gray-Scott system, the hypercycle Eigen and Schuster, angiogenesis, and the generalized Gierer-Meinhardt
system.
We give some sufficient and explicit conditions for stability
by studying the corresponding nonlocal eigenvalue problem in a new
range of parameters
Universal spectral parameter-dependent Lax operators for the Drinfeld double of the dihedral group
Two universal spectral parameter-dependent Lax operators are presented in
terms of the elements of the Drinfeld double of the dihedral group
. Applying representations of to these yields matrix solutions of
the Yang-Baxter equation with spectral parameter.Comment: 6 page
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
Multicloud solutions with massless and massive monopoles
Certain spontaneously broken gauge theories contain massless magnetic
monopoles. These are realized classically as clouds of non-Abelian fields
surrounding one or more massive monopoles. In order to gain a better
understanding of these clouds, we study BPS solutions with four massive and six
massless monopoles in an SU(6) gauge theory. We develop an algebraic procedure,
based on the Nahm construction, that relates these solutions to previously
known examples. Explicit implementation of this procedure for a number of
limiting cases reveals that the six massless monopoles condense into four
distinct clouds, of two different types. By analyzing these limiting solutions,
we clarify the correspondence between clouds and massless monopoles, and infer
a set of rules that describe the conditions under which a finite size cloud can
be formed. Finally, we identify the parameters entering the general solution
and describe their physical significance.Comment: 58 pages, 5 figure
On Non-Abelian Symplectic Cutting
We discuss symplectic cutting for Hamiltonian actions of non-Abelian compact
groups. By using a degeneration based on the Vinberg monoid we give, in good
cases, a global quotient description of a surgery construction introduced by
Woodward and Meinrenken, and show it can be interpreted in algebro-geometric
terms. A key ingredient is the `universal cut' of the cotangent bundle of the
group itself, which is identified with a moduli space of framed bundles on
chains of projective lines recently introduced by the authors.Comment: Various edits made, to appear in Transformation Groups. 28 pages, 8
figure
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
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