31,706 research outputs found
Singularity dominated strong fluctuations for some random matrix averages
The circular and Jacobi ensembles of random matrices have their eigenvalue
support on the unit circle of the complex plane and the interval of the
real line respectively. The averaged value of the modulus of the corresponding
characteristic polynomial raised to the power diverges, for , at points approaching the eigenvalue support. Using the theory of
generalized hypergeometric functions based on Jack polynomials, the functional
form of the leading asymptotic behaviour is established rigorously. In the
circular ensemble case this confirms a conjecture of Berry and Keating.Comment: 11 pages, to appear Commun. Math. Phy
Nodal domain distributions for quantum maps
The statistics of the nodal lines and nodal domains of the eigenfunctions of
quantum billiards have recently been observed to be fingerprints of the
chaoticity of the underlying classical motion by Blum et al. (Phys. Rev. Lett.,
Vol. 88 (2002), 114101) and by Bogomolny and Schmit (Phys. Rev. Lett., Vol. 88
(2002), 114102). These statistics were shown to be computable from the random
wave model of the eigenfunctions. We here study the analogous problem for
chaotic maps whose phase space is the two-torus. We show that the distributions
of the numbers of nodal points and nodal domains of the eigenvectors of the
corresponding quantum maps can be computed straightforwardly and exactly using
random matrix theory. We compare the predictions with the results of numerical
computations involving quantum perturbed cat maps.Comment: 7 pages, 2 figures. Second version: minor correction
Observing the Galaxy's massive black hole with gravitational wave bursts
An extreme-mass-ratio burst (EMRB) is a gravitational wave signal emitted
when a compact object passes through periapsis on a highly eccentric orbit
about a much more massive object, in our case a stellar mass object about a
10^6 M_sol black hole. EMRBs are a relatively unexplored means of probing the
spacetime of massive black holes (MBHs). We conduct an investigation of the
properties of EMRBs and how they could allow us to constrain the parameters,
such as spin, of the Galaxy's MBH. We find that if an EMRB event occurs in the
Galaxy, it should be detectable for periapse distances r_p < 65 r_g for a \mu =
10 M_sol orbiting object, where r_g = GM/c^2 is the gravitational radius. The
signal-to-noise ratio scales as \rho ~ -2.7 log(r_p/r_g) + log(\mu/M_sol) +
4.9. For periapses r_p < 10 r_g, EMRBs can be informative, and provide good
constraints on both the MBH's mass and spin. Closer orbits provide better
constraints, with the best giving accuracies of better than one part in 10^4
for both the mass and spin parameter.Comment: 25 pages, 17 figures, 1 appendix. One more typo fixe
Expectations for extreme-mass-ratio bursts from the Galactic Centre
When a compact object on a highly eccentric orbit about a much more massive
body passes through periapsis it emits a short gravitational wave signal known
as an extreme-mass-ratio burst (EMRB). We consider stellar mass objects
orbiting the massive black hole (MBH) found in the Galactic Centre. EMRBs
provide a novel means of extracting information about the MBH; an EMRB from the
Galactic MBH could be highly informative regarding the MBH's mass and spin if
the orbital periapsis is small enough. However, to be a useful astronomical
tool EMRBs must be both informative and sufficiently common to be detectable
with a space-based interferometer. We construct a simple model to predict the
event rate for Galactic EMRBs. We estimate there could be on average ~2 bursts
in a two year mission lifetime for LISA. Stellar mass black holes dominate the
event rate. Creating a sample of 100 mission realisations, we calculate what we
could learn about the MBH. On average, we expect to be able to determine the
MBH mass to ~1% and the spin to ~0.1 using EMRBs.Comment: 22 pages, 5 figures, 2 appendices. Minor changes to reflect published
versio
Methods of calculation of a friction coefficient: Application to the nanotubes
In this work we develop theoretical and numerical methods of calculation of a
dynamic friction coefficient. The theoretical method is based on an adiabatic
approximation which allows us to express the dynamic friction coefficient in
terms of the time integral of the autocorrelation function of the force between
both sliding objects. The motion of the objects and the autocorrelation
function can be numerically calculated by molecular-dynamics simulations. We
have successfully applied these methods to the evaluation of the dynamic
friction coefficient of the relative motion of two concentric carbon nanotubes.
The dynamic friction coefficient is shown to increase with the temperature.Comment: 4 pages, 6 figure
Charge order in Magnetite. An LDA+ study
The electronic structure of the monoclinic structure of FeO is
studied using both the local density approximation (LDA) and the LDA+. The
LDA gives only a small charge disproportionation, thus excluding that the
structural distortion should be sufficient to give a charge order. The LDA+
results in a charge disproportion along the c-axis in good agreement with the
experiment. We also show how the effective can be calculated within the
augmented plane wave methods
Decimation and Harmonic Inversion of Periodic Orbit Signals
We present and compare three generically applicable signal processing methods
for periodic orbit quantization via harmonic inversion of semiclassical
recurrence functions. In a first step of each method, a band-limited decimated
periodic orbit signal is obtained by analytical frequency windowing of the
periodic orbit sum. In a second step, the frequencies and amplitudes of the
decimated signal are determined by either Decimated Linear Predictor, Decimated
Pade Approximant, or Decimated Signal Diagonalization. These techniques, which
would have been numerically unstable without the windowing, provide numerically
more accurate semiclassical spectra than does the filter-diagonalization
method.Comment: 22 pages, 3 figures, submitted to J. Phys.
The design of digital-adaptive controllers for VTOL aircraft
Design procedures for VTOL automatic control systems have been developed and are presented. Using linear-optimal estimation and control techniques as a starting point, digital-adaptive control laws have been designed for the VALT Research Aircraft, a tandem-rotor helicopter which is equipped for fully automatic flight in terminal area operations. These control laws are designed to interface with velocity-command and attitude-command guidance logic, which could be used in short-haul VTOL operations. Developments reported here include new algorithms for designing non-zero-set-point digital regulators, design procedures for rate-limited systems, and algorithms for dynamic control trim setting
Modern digital flight control system design for VTOL aircraft
Methods for and results from the design and evaluation of a digital flight control system (DFCS) for a CH-47B helicopter are presented. The DFCS employed proportional-integral control logic to provide rapid, precise response to automatic or manual guidance commands while following conventional or spiral-descent approach paths. It contained altitude- and velocity-command modes, and it adapted to varying flight conditions through gain scheduling. Extensive use was made of linear systems analysis techniques. The DFCS was designed, using linear-optimal estimation and control theory, and the effects of gain scheduling are assessed by examination of closed-loop eigenvalues and time responses
Evidence for the Validity of the Berry-Robnik Surmise in a Periodically Pulsed Spin System
We study the statistical properties of the spectrum of a quantum dynamical
system whose classical counterpart has a mixed phase space structure consisting
of two regular regions separated by a chaotical one. We make use of a simple
symmetry of the system to separate the eigenstates of the time-evolution
operator into two classes in agreement with the Percival classification scheme
\cite{Per}. We then use a method firstly developed by Bohigas et. al.
\cite{BoUlTo} to evaluate the fractional measure of states belonging to the
regular class, and finally present the level spacings statistics for each class
which confirm the validity of the Berry-Robnik surmise in our model.Comment: 15 pages, 9 figures available upon request, Latex fil
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