8,864 research outputs found
A reliable Pade analytical continuation method based on a high accuracy symbolic computation algorithm
We critique a Pade analytic continuation method whereby a rational polynomial
function is fit to a set of input points by means of a single matrix inversion.
This procedure is accomplished to an extremely high accuracy using a novel
symbolic computation algorithm. As an example of this method in action we apply
it to the problem of determining the spectral function of a one-particle
thermal Green's function known only at a finite number of Matsubara frequencies
with two example self energies drawn from the T-matrix theory of the Hubbard
model. We present a systematic analysis of the effects of error in the input
points on the analytic continuation, and this leads us to propose a procedure
to test quantitatively the reliability of the resulting continuation, thus
eliminating the black magic label frequently attached to this procedure.Comment: 11 pages, 8 eps figs, revtex format; revised version includes
reference to anonymous ftp site containing example codes (MapleVr5.1
worksheets) displaying the implementation of the algorithm, including the
padematinv.m library packag
Imprints of the nuclear symmetry energy on gravitational waves from the axial w-modes of neutron stars
The eigen-frequencies of the axial w-modes of oscillating neutron stars are
studied using the continued fraction method with an Equation of State (EOS)
partially constrained by the recent terrestrial nuclear laboratory data. It is
shown that the density dependence of the nuclear symmetry energy
affects significantly both the frequencies and the damping
times of these modes. Besides confirming the previously found universal
behavior of the mass-scaled eigen-frequencies as functions of the compactness
of neutron stars, we explored several alternative universal scaling functions.
Moreover, the -mode is found to exist only for neutron stars having a
compactness of independent of the EOS used.Comment: Version appeared in Phys. Rev. C80, 025801 (2009
Quantum interference between charge excitation paths in a solid state Mott insulator
The competition between electron localization and de-localization in Mott
insulators underpins the physics of strongly-correlated electron systems.
Photo-excitation, which re-distributes charge between sites, can control this
many-body process on the ultrafast timescale. To date, time-resolved studies
have been performed in solids in which other degrees of freedom, such as
lattice, spin, or orbital excitations come into play. However, the underlying
quantum dynamics of bare electronic excitations has remained out of reach.
Quantum many-body dynamics have only been detected in the controlled
environment of optical lattices where the dynamics are slower and lattice
excitations are absent. By using nearly-single-cycle near-IR pulses, we have
measured coherent electronic excitations in the organic salt ET-F2TCNQ, a
prototypical one-dimensional Mott Insulator. After photo-excitation, a new
resonance appears on the low-energy side of the Mott gap, which oscillates at
25 THz. Time-dependent simulations of the Mott-Hubbard Hamiltonian reproduce
the oscillations, showing that electronic delocalization occurs through quantum
interference between bound and ionized holon-doublon pairs.Comment: 4 figures and supplementary informatio
Continued fraction solution of Krein's inverse problem
The spectral data of a vibrating string are encoded in its so-called
characteristic function. We consider the problem of recovering the distribution
of mass along the string from its characteristic function. It is well-known
that Stieltjes' continued fraction provides a solution of this inverse problem
in the particular case where the distribution of mass is purely discrete. We
show how to adapt Stieltjes' method to solve the inverse problem for a related
class of strings. An application to the excursion theory of diffusion processes
is presented.Comment: 18 pages, 2 figure
Space Launch System Implementation of Adaptive Augmenting Control
Given the complex structural dynamics, challenging ascent performance requirements, and rigorous flight certification constraints owing to its manned capability, the NASA Space Launch System (SLS) launch vehicle requires a proven thrust vector control algorithm design with highly optimized parameters to provide stable and high-performance flight. On its development path to Preliminary Design Review (PDR), the SLS flight control system has been challenged by significant vehicle flexibility, aerodynamics, and sloshing propellant. While the design has been able to meet all robust stability criteria, it has done so with little excess margin. Through significant development work, an Adaptive Augmenting Control (AAC) algorithm has been shown to extend the envelope of failures and flight anomalies the SLS control system can accommodate while maintaining a direct link to flight control stability criteria such as classical gain and phase margin. In this paper, the work performed to mature the AAC algorithm as a baseline component of the SLS flight control system is presented. The progress to date has brought the algorithm design to the PDR level of maturity. The algorithm has been extended to augment the full SLS digital 3-axis autopilot, including existing load-relief elements, and the necessary steps for integration with the production flight software prototype have been implemented. Several updates which have been made to the adaptive algorithm to increase its performance, decrease its sensitivity to expected external commands, and safeguard against limitations in the digital implementation are discussed with illustrating results. Monte Carlo simulations and selected stressing case results are also shown to demonstrate the algorithm's ability to increase the robustness of the integrated SLS flight control system
Space Launch System Implementation of Adaptive Augmenting Control
Given the complex structural dynamics, challenging ascent performance requirements, and rigorous flight certification constraints owing to its manned capability, the NASA Space Launch System (SLS) launch vehicle requires a proven thrust vector control algorithm design with highly optimized parameters to robustly demonstrate stable and high performance flight. On its development path to preliminary design review (PDR), the stability of the SLS flight control system has been challenged by significant vehicle flexibility, aerodynamics, and sloshing propellant dynamics. While the design has been able to meet all robust stability criteria, it has done so with little excess margin. Through significant development work, an adaptive augmenting control (AAC) algorithm previously presented by Orr and VanZwieten, has been shown to extend the envelope of failures and flight anomalies for which the SLS control system can accommodate while maintaining a direct link to flight control stability criteria (e.g. gain & phase margin). In this paper, the work performed to mature the AAC algorithm as a baseline component of the SLS flight control system is presented. The progress to date has brought the algorithm design to the PDR level of maturity. The algorithm has been extended to augment the SLS digital 3-axis autopilot, including existing load-relief elements, and necessary steps for integration with the production flight software prototype have been implemented. Several updates to the adaptive algorithm to increase its performance, decrease its sensitivity to expected external commands, and safeguard against limitations in the digital implementation are discussed with illustrating results. Monte Carlo simulations and selected stressing case results are shown to demonstrate the algorithm's ability to increase the robustness of the integrated SLS flight control system
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