9,149 research outputs found
MEXIT: Maximal un-coupling times for stochastic processes
Classical coupling constructions arrange for copies of the \emph{same} Markov
process started at two \emph{different} initial states to become equal as soon
as possible. In this paper, we consider an alternative coupling framework in
which one seeks to arrange for two \emph{different} Markov (or other
stochastic) processes to remain equal for as long as possible, when started in
the \emph{same} state. We refer to this "un-coupling" or "maximal agreement"
construction as \emph{MEXIT}, standing for "maximal exit". After highlighting
the importance of un-coupling arguments in a few key statistical and
probabilistic settings, we develop an explicit \MEXIT construction for
stochastic processes in discrete time with countable state-space. This
construction is generalized to random processes on general state-space running
in continuous time, and then exemplified by discussion of \MEXIT for Brownian
motions with two different constant drifts.Comment: 28 page
Microwave remote sensing of soil moisture, volume 1
Multifrequency sensor data from NASA's C-130 aircraft were used to determine which of the all weather microwave sensors demonstrated the highest correlation to surface soil moisture over optimal bare soil conditions, and to develop and test techniques which use visible/infrared sensors to compensate for the vegetation effect in this sensor's response to soil moisture. The L-band passive microwave radiometer was found to be the most suitable single sensor system to estimate soil moisture over bare fields. The perpendicular vegetation index (PVI) as determined from the visible/infrared sensors was useful as a measure of the vegetation effect on the L-band radiometer response to soil moisture. A linear equation was developed to estimate percent field capacity as a function of L-band emissivity and the vegetation index. The prediction algorithm improves the estimation of moisture significantly over predictions from L-band emissivity alone
Development of visible/infrared/microwave agriculture classification and biomass estimation algorithms, volume 2
Agricultural crop classification models using two or more spectral regions (visible through microwave) were developed and tested and biomass was estimated by including microwave with visible and infrared data. The study was conducted at Guymon, Oklahoma and Dalhart, Texas utilizing aircraft multispectral data and ground truth soil moisture and biomass information. Results indicate that inclusion of C, L, and P band active microwave data from look angles greater than 35 deg from nadir with visible and infrared data improved crop discrimination and biomass estimates compared to results using only visible and infrared data. The active microwave frequencies were sensitive to different biomass levels. In addition, two indices, one using only active microwave data and the other using data from the middle and near infrared bands, were well correlated to total biomass
Multifrequency remote sensing of soil moisture
Multifrequency sensor data collected at Guymon, Oklahoma and Dalhart, Texas using NASA's C-130 aircraft were used to determine which of the all-weather microwave sensors demonstrated the highest correlation to surface soil moisture over optimal bare soil conditions, and to develop and test techniques which use visible/infrared sensors to compensate for the vegetation effect in this sensor's response to soil moisture. The L-band passive microwave radiometer was found to be the most suitable single sensor system to estimate soil moisture over bare fields. In comparison to other active and passive microwave sensors the L-band radiometer (1) was influenced least by ranges in surface roughness; (2) demonstrated the most sensitivity to soil moisture differences in terms of the range of return from the full range of soil moisture; and (3) was less sensitive to errors in measurement in relation to the range of sensor response. L-band emissivity related more strongly to soil moisture when moisture was expressed as percent of field capacity. The perpendicular vegetation index as determined from the visible/infrared sensors was useful as a measure of the vegetation effect on the L-band radiometer response to soil moisture
Development of visible/infrared/microwave agriculture classification and biomass estimation algorithms
Agricultural crop classification models using two or more spectral regions (visible through microwave) are considered in an effort to estimate biomass at Guymon, Oklahoma Dalhart, Texas. Both grounds truth and aerial data were used. Results indicate that inclusion of C, L, and P band active microwave data, from look angles greater than 35 deg from nadir, with visible and infrared data improve crop discrimination and biomass estimates compared to results using only visible and infrared data. The microwave frequencies were sensitive to different biomass levels. The K and C band were sensitive to differences at low biomass levels, while P band was sensitive to differences at high biomass levels. Two indices, one using only active microwave data and the other using data from the middle and near infrared bands, were well correlated to total biomass. It is implied that inclusion of active microwave sensors with visible and infrared sensors on future satellites could aid in crop discrimination and biomass estimation
Peaks and Troughs in Helioseismology: The Power Spectrum of Solar Oscillations
I present a matched-wave asymptotic analysis of the driving of solar
oscillations by a general localised source. The analysis provides a simple
mathematical description of the asymmetric peaks in the power spectrum in terms
of the relative locations of eigenmodes and troughs in the spectral response.
It is suggested that the difference in measured phase function between the
modes and the troughs in the spectrum will provide a key diagnostic of the
source of the oscillations. I also suggest a form for the asymmetric line
profiles to be used in the fitting of solar power spectra.
Finally I present a comparison between the numerical and asymptotic
descriptions of the oscillations. The numerical results bear out the
qualitative features suggested by the asymptotic analysis but suggest that
numerical calculations of the locations of the troughs will be necessary for a
quantitative comparison with the observations.Comment: 18 pages + 8 separate figures. To appear in Ap
Orbital evolution of a test particle around a black hole: Indirect determination of the self force in the post Newtonian approximation
Comparing the corrections to Kepler's law with orbital evolution under a self
force, we extract the finite, already regularized part of the latter in a
specific gauge. We apply this method to a quasi-circular orbit around a
Schwarzschild black hole of an extreme mass ratio binary, and determine the
first- and second-order conservative gravitational self force in a post
Newtonian expansion. We use these results in the construction of the
gravitational waveform, and revisit the question of the relative contribution
of the self force and spin-orbit coupling.Comment: 5 pages, 2 figure
Second-order gravitational self-force
We derive an expression for the second-order gravitational self-force that
acts on a self-gravitating compact-object moving in a curved background
spacetime. First we develop a new method of derivation and apply it to the
derivation of the first-order gravitational self-force. Here we find that our
result conforms with the previously derived expression. Next we generalize our
method and derive a new expression for the second-order gravitational
self-force. This study also has a practical motivation: The data analysis for
the planned gravitational wave detector LISA requires construction of waveforms
templates for the expected gravitational waves. Calculation of the two leading
orders of the gravitational self-force will enable one to construct highly
accurate waveform templates, which are needed for the data analysis of
gravitational-waves that are emitted from extreme mass-ratio binaries.Comment: 35 page
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