707 research outputs found
The York map as a Shanmugadhasan canonical transformation in tetrad gravity and the role of non-inertial frames in the geometrical view of the gravitational field
A new parametrization of the 3-metric allows to find explicitly a York map in
canonical ADM tetrad gravity, the two pairs of physical tidal degrees of
freedom and 14 gauge variables. These gauge quantities (generalized inertial
effects) are all configurational except the trace of
the extrinsic curvature of the instantaneous 3-spaces (clock
synchronization convention) of a non-inertial frame. The Dirac hamiltonian is
the sum of the weak ADM energy (whose density is coordinate-dependent due to the inertial
potentials) and of the first-class constraints. Then: i) The explicit form of
the Hamilton equations for the two tidal degrees of freedom in an arbitrary
gauge: a deterministic evolution can be defined only in a completely fixed
gauge, i.e. in a non-inertial frame with its pattern of inertial forces. ii) A
general solution of the super-momentum constraints, which shows the existence
of a generalized Gribov ambiguity associated to the 3-diffeomorphism gauge
group. It influences: a) the explicit form of the weak ADM energy and of the
super-momentum constraint; b) the determination of the shift functions and then
of the lapse one. iii) The dependence of the Hamilton equations for the two
pairs of dynamical gravitational degrees of freedom (the generalized tidal
effects) and for the matter, written in a completely fixed 3-orthogonal
Schwinger time gauge, upon the gauge variable ,
determining the convention of clock synchronization. Therefore it should be
possible (for instance in the weak field limit but with relativistic motion) to
try to check whether in Einstein's theory the {\it dark matter} is a gauge
relativistic inertial effect induced by .Comment: 90 page
Structured matrices, continued fractions, and root localization of polynomials
We give a detailed account of various connections between several classes of
objects: Hankel, Hurwitz, Toeplitz, Vandermonde and other structured matrices,
Stietjes and Jacobi-type continued fractions, Cauchy indices, moment problems,
total positivity, and root localization of univariate polynomials. Along with a
survey of many classical facts, we provide a number of new results.Comment: 79 pages; new material added to the Introductio
Stratification of the orbit space in gauge theories. The role of nongeneric strata
Gauge theory is a theory with constraints and, for that reason, the space of
physical states is not a manifold but a stratified space (orbifold) with
singularities. The classification of strata for smooth (and generalized)
connections is reviewed as well as the formulation of the physical space as the
zero set of a momentum map. Several important features of nongeneric strata are
discussed and new results are presented suggesting an important role for these
strata as concentrators of the measure in ground state functionals and as a
source of multiple structures in low-lying excitations.Comment: 22 pages Latex, 1 figur
Fabrication and characterization of thin, selfâsupporting germanium single crystals
Thin Gesingle crystals (â€1 ÎŒm) up to 4 mm in diameter have been fabricated from epitaxialGefilmsgrown by atmospheric pressurechemical vapor deposition on Si(100) wafers. The thin Ge windows are formed by chemically etching away both the Si substrate and the region of the Gefilm near the interface that contains misfit dislocations associated with heteroepitaxialgrowth and relaxation of the Gefilms. The resulting Gefilms are comparable in crystalline quality to bulk Ge wafers, as indicated by ion channeling studies
Modeling Kelvin wave cascades in superfluid helium
We study two different types of simplified models for Kelvin wave turbulence on quantized vortex lines in superfluids near zero temperature. Our first model is obtained from a truncated expansion of the Local Induction Approximation (Truncated-LIA) and it is shown to possess the same scalings and the essential behaviour as the full Biot-Savart model, being much simpler than the later and, therefore, more amenable to theoretical and numerical investigations. The Truncated-LIA model supports six-wave interactions and dual cascades, which are clearly demonstrated via the direct numerical simulation of this model in the present paper. In particular, our simulations confirm presence of the weak turbulence regime and the theoretically predicted spectra for the direct energy cascade and the inverse wave action cascade. The second type of model we study, the Differential Approximation Model (DAM), takes a further drastic simplification by assuming locality of interactions in k-space via using a differential closure that preserves the main scalings of the Kelvin wave dynamics. DAMs are even more amenable to study and they form a useful tool by providing simple analytical solutions in the cases when extra physical effects are present, e.g. forcing by reconnections, friction dissipation and phonon radiation. We study these models numerically and test their theoretical predictions, in particular the formation of the stationary spectra, and closeness of numerics for the higher-order DAM to the analytical predictions for the lower-order DAM
