298 research outputs found
Dynamic relaxation oscillations in a nonlinearly driven quartz crystal
We demonstrate thermo-mechanical relaxation oscillations in a strongly driven
quartz crystal. Dynamic bifurcation leads to two stable oscillation states with
a distinct electrical impedance. Slow Joule-heating, which shifts the
susceptibility of the crystal, provides a feedback that leads to
thermally-induced oscillations, in which the amplitude of the crystal is
modulated by a relaxation cycle. The frequency of the relaxation cycle is
roughly a million times lower than the resonance frequency of the crystal, and
it can be adjusted by the detuning from the critical point for dynamic
bifurcation. The experimental observations are reproduced by a simple model
that takes into account the slow dynamics of the system.Comment: Main text: 8 pages, 4 figures. Supplementary information: 4 pages, 3
figure
Local metrics admitting a principal Killing-Yano tensor with torsion
In this paper we initiate a classification of local metrics admitting the
principal Killing--Yano tensor with a skew-symmetric torsion. It is
demonstrated that in such spacetimes rank-2 Killing tensors occur naturally and
mutually commute. We reduce the classification problem to that of solving a set
of partial differential equations, and we present some solutions to these PDEs.
In even dimensions, three types of local metrics are obtained: one of them
naturally generalizes the torsionless case while the others occur only when the
torsion is present. In odd dimensions, we obtain more varieties of local
metrics. The explicit metrics constructed in this paper are not the most
general possible admitting the required symmetry, nevertheless, it is
demonstrated that they cover a wide variety of solutions of various
supergravities, such as the Kerr-Sen black holes of (un-)gauged abelian
heterotic supergravity, the Chong-Cvetic-L\"u-Pope black hole solution of
five-dimensional minimal supergravity, or the K\"ahler with torsion manifolds.
The relation between generalized Killing--Yano tensors and various torsion
Killing spinors is also discussed.Comment: 36pages, no figure
JOINT VENTURE LAW IN THE SOVIET UNION (PRACTICING LAW AND DOING BUSINESS IN THE SOVIET UNION)
And what if gravity is intrinsically quantic ?
Since the early days of search for a quantum theory of gravity the attempts
have been mostly concentrated on the quantization of an otherwise classical
system. The two most contentious candidate theories of gravity, sting theory
and quantum loop gravity are based on a quantum field theory - the latter is a
quantum field theory of connections on a SU(2) group manifold and former a
quantum field theory in two dimensional spaces. Here we argue that there is a
very close relation between quantum mechanics and gravity. Without gravity
quantum mechanics becomes ambiguous. We consider this observation as the
evidence for an intrinsic relation between these fundamental laws of nature. We
suggest a quantum role and definition for gravity in the context of a quantum
universe, and present a preliminary formulation for gravity in a system with a
finite number of particles.Comment: 8 pages, 1 figure. To appear in the proceedings of the DICE2008
conference, Castiglioncello, Tuscany, Italy, 22-26 Sep. 2008. V2: some typos
remove
Hidden symmetry in the presence of fluxes
We derive the most general first order symmetry operator for the Dirac
equation coupled to arbitrary fluxes. Such an operator is given in terms of an
inhomogenous form omega which is a solution to a coupled system of first order
partial differential equations which we call the generalized conformal
Killing-Yano system. Except trivial fluxes, solutions of this system are
subject to additional constraints. We discuss various special cases of physical
interest. In particular, we demonstrate that in the case of a Dirac operator
coupled to the skew symmetric torsion and U(1) field, the system of generalized
conformal Killing-Yano equations decouples into the homogenous conformal
Killing-Yano equations with torsion introduced in [arXiv:0905.0722] and the
symmetry operator is essentially the one derived in [arXiv:1002.3616]. We also
discuss the Dirac field coupled to a scalar potential and in the presence of
5-form and 7-form fluxes.Comment: 13 pages, no figure
A Deformation of Sasakian Structure in the Presence of Torsion and Supergravity Solutions
We discuss a deformation of Sasakian structure in the presence of totally
skew-symmetric torsion by introducing odd dimensional manifolds whose metric
cones are K\"ahler with torsion. It is shown that such a geometry inherits
similar properties to those of Sasakian geometry. As an example of them, we
present an explicit expression of local metrics and see how Sasakian structure
is deformed by the presence of torsion. We also demonstrate that our example of
the metrics admits the existence of hidden symmetries described by non-trivial
odd-rank generalized closed conformal Killing-Yano tensors. Furthermore, using
these metrics as an {\it ansatz}, we construct exact solutions in five
dimensional minimal (un-)gauged supergravity and eleven dimensional
supergravity. Finally, we discuss the global structures of the solutions and
obtain regular metrics on compact manifolds in five dimensions, which give
natural generalizations of Sasaki--Einstein manifolds and
. We also discuss regular metrics on non-compact manifolds in eleven
dimensions.Comment: 38 pages, 1 table, v2: version to appear in Class. Quant. Gra
- …