11,783 research outputs found
Generalizing Optical Geometry
We show that by employing the standard projected curvature as a measure of
spatial curvature, we can make a certain generalization of optical geometry
(Abramowicz and Lasota 1997, Class. Quantum Grav. 14 (1997) A23). This
generalization applies to any spacetime that admits a hypersurface orthogonal
shearfree congruence of worldlines. This is a somewhat larger class of
spacetimes than the conformally static spacetimes assumed in standard optical
geometry. In the generalized optical geometry, which in the generic case is
time dependent, photons move with unit speed along spatial geodesics and the
sideways force experienced by a particle following a spatially straight line is
independent of the velocity. Also gyroscopes moving along spatial geodesics do
not precess (relative to the forward direction). Gyroscopes that follow a
curved spatial trajectory precess according to a very simple law of
three-rotation. We also present an inertial force formalism in coordinate
representation for this generalization. Furthermore, we show that by employing
a new sense of spatial curvature (Jonsson, Class. Quantum Grav. 23 (2006) 1)
closely connected to Fermat's principle, we can make a more extensive
generalization of optical geometry that applies to arbitrary spacetimes. In
general this optical geometry will be time dependent, but still geodesic
photons move with unit speed and follow lines that are spatially straight in
the new sense. Also, the sideways experienced (comoving) force on a test
particle following a line that is straight in the new sense will be independent
of the velocity.Comment: 19 pages, 1 figure. A more general analysis is presented than in the
former version. See also the companion papers arXiv:0708.2493,
arXiv:0708.2533 and arXiv:0708.253
The inverse conjunction fallacy
If people believe that some property is true of all members of a class such as sofas, then they should also believe that the same property is true of all members of a conjunctively defined subset of that class such as uncomfortable handmade sofas. A series of experiments demonstrated a failure to observe this constraint, leading to what is termed the inverse conjunction fallacy. Not only did people often express a belief in the more general statement but not in the more specific, but also when they accepted both beliefs, they were inclined to give greater confidence to the more general. It is argued that this effect underlies a number of other demonstrations of fallacious reasoning, particularly in category-based induction. Alternative accounts of the phenomenon are evaluated, and it is concluded that the effect is best interpreted in terms of intensional reasoning [Tversky, A., & Kahneman, D. (1983). Extensional versus intuitive reasoning: the conjunction fallacy in probability judgment. Psychological Review, 90, 293–315.]
Inertial forces and the foundations of optical geometry
Assuming a general timelike congruence of worldlines as a reference frame, we
derive a covariant general formalism of inertial forces in General Relativity.
Inspired by the works of Abramowicz et. al. (see e.g. Abramowicz and Lasota,
Class. Quantum Grav. 14 (1997) A23), we also study conformal rescalings of
spacetime and investigate how these affect the inertial force formalism. While
many ways of describing spatial curvature of a trajectory has been discussed in
papers prior to this, one particular prescription (which differs from the
standard projected curvature when the reference is shearing) appears novel. For
the particular case of a hypersurface-forming congruence, using a suitable
rescaling of spacetime, we show that a geodesic photon is always following a
line that is spatially straight with respect to the new curvature measure. This
fact is intimately connected to Fermat's principle, and allows for a certain
generalization of the optical geometry as will be further pursued in a
companion paper (Jonsson and Westman, Class. Quantum Grav. 23 (2006) 61). For
the particular case when the shear-tensor vanishes, we present the inertial
force equation in three-dimensional form (using the bold face vector notation),
and note how similar it is to its Newtonian counterpart. From the spatial
curvature measures that we introduce, we derive corresponding covariant
differentiations of a vector defined along a spacetime trajectory. This allows
us to connect the formalism of this paper to that of Jantzen et. al. (see e.g.
Bini et. al., Int. J. Mod. Phys. D 6 (1997) 143).Comment: 42 pages, 7 figure
An intuitive approach to inertial forces and the centrifugal force paradox in general relativity
As the velocity of a rocket in a circular orbit near a black hole increases,
the outwardly directed rocket thrust must increase to keep the rocket in its
orbit. This feature might appear paradoxical from a Newtonian viewpoint, but we
show that it follows naturally from the equivalence principle together with
special relativity and a few general features of black holes. We also derive a
general relativistic formalism of inertial forces for reference frames with
acceleration and rotation. The resulting equation relates the real experienced
forces to the time derivative of the speed and the spatial curvature of the
particle trajectory relative to the reference frame. We show that an observer
who follows the path taken by a free (geodesic) photon will experience a force
perpendicular to the direction of motion that is independent of the observers
velocity. We apply our approach to resolve the submarine paradox, which regards
whether a submerged submarine in a balanced state of rest will sink or float
when given a horizontal velocity if we take relativistic effects into account.
