3,794 research outputs found
Perturbation analysis of the limit cycle of the free van der Pol equation
A power series expansion in the damping parameter, epsilon, of the limit cycle of the free van der Pol equation is constructed and analyzed. Coefficients in the expansion are computed in exact rational arithmetic using the symbolic manipulation system MACSYMA and using a FORTRAN program. The series is analyzed using Pade approximants. The convergence of the series for the maximum amplitude of the limit cycle is limited by two pair of complex conjugate singularities in the complex epsilon-plane. A new expansion parameter is introduced which maps these singularities to infinity and leads to a new expansion for the amplitude which converges for all real values of epsilon. Amplitudes computed from this transformed series agree very well with reported numerical and asymptotic results. For the limit cycle itself, convergence of the series expansion is limited by three pair of complex conjugate branch point singularities. Two pair remain fixed throughout the cycle, and correspond to the singularities found in the maximum amplitude series, while the third pair moves in the epsilon-plane as a function of t from one of the fixed pairs to the other. The limit cycle series is transformed using a new expansion parameter, which leads to a new series that converges for larger values of epsilon
Comparison of uniform perturbation solutions and numerical solutions for some potential flows past slender bodies
Approximate solutions for potential flow past an axisymmetric slender body and past a thin airfoil are calculated using a uniform perturbation method and then compared with either the exact analytical solution or the solution obtained using a purely numerical method. The perturbation method is based upon a representation of the disturbance flow as the superposition of singularities distributed entirely within the body, while the numerical (panel) method is based upon a distribution of singularities on the surface of the body. It is found that the perturbation method provides very good results for small values of the slenderness ratio and for small angles of attack. Moreover, for comparable accuracy, the perturbation method is simpler to implement, requires less computer memory, and generally uses less computation time than the panel method. In particular, the uniform perturbation method yields good resolution near the regions of the leading and trailing edges where other methods fail or require special attention
Non semi-simple sl(2) quantum invariants, spin case
Invariants of 3-manifolds from a non semi-simple category of modules over a
version of quantum sl(2) were obtained by the last three authors in
[arXiv:1404.7289]. In their construction the quantum parameter is a root of
unity of order where is odd or congruent to modulo . In this
paper we consider the remaining cases where is congruent to zero modulo
and produce invariants of -manifolds with colored links, equipped with
generalized spin structure. For a given -manifold , the relevant
generalized spin structures are (non canonically) parametrized by
.Comment: 13 pages, 16 figure
Lined Seahorse Distribution, Abundance, and Habitat Preferences from the VIMS Trawl Survey 1979-2000
Study of high-speed angular-contact ball bearings under dynamic load
Research program studies behavior of specific high-speed, angular-contact ball bearings. Program is aimed at detailed investigation of ball-separator behavior and lubrication surface-finish effects in a specific gyro wheel
Detecting multivariate interactions in spatial point patterns with Gibbs models and variable selection
We propose a method for detecting significant interactions in very large
multivariate spatial point patterns. This methodology develops high dimensional
data understanding in the point process setting. The method is based on
modelling the patterns using a flexible Gibbs point process model to directly
characterise point-to-point interactions at different spatial scales. By using
the Gibbs framework significant interactions can also be captured at small
scales. Subsequently, the Gibbs point process is fitted using a
pseudo-likelihood approximation, and we select significant interactions
automatically using the group lasso penalty with this likelihood approximation.
Thus we estimate the multivariate interactions stably even in this setting. We
demonstrate the feasibility of the method with a simulation study and show its
power by applying it to a large and complex rainforest plant population data
set of 83 species
A New Limit on the Antiproton Lifetime
Measurements of the cosmic ray pbar/p ratio are compared to predictions from
an inhomogeneous disk-diffusion model of pbar production and propagation within
the Galaxy, combined with a calculation of the modulation of the interstellar
cosmic ray spectra as the particles propagate through the heliosphere to the
Earth. The predictions agree with the observed pbar/p spectrum. Adding a finite
pbar lifetime to the model, we obtain the limit tau_pbar > 0.8 Myr (90 % C.L.).Comment: 13 pages, 3 encapsulated Postscript figures, uses AASTeX; accepted by
Astrophysical Journal; minor change
Search for muonic decays of the antiproton at the Fermilab Antiproton Accumulator
A search for antiproton decay has been made at the Fermilab Antiproton
Accumulator. Limits are placed on six antiproton decay modes which contain a
final-state muon. At the 90% C.L. we find that
tau/B(mu gamma) > 5.0 x 10^4 yr,
tau/B(mu pi0) > 4.8 x 10^4 yr,
tau/B(mu eta) > 7.9 x 10^3 yr,
tau/B(mu gamma gamma) > 2.3 x 10^4 yr,
tau/B(mu K0S > 4.3 x 10^3 yr, and
tau/B(mu K0L) > 6.5 x 10^3 yr.Comment: 8 pages + 3 Postscript figure
Search for antiproton decay at the Fermilab Antiproton Accumulator
A search for antiproton decay has been made at the Fermilab Antiproton
Accumulator. Limits are placed on thirteen antiproton decay modes. The results
include the first explicit experimental limits on the muonic decay modes of the
antiproton, and the first limits on the decay modes e- gamma gamma, and e-
omega. The most stringent limit is for the decay mode pbar-> e- gamma. At 90%
C.L. we find that tau/B(pbar-> e- gamma) > 7 x 10^5 yr. The most stringent
limit for decay modes with a muon in the final state is for the decay pbar->
mu- gamma. At 90% C.L. we find that tau/B(pbar-> mu- gamma) > 5 x 10^4 yr.Comment: 20 pages, 8 figures. Submitted to Phys. Rev. D. Final results on 13
channels (was 15) are presente
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