757 research outputs found
Ballistic trajectory: parabola, ellipse, or what?
Mechanics texts tell us that a particle in a bound orbit under gravitational
central force moves on an ellipse, while introductory physics texts approximate
the earth as flat, and tell us that the particle moves in a parabola. The
uniform-gravity, flat-earth parabola is clearly meant to be an approximation to
a small segment of the true central-force/ellipse orbit. To look more deeply
into this connection we convert earth-centered polar coordinates to
``flat-earth coordinates'' by treating radial lines as vertical, and by
treating lines of constant radial distance as horizontal. With the exact
trajectory and dynamics in this system, we consider such questions as whether
gravity is purely vertical in this picture, and whether the central force
nature of gravity is important only when the height or range of a ballistic
trajectory is comparable to the earth radius. Somewhat surprisingly, the
answers to both questions is ``no,'' and therein lie some interesting lessons.Comment: 7 pages, 3 figure
MAC with Action-Dependent State Information at One Encoder
Problems dealing with the ability to take an action that affects the states
of state-dependent communication channels are of timely interest and
importance. Therefore, we extend the study of action-dependent channels, which
until now focused on point-to-point models, to multiple-access channels (MAC).
In this paper, we consider a two-user, state-dependent MAC, in which one of the
encoders, called the informed encoder, is allowed to take an action that
affects the formation of the channel states. Two independent messages are to be
sent through the channel: a common message known to both encoders and a private
message known only to the informed encoder. In addition, the informed encoder
has access to the sequence of channel states in a non-causal manner. Our
framework generalizes previously evaluated settings of state dependent
point-to-point channels with actions and MACs with common messages. We derive a
single letter characterization of the capacity region for this setting. Using
this general result, we obtain and compute the capacity region for the Gaussian
action-dependent MAC. The unique methods used in solving the Gaussian case are
then applied to obtain the capacity of the Gaussian action-dependent
point-to-point channel; a problem was left open until this work. Finally, we
establish some dualities between action-dependent channel coding and source
coding problems. Specifically, we obtain a duality between the considered MAC
setting and the rate distortion model known as "Successive Refinement with
Actions". This is done by developing a set of simple duality principles that
enable us to successfully evaluate the outcome of one problem given the other.Comment: 1. Parts of this paper appeared in the IEEE International Symposium
on Information Theory (ISIT 2012),Cambridge, MA, US, July 2012 and at the
IEEE 27th Convention of Electrical and Electronics Engineers in Israel (IEEEI
2012), Nov. 2012. 2. This work has been supported by the CORNET Consortium
Israel Ministry for Industry and Commerc
Late time tails from momentarily stationary, compact initial data in Schwarzschild spacetimes
An L-pole perturbation in Schwarzschild spacetime generally falls off at late
times t as t^{-2L-3}. It has recently been pointed out by Karkowski,
Swierczynski and Malec, that for initial data that is of compact support, and
is initially momentarily static, the late-time behavior is different, going as
t^{-2L-4}. By considering the Laplace transforms of the fields, we show here
why the momentarily stationary case is exceptional. We also explain, using a
time-domain description, the special features of the time development in this
exceptional case.Comment: 7 pages, 5 figure
Analyses of deep mammalian sequence alignments and constraint predictions for 1% of the human genome
A key component of the ongoing ENCODE project involves rigorous comparative sequence analyses for the initially targeted 1% of the human genome. Here, we present orthologous sequence generation, alignment, and evolutionary constraint analyses of 23 mammalian species for all ENCODE targets. Alignments were generated using four different methods; comparisons of these methods reveal large-scale consistency but substantial differences in terms of small genomic rearrangements, sensitivity (sequence coverage), and specificity (alignment accuracy). We describe the quantitative and qualitative trade-offs concomitant with alignment method choice and the levels of technical error that need to be accounted for in applications that require multisequence alignments. Using the generated alignments, we identified constrained regions using three different methods. While the different constraint-detecting methods are in general agreement, there are important discrepancies relating to both the underlying alignments and the specific algorithms. However, by integrating the results across the alignments and constraint-detecting methods, we produced constraint annotations that were found to be robust based on multiple independent measures. Analyses of these annotations illustrate that most classes of experimentally annotated functional elements are enriched for constrained sequences; however, large portions of each class (with the exception of protein-coding sequences) do not overlap constrained regions. The latter elements might not be under primary sequence constraint, might not be constrained across all mammals, or might have expendable molecular functions. Conversely, 40% of the constrained sequences do not overlap any of the functional elements that have been experimentally identified. Together, these findings demonstrate and quantify how many genomic functional elements await basic molecular characterization
Computational Efficiency of Frequency-- and Time--Domain Calculations of Extreme Mass--Ratio Binaries: Equatorial Orbits
Gravitational waveforms and fluxes from extreme mass--ratio inspirals can be
computed using time--domain methods with accuracy that is fast approaching that
of frequency--domain methods. We study in detail the computational efficiency
of these methods for equatorial orbits of fast spinning Kerr black holes, and
find the number of modes needed in either method --as functions of the orbital
parameters-- in order to achieve a desired accuracy level. We then estimate the
total computation time and argue that for high eccentricity orbits the
time--domain approach is more efficient computationally. We suggest that in
practice low-- modes are computed using the frequency--domain approach, and
high-- modes are computed using the time--domain approach, where is the
azimuthal mode number.Comment: 19 figures, 6 table
Universality of massive scalar field late-time tails in black-hole spacetimes
The late-time tails of a massive scalar field in the spacetime of black holes
are studied numerically. Previous analytical results for a Schwarzschild black
hole are confirmed: The late-time behavior of the field as recorded by a static
observer is given by , where
depends weakly on time. This result is carried over to the case of
a Kerr black hole. In particular, it is found that the power-law index of -5/6
depends on neither the multipole mode nor on the spin rate of the black
hole . In all black hole spacetimes, massive scalar fields have the same
late-time behavior irrespective of their initial data (i.e., angular
distribution). Their late-time behavior is universal.Comment: 11 pages, 14 figures, published versio
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