Energetics and Possible Formation and Decay Mechanisms of Vortices in Helium Nanodroplets
The energy and angular momentum of both straight and curved vortex states of
a helium nanodroplet are examined as a function of droplet size. For droplets
in the size range of many experiments, it is found that during the pickup of
heavy solutes, a significant fraction of events deposit sufficient energy and
angular momentum to form a straight vortex line. Curved vortex lines exist down
to nearly zero angular momentum and energy, and thus could in principle form in
almost any collision. Further, the coalescence of smaller droplets during the
cooling by expansion could also deposit sufficient angular momentum to form
vortex lines. Despite their high energy, most vortices are predicted to be
stable at the final temperature (0.38 K) of helium nanodroplets due to lack of
decay channels that conserve both energy and angular momentum.Comment: 10 pages, 8 figures, RevTex 4, submitted to Phys. Rev.
The sensitivity of the vortex filament method to different reconnection models
We present a detailed analysis on the effect of using different algorithms to
model the reconnection of vortices in quantum turbulence, using the
thin-filament approach. We examine differences between four main algorithms for
the case of turbulence driven by a counterflow. In calculating the velocity
field we use both the local induction approximation (LIA) and the full
Biot-Savart integral. We show that results of Biot-Savart simulations are not
sensitive to the particular reconnection method used, but LIA results are.Comment: 9 pages, 9 figure
Dirac's Observables for the Rest-Frame Instant Form of Tetrad Gravity in a Completely Fixed 3-Orthogonal Gauge
We define the {\it rest-frame instant form} of tetrad gravity restricted to
Christodoulou-Klainermann spacetimes. After a study of the Hamiltonian group of
gauge transformations generated by the 14 first class constraints of the
theory, we define and solve the multitemporal equations associated with the
rotation and space diffeomorphism constraints, finding how the cotriads and
their momenta depend on the corresponding gauge variables. This allows to find
quasi-Shanmugadhasan canonical transformation to the class of 3-orthogonal
gauges and to find the Dirac observables for superspace in these gauges.
The construction of the explicit form of the transformation and of the
solution of the rotation and supermomentum constraints is reduced to solve a
system of elliptic linear and quasi-linear partial differential equations. We
then show that the superhamiltonian constraint becomes the Lichnerowicz
equation for the conformal factor of the 3-metric and that the last gauge
variable is the momentum conjugated to the conformal factor. The gauge
transformations generated by the superhamiltonian constraint perform the
transitions among the allowed foliations of spacetime, so that the theory is
independent from its 3+1 splittings. In the special 3-orthogonal gauge defined
by the vanishing of the conformal factor momentum we determine the final Dirac
observables for the gravitational field even if we are not able to solve the
Lichnerowicz equation. The final Hamiltonian is the weak ADM energy restricted
to this completely fixed gauge.Comment: RevTeX file, 141 page
Tree method for quantum vortex dynamics
We present a numerical method to compute the evolution of vortex filaments in
superfluid helium. The method is based on a tree algorithm which considerably
speeds up the calculation of Biot-Savart integrals. We show that the
computational cost scales as Nlog{(N) rather than N squared, where is the
number of discretization points. We test the method and its properties for a
variety of vortex configurations, ranging from simple vortex rings to a
counterflow vortex tangle, and compare results against the Local Induction
Approximation and the exact Biot-Savart law.Comment: 12 pages, 10 figure
- âŠ