28,544 research outputs found
Stability test and dominant eigenvalues computation for second-order linear systems with multiple time-delays using receptance method
© 2019 Elsevier Ltd Stability analysis and dominant eigenvalues computation for second-order linear systems with multiple time-delays are addressed by using a reduced characteristic function and the associated characteristic matrix comprised of measured open-loop receptances. This reduced characteristic function is derived from the original characteristic function of the second-order time delayed systems based on a reasonable assumption that eigenvalues of the closed-loop system are distinct from those of the open-loop system. Then a contour integral is used to test the stability and provide the stability chart with respect to different displacement and velocity feedback time-delays, and a Newton-type method to compute the dominant eigenvalues via this characteristic function. The proposed approach also utilizes the spectrum distribution features of the retarded time-delay systems. Finally, numerical examples are given to illustrate the effectiveness of the proposed approach
Imaging and Nulling with the Space Interferometry Mission
We present numerical simulations for a possible synthesis imaging mode of the
Space Interferometer Mission (SIM). We summarize the general techniques that
SIM offers to perform imaging of high surface brightness sources, and discuss
their strengths and weaknesses. We describe an interactive software package
that is used to provide realistic, photometrically correct estimates of SIM
performance for various classes of astronomical objects. In particular, we
simulate the cases of gaseous disks around black holes in the nuclei of
galaxies, and zodiacal dust disks around young stellar objects. Regarding the
first, we show that a Keplerian velocity gradient of the line-emitting gaseous
disk -- and thus the mass of the putative black hole -- can be determined with
SIM to unprecedented accuracy in about 5 hours of integration time for objects
with H_alpha surface brigthness comparable to the prototype M 87. Detections
and observations of exo-zodiacal dust disks depend critically on the disk
properties and the nulling capabilities of SIM. Systems with similar disk size
and at least one tenth of the dust content of beta Pic can be detected by SIM
at distances between 100 pc and a few kpc, if a nulling efficiency of 1/10000
is achieved. Possible inner clear regions indicative of the presence of massive
planets can also be detected and imaged. On the other hand, exo-zodiacal disks
with properties more similar to the solar system will not be found in
reasonable integration times with SIM.Comment: 28 pages, incl. 8 postscript figures, excl. 10 gif-figures Submitted
to Ap
An Investigation of Stochastic Cooling in the Framework of Control Theory
This report provides a description of unbunched beam stochastic cooling in
the framework of control theory. The main interest in the investigation is
concentrated on the beam stability in an active cooling system. A stochastic
cooling system must be considered as a closed-loop, similar to the feedback
systems used to damp collective instabilities. These systems, which are able to
act upon themselves, are potentially unstable.
The self-consistent solution for the beam motion is derived by means of a
mode analysis of the collective beam motion. This solution yields a criterion
for the stability of each collective mode. The expressions also allow for
overlapping frequency bands in the beam spectrum and thus are valid over the
entire frequency range.
Having established the boundaries of stability in this way, the Fokker-Planck
equation is used to describe the cooling process. This description does not
include collective effects and thus a stable beam must be assumed. Hence the
predictions about the cooling process following from the Fokker-Planck equation
only make physical sense within the boundaries of beam stability. Finally it is
verified that the parameters of the cooling system which give the best cooling
results are compatible with the stability of the beam.Comment: 64 pages, latex, 11 eps-figures appended as uuencoded file, german
hyphenation corrected I
An integral method for solving nonlinear eigenvalue problems
We propose a numerical method for computing all eigenvalues (and the
corresponding eigenvectors) of a nonlinear holomorphic eigenvalue problem that
lie within a given contour in the complex plane. The method uses complex
integrals of the resolvent operator, applied to at least column vectors,
where is the number of eigenvalues inside the contour. The theorem of
Keldysh is employed to show that the original nonlinear eigenvalue problem
reduces to a linear eigenvalue problem of dimension .
No initial approximations of eigenvalues and eigenvectors are needed. The
method is particularly suitable for moderately large eigenvalue problems where
is much smaller than the matrix dimension. We also give an extension of the
method to the case where is larger than the matrix dimension. The
quadrature errors caused by the trapezoid sum are discussed for the case of
analytic closed contours. Using well known techniques it is shown that the
error decays exponentially with an exponent given by the product of the number
of quadrature points and the minimal distance of the eigenvalues to the
contour
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