On the number of trees with n terminal nodes

Number of trees with arbitrary number of terminal node

Outline bibliography, and KWIC index on mechanical theorem proving and its applications

Bibliography and KWIC index on mechanical theorem proving and its application

Statistics of the Island-Around-Island Hierarchy in Hamiltonian Phase Space

The phase space of a typical Hamiltonian system contains both chaotic and regular orbits, mixed in a complex, fractal pattern. One oft-studied phenomenon is the algebraic decay of correlations and recurrence time distributions. For area-preserving maps, this has been attributed to the stickiness of boundary circles, which separate chaotic and regular components. Though such dynamics has been extensively studied, a full understanding depends on many fine details that typically are beyond experimental and numerical resolution. This calls for a statistical approach, the subject of the present work. We calculate the statistics of the boundary circle winding numbers, contrasting the distribution of the elements of their continued fractions to that for uniformly selected irrationals. Since phase space transport is of great interest for dynamics, we compute the distributions of fluxes through island chains. Analytical fits show that the "level" and "class" distributions are distinct, and evidence for their universality is given.Comment: 31 pages, 13 figure

On the Spectrum of the Resonant Quantum Kicked Rotor

It is proven that none of the bands in the quasi-energy spectrum of the Quantum Kicked Rotor is flat at any primitive resonance of any order. Perturbative estimates of bandwidths at small kick strength are established for the case of primitive resonances of prime order. Different bands scale with different powers of the kick strength, due to degeneracies in the spectrum of the free rotor.Comment: Description of related published work has been expanded in the Introductio

Extent and mechanism of sealing in transected giant axons of squid and earthworms

Transected axons are often assumed to seal at their cut ends by the formation of continuous membrane barriers that allow for the restoration of function in the axonal stumps. We have used several electrophysiological measures (membrane potential, input resistance, injury current density) and several morphological measures (phase-contrast, video-enhanced differential interference contrast, light, and electron microscopies) of living and fixed material to assess the extent and mechanism of sealing within hours after transecting giant axons of squid (Loligo pealeiand Sepioteuthis lessoniana) and earthworms (Lumbricus terrestris). Our electrophysiological data suggest that the proximal and distal ends of transected squid giant axons do not completely seal within 2.5 hr in physiological saline. In contrast, the same set of measures suggest that proximal and distal ends of transected earthworm giant axons seal within 1 hr in physiological saline. Our morphological data show that the cut ends of both squid and earthworm axons constrict, but that a 20- 70-am-diameter opening always remains at the cut end that is filled with vesicles. Axonal transection induces the formation of vesicles that are observed in the axoplasm within minutes in standard salines and that rapidly migrate to the cut ends. These injury-induced vesicles are loosely packed near the cut ends of squid giant axons, which do not functionally seal within 2.5 hr of transection. In contrast, vesicles formed a tightly packed plug at the cut ends of earthworm medial giant axons, which do functionally seal within 1 hr of transection in physiological saline. Since we detect no single continuous membrane that spans the cut end, sealing does not appear to occur by the fusion of constricted axolemmal membrane or the formation of a membranous partition at the cut end. Rather, our data are consistent with the hypothesis that a tightly packed vesicular plug is responsible for sealing of earthworm giant axons.This work was supported in part by NIH Grant NS31256 and ONR Grant N00014-90-J-1137 to H.M.F., an NIAAA fellowship to T.L.K., and an ATP grant to G.D.B.Neuroscienc

Spin Diffusion in Double-Exchange Manganites

The theoretical study of spin diffusion in double-exchange magnets by means of dynamical mean-field theory is presented. We demonstrate that the spin-diffusion coefficient becomes independent of the Hund's coupling JH in the range of parameters JH*S >> W >> T, W being the bandwidth, relevant to colossal magnetoresistive manganites in the metallic part of their phase diagram. Our study reveals a close correspondence as well as some counterintuitive differences between the results on Bethe and hypercubic lattices. Our results are in accord with neutron scattering data and with previous theoretical work for high temperatures.Comment: 4.0 pages, 3 figures, RevTeX 4, replaced with the published versio

Particle Acceleration, Magnetic Field Generation, and Associated Emission in Collisionless Relativistic Jets

Nonthermal radiation observed from astrophysical systems containing relativistic jets and shocks, e.g., active galactic nuclei (AGNs), gamma-ray bursts (GRBs), and Galactic microquasar systems usually have power-law emission spectra. Recent PIC simulations using injected relativistic electron-ion (electro-positron) jets show that acceleration occurs within the downstream jet. Shock acceleration is a ubiquitous phenomenon in astrophysical plasmas. Plasma waves and their associated instabilities (e.g., the Buneman instability, other two-streaming instability, and the Weibel instability) created in the shocks are responsible for particle (electron, positron, and ion) acceleration. The simulation results show that the Weibel instability is responsible for generating and amplifying highly nonuniform, small-scale magnetic fields. These magnetic fields contribute to the electron's transverse deflection behind the jet head. The ``jitter'' radiation from deflected electrons has different properties than synchrotron radiation which assumes a uniform magnetic field. This jitter radiation may be important to understanding the complex time evolution and/or spectral structure in gamma-ray bursts, relativistic jets, and supernova remnants.Comment: 4 pages, 3 figures, contributed talk at the workshop: High Energy Phenomena in Relativistic Outflows (HEPRO), Dublin, 24-28 September 2007. Fig. 3 is replaced by the correct versio

Spin Dynamics of a Canted Antiferromagