10,694 research outputs found
Phase noise in pulsed Doppler lidar and limitations on achievable single-shot velocity accuracy
The smaller sampling volumes afforded by Doppler lidars compared to radars allows for spatial resolutions at and below some sheer and turbulence wind structure scale sizes. This has brought new emphasis on achieving the optimum product of wind velocity and range resolutions. Several recent studies have considered the effects of amplitude noise, reduction algorithms, and possible hardware related signal artifacts on obtainable velocity accuracy. We discuss here the limitation on this accuracy resulting from the incoherent nature and finite temporal extent of backscatter from aerosols. For a lidar return from a hard (or slab) target, the phase of the intermediate frequency (IF) signal is random and the total return energy fluctuates from shot to shot due to speckle; however, the offset from the transmitted frequency is determinable with an accuracy subject only to instrumental effects and the signal to noise ratio (SNR), the noise being determined by the LO power in the shot noise limited regime. This is not the case for a return from a media extending over a range on the order of or greater than the spatial extent of the transmitted pulse, such as from atmospheric aerosols. In this case, the phase of the IF signal will exhibit a temporal random walk like behavior. It will be uncorrelated over times greater than the pulse duration as the transmitted pulse samples non-overlapping volumes of scattering centers. Frequency analysis of the IF signal in a window similar to the transmitted pulse envelope will therefore show shot-to-shot frequency deviations on the order of the inverse pulse duration reflecting the random phase rate variations. Like speckle, these deviations arise from the incoherent nature of the scattering process and diminish if the IF signal is averaged over times greater than a single range resolution cell (here the pulse duration). Apart from limiting the high SNR performance of a Doppler lidar, this shot-to-shot variance in velocity estimates has a practical impact on lidar design parameters. In high SNR operation, for example, a lidar's efficiency in obtaining mean wind measurements is determined by its repetition rate and not pulse energy or average power. In addition, this variance puts a practical limit on the shot-to-shot hard target performance required of a lidar
Scalar Field Cosmologies with Viscous Fluid
We investigate cosmological models with a free scalar field and a viscous
fluid. We find exact solutions for a linear and nonlinear viscosity pressure.
Both yield singular and bouncing solutions. In the first regime, a de Sitter
stage is asymptotically stable, while in the second case we find power-law
evolutions for vanishing cosmological constant.Comment: 8 pages, LaTeX. To be published in International Journal of Modern
Physics
Perfect fluid cosmologies with varying light speed
We have found exact constant solutions for the cosmological density parameter
using a generalization of general relativity that incorporates a cosmic
time-variation of the velocity of light in vacuum and the Newtonian gravitation
constant. We have determined the conditions when these solutions are attractors
for an expanding universe and solved the problems of the Standard Big Bang
model for perfect fluids.Comment: 10 pages, LaTeX 2.09. To be published in International Journal of
Modern Physics
Bounds for partial derivatives: necessity of UMD and sharp constants
We prove the necessity of the UMD condition, with a quantitative estimate of
the UMD constant, for any inequality in a family of bounds between
different partial derivatives of . In particular, we show that the estimate
characterizes the UMD property,
and the best constant is equal to one half of the UMD constant. This
precise value of seems to be new even for scalar-valued functions.Comment: v2: corrected typo in the reference
Quantum Geometry as a Relational Construct
The problem of constructing a quantum theory of gravity is considered from a
novel viewpoint. It is argued that any consistent theory of gravity should
incorporate a relational character between the matter constituents of the
theory.
In particular, the traditional approach of quantizing a space-time metric is
criticized and two possible avenues for constructing a satisfactory theory are
put forward.Comment: 14 pages, revtex file. Submitted to MPL
The geodesic flow on nilmanifolds
In this paper we study the geodesic flow on nilmanifolds equipped with a
left-invariant metric. We write the underlying definitions and find general
formulas for the Poisson involution. As an example we develop the Heisenberg
Lie group equipped with its canonical metric. We prove that a family of first
integrals giving the complete integrability can be read off at the Lie algebra
of the isometry group. We also explain the complete integrability on compact
quotients and for any invariant metric.Comment: 24 page
Quantization of the Jackiw-Teitelboim model
We study the phase space structure of the Jackiw-Teitelboim model in its
connection variables formulation where the gauge group of the field theory is
given by local SL(2,R) (or SU(2) for the Euclidean model), i.e. the de Sitter
group in two dimensions. In order to make the connection with two dimensional
gravity explicit, a partial gauge fixing of the de Sitter symmetry can be
introduced that reduces it to spacetime diffeomorphisms. This can be done in
different ways. Having no local physical degrees of freedom, the reduced phase
space of the model is finite dimensional. The simplicity of this gauge field
theory allows for studying different avenues for quantization, which may use
various (partial) gauge fixings. We show that reduction and quantization are
noncommuting operations: the representation of basic variables as operators in
a Hilbert space depend on the order chosen for the latter. Moreover, a
representation that is natural in one case may not even be available in the
other leading to inequivalent quantum theories.Comment: Published version, a short note (not present in the published
version) on the quantization of the null sector has been adde
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