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

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 $q$ is a root of unity of order $2r$ where $r>1$ is odd or congruent to $2$ modulo $4$. In this paper we consider the remaining cases where $r$ is congruent to zero modulo $4$ and produce invariants of $3$-manifolds with colored links, equipped with generalized spin structure. For a given $3$-manifold $M$, the relevant generalized spin structures are (non canonically) parametrized by $H^1(M;\mathbb C/2\mathbb Z)$.Comment: 13 pages, 16 figure

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

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

Nuclear Interaction Cross Sections for UltraHeavy Nuclei

We summarize additions to our data base of charge-changing cross sections for relativistic ultraheavy nuclei interacting in targets ranging from H to Pb. We have improved parametric fits to those cross sections as functions of energy and of projectile, target, and fragment charge. At high energies, we have determined cross sections for Au projectiles at 10.6 GeV /nucleon in targets of H, CH_2, C, Al, Cu, Sn, and Pb. Compared with cross sections at 1 GeV /n, fragment production is substantially changed, especially for the H target. These changes have important implications for calculations of interstellar propagation of ultraheavy nuclei. At lower energies, we have added Kr and Ag to our list of projectiles. Analysis of these data has led to a better understanding of the systematics of these cross sections, hence more physically meaningful parameterizations for fragmentation at high energies and for charge pickup

Rhodium complexes in p-C bond formation: Key role of a hydrido ligand

Olefin hydrophosphanation is an attractive route for the atom-economical synthesis of functionalized phosphanes. This reaction involves the formation of P-C and H-C bonds. Thus, complexes that contain both hydrido and phosphanido functionalities are of great interest for the development of effective and fast catalysts. Herein, we showcase the excellent activity of one of them, [Rh(Tp)H(PMe3)(PPh2)] (1), in the hydrophosphanation of a wide range of olefins. In addition to the required nucleophilicity of the phosphanido moiety to accomplish the P-C bond formation, the key role of the hydride ligand in 1 has been disclosed by both experimental results and DFT calculations. An additional Rh-H··· C stabilization in some intermediates or transition states favors the hydrogen transfer reaction from rhodium to carbon to form the H-C bond. Further support for our proposal arises from the poor activity exhibited by the related chloride complex [Rh(Tp)Cl(PMe3)(PPh2)] as well as from stoichiometric and kinetic studies

UHCR: A Cosmic Ray Mission to Study Nuclei in the Charge Range From 20 ≤Z ≤100

A definitive study of the elemental abundances of nuclei over the charge range of 20 ≤ Z ≤ 100 requires a satellite mission capable of obtaining high statistics and excellent charge resolution over the full charge range. Such a mission, utilizing an electronic instrument which is an evolution of the HEA0-3 Heavy Nuclei Experiment, is described here