177 research outputs found
The Puzzle of the Flyby Anomaly
Close planetary flybys are frequently employed as a technique to place
spacecraft on extreme solar system trajectories that would otherwise require
much larger booster vehicles or may not even be feasible when relying solely on
chemical propulsion. The theoretical description of the flybys, referred to as
gravity assists, is well established. However, there seems to be a lack of
understanding of the physical processes occurring during these dynamical
events. Radio-metric tracking data received from a number of spacecraft that
experienced an Earth gravity assist indicate the presence of an unexpected
energy change that happened during the flyby and cannot be explained by the
standard methods of modern astrodynamics. This puzzling behavior of several
spacecraft has become known as the flyby anomaly. We present the summary of the
recent anomalous observations and discuss possible ways to resolve this puzzle.Comment: 6 pages, 1 figure. Accepted for publication by Space Science Review
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On the distribution of bids for construction contract auctions
The statistical distribution representing bid values constitutes an essential part of many auction models and has involved a wide range of assumptions, including the Uniform, Normal, Lognormal and Weibull densities. From a modelling point of view, its goodness is defined by how well it enables the probability of a particular bid value to be estimated – a past bid for ex-post analysis and a future bid for ex-ante (forecasting) analysis. However, there is no agreement to date of what is the most appropriate form and empirical work is sparse.
Twelve extant construction datasets from four continents over different time periods are analysed in this paper for their fit to a variety of candidate statistical distributions assuming homogeneity of bidders (ID not known). The results show there is no one single fit-all distribution, but that the 3p Log-Normal, Fréchet/2p Log-Normal, Normal, Gamma and Gumbel generally rank the best ex-post, and the 2p Log-Normal, Normal, Gamma and Gumbel the best ex-ante – with ex-ante having around three to four times worse fit than ex-post. Final comments focus on the results relating to the third and fourth standardised moments of the bids and a post-hoc rationalisation of the empirical outcome of the analysis
Cosmological Perturbations from the No Boundary Euclidean Path Integral
We compute, from first principles, the quantum fluctuations about instanton
saddle points of the Euclidean path integral for Einstein gravity coupled to a
scalar field. The Euclidean two-point correlator is analytically continued into
the Lorentzian region where it describes the quantum mechanical vacuum
fluctuations in the state described by no boundary proposal initial conditions.
We concentrate on the density perturbations in open inflationary universes
produced from cosmological instantons, describing the differences between
non-singular Coleman-De Luccia and singular Hawking-Turok instantons. We show
how the Euclidean path integral uniquely specifies the fluctuations in both
cases.Comment: 21 pages, RevTex file, including five postscript figure file
Aspects of electrostatics in a weak gravitational field
Several features of electrostatics of point charged particles in a weak,
homogeneous, gravitational field are discussed using the Rindler metric to
model the gravitational field. Some previously known results are obtained by
simpler and more transparent procedures and are interpreted in an intuitive
manner. Specifically: (i) We show that the electrostatic potential of a charge
at rest in the Rindler frame is expressible as A_0=(q/l) where l is the affine
parameter distance along the null geodesic from the charge to the field point.
(ii) We obtain the sum of the electrostatic forces exerted by one charge on
another in the Rindler frame and discuss its interpretation. (iii) We show how
a purely electrostatic term in the Rindler frame appears as a radiation term in
the inertial frame. (In part, this arises because charges at rest in a weak
gravitational field possess additional weight due to their electrostatic
energy. This weight is proportional to the acceleration and falls inversely
with distance -- which are the usual characteristics of a radiation field.)
(iv) We also interpret the origin of the radiation reaction term by extending
our approach to include a slowly varying acceleration. Many of these results
might have possible extensions for the case of electrostatics in an arbitrary
static geometry. [Abridged Abstract]Comment: 26 pages; accepted for publication in Gen.Rel.Gra
Bandlimited approximations to the truncated Gaussian and applications
In this paper we extend the theory of optimal approximations of functions in the -metric by entire functions of prescribed
exponential type (bandlimited functions). We solve this problem for the
truncated and the odd Gaussians using explicit integral representations and
fine properties of truncated theta functions obtained via the maximum principle
for the heat operator. As applications, we recover most of the previously known
examples in the literature and further extend the class of truncated and odd
functions for which this extremal problem can be solved, by integration on the
free parameter and the use of tempered distribution arguments. This is the
counterpart of the work \cite{CLV}, where the case of even functions is
treated.Comment: to appear in Const. Appro
Systems of Hess-Appel'rot type
We construct higher-dimensional generalizations of the classical
Hess-Appel'rot rigid body system. We give a Lax pair with a spectral parameter
leading to an algebro-geometric integration of this new class of systems, which
is closely related to the integration of the Lagrange bitop performed by us
recently and uses Mumford relation for theta divisors of double unramified
coverings. Based on the basic properties satisfied by such a class of systems
related to bi-Poisson structure, quasi-homogeneity, and conditions on the
Kowalevski exponents, we suggest an axiomatic approach leading to what we call
the "class of systems of Hess-Appel'rot type".Comment: 40 pages. Comm. Math. Phys. (to appear
Enhanced Group Analysis and Exact Solutions of Variable Coefficient Semilinear Diffusion Equations with a Power Source
A new approach to group classification problems and more general
investigations on transformational properties of classes of differential
equations is proposed. It is based on mappings between classes of differential
equations, generated by families of point transformations. A class of variable
coefficient (1+1)-dimensional semilinear reaction-diffusion equations of the
general form () is studied from the
symmetry point of view in the framework of the approach proposed. The singular
subclass of the equations with is singled out. The group classifications
of the entire class, the singular subclass and their images are performed with
respect to both the corresponding (generalized extended) equivalence groups and
all point transformations. The set of admissible transformations of the imaged
class is exhaustively described in the general case . The procedure of
classification of nonclassical symmetries, which involves mappings between
classes of differential equations, is discussed. Wide families of new exact
solutions are also constructed for equations from the classes under
consideration by the classical method of Lie reductions and by generation of
new solutions from known ones for other equations with point transformations of
different kinds (such as additional equivalence transformations and mappings
between classes of equations).Comment: 40 pages, this is version published in Acta Applicanda Mathematica
Phenomenology of the Lense-Thirring effect in the Solar System
Recent years have seen increasing efforts to directly measure some aspects of
the general relativistic gravitomagnetic interaction in several astronomical
scenarios in the solar system. After briefly overviewing the concept of
gravitomagnetism from a theoretical point of view, we review the performed or
proposed attempts to detect the Lense-Thirring effect affecting the orbital
motions of natural and artificial bodies in the gravitational fields of the
Sun, Earth, Mars and Jupiter. In particular, we will focus on the evaluation of
the impact of several sources of systematic uncertainties of dynamical origin
to realistically elucidate the present and future perspectives in directly
measuring such an elusive relativistic effect.Comment: LaTex, 51 pages, 14 figures, 22 tables. Invited review, to appear in
Astrophysics and Space Science (ApSS). Some uncited references in the text
now correctly quoted. One reference added. A footnote adde
Metastability Driven by Soft Quantum Fluctuation Modes
The semiclassical Euclidean path integral method is applied to compute the
low temperature quantum decay rate for a particle placed in the metastable
minimum of a cubic potential in a {\it finite} time theory. The classical path,
which makes a saddle for the action, is derived in terms of Jacobian elliptic
functions whose periodicity establishes the one-to-one correspondence between
energy of the classical motion and temperature (inverse imaginary time) of the
system. The quantum fluctuation contribution has been computed through the
theory of the functional determinants for periodic boundary conditions. The
decay rate shows a peculiar temperature dependence mainly due to the softening
of the low lying quantum fluctuation eigenvalues. The latter are determined by
solving the Lam\`{e} equation which governs the fluctuation spectrum around the
time dependent classical bounce.Comment: Journal of Low Temperature Physics (2008) Publisher: Springer
Netherland
Overstory influences on light attenuation patterns and understory plant community diversity and composition in southern boreal forests of Quebec
We have characterized overstory light transmission, understory light levels, and plant communities in mixedwood boreal forests of northwestern Quebec with the objective of understanding how overstory light transmission interacts with composition and time since disturbance to influence the diversity and composition of understory vegetation, and, in turn, the further attenuation of light to the forest floor by the understory. Overstory light transmission differed among three forest types (aspen, mixed deciduous-conifer, and old cedar-dominated), with old forests having higher proportions of high light levels than aspen and mixed forests, which were characterized by intermediate light levels. The composition of the understory plant communities in old forests showed the weakest correlation to overstory light transmission, although those forests had the largest range of light transmission. The strongest correlation between characteristics of overstory light transmission and understory communities was found in aspen forests. Species diversity indices were consistently higher in aspen forests but showed weak relationships with overstory light transmission. Light attenuation by the understory vegetation and total height of the understory vegetation were strongly and positively related to overstory light transmission but not forest type. Therefore, light transmission through the overstory influenced the structure and function of understory plants more than their diversity and composition. This is likely due to the strong effect of the upper understory layers, which tend to homogenize light levels at the forest floor regardless of forest type. The understory plant community acts as a filter, thereby reducing light levels at the forest floor to uniformly low levels
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