We extend earlier treatments of this topic to include spherical oceans and show
that for the case of the Earth the submarine floats upward if we take the
curvature of the ocean into account.Comment: 14 pages, 21 figure
Aerosol and Cloud Microphysical Characteristics of Rifts and Gradients in Maritime Stratocumulus Clouds
A cloud rift is characterized as a large-scale, persistent area of broken, low-reflectivity stratocumulus clouds usually surrounded by a solid deck of stratocumulus. A rift observed off the coast of California was investigated using an instrumented aircraft to compare the aerosol, cloud microphysical, and thermodynamic properties in the rift with those of the surrounding solid stratocumulus deck. The microphysical characteristics in the solid stratocumulus deck differ substantially from those of a broken, cellular rift where cloud droplet concentrations are a factor of 2 lower than those in the solid cloud. Furthermore, cloud condensation nuclei (CCN) concentrations were found to be about 3 times greater in the solid-cloud area compared with those in the rift. Although drizzle was observed near cloud top in parts of the solid stratocumulus cloud, the largest drizzle rates were associated with the broken clouds within the rift area and with extremely large effective droplet sizes retrieved from satellite data. Minimal thermodynamic differences between the rift and solid cloud deck were observed. In addition to marked differences in particle concentrations, evidence of a mesoscale circulation near the solid cloud–rift boundary is presented. This mesoscale circulation may provide a mechanism for maintaining a rift, but further study is required to understand the initiation of a rift and the conditions that may cause it to fill. A review of results from previous studies indicates similar microphysical characteristics in rift features sampled serendipitously. These observations indicate that cloud rifts are depleted of aerosols through the cleansing associated with drizzle and are a manifestation of natural processes occurring in marine stratocumulus
Balloon-borne radiometer measurement of Northern Hemisphere mid-latitude stratospheric HNO3 profiles spanning 12 years
Low-resolution atmospheric thermal emission spectra collected by balloon-borne radiometers over the time span of 1990–2002 are used to retrieve vertical profiles of HNO3, CFC-11 and CFC-12 volume mixing ratios between approximately 10 and 35 km altitude. All of the data analyzed have been collected from launches from a Northern Hemisphere mid-latitude site, during late summer, when stratospheric dynamic variability is at a minimum. The retrieval technique incorporates detailed forward modeling of the instrument and the radiative properties of the atmosphere, and obtains a best fit between modeled and measured spectra through a combination of onion-peeling and global optimization steps. The retrieved HNO3 profiles are consistent over the 12-year period, and are consistent with recent measurements by the Atmospheric Chemistry Experiment-Fourier transform spectrometer satellite instrument. This suggests that, to within the errors of the 1990 measurements, there has been no significant change in the HNO3 summer mid-latitude profile
Tropically convex constraint satisfaction
A semilinear relation S is max-closed if it is preserved by taking the
componentwise maximum. The constraint satisfaction problem for max-closed
semilinear constraints is at least as hard as determining the winner in Mean
Payoff Games, a notorious problem of open computational complexity. Mean Payoff
Games are known to be in the intersection of NP and co-NP, which is not known
for max-closed semilinear constraints. Semilinear relations that are max-closed
and additionally closed under translations have been called tropically convex
in the literature. One of our main results is a new duality for open tropically
convex relations, which puts the CSP for tropically convex semilinaer
constraints in general into NP intersected co-NP. This extends the
corresponding complexity result for scheduling under and-or precedence
constraints, or equivalently the max-atoms problem. To this end, we present a
characterization of max-closed semilinear relations in terms of syntactically
restricted first-order logic, and another characterization in terms of a finite
set of relations L that allow primitive positive definitions of all other
relations in the class. We also present a subclass of max-closed constraints
where the CSP is in P; this class generalizes the class of max-closed
constraints over finite domains, and the feasibility problem for max-closed
linear inequalities. Finally, we show that the class of max-closed semilinear
constraints is maximal in the sense that as soon as a single relation that is
not max-closed is added to L, the CSP becomes NP-hard.Comment: 29 pages, 2 figure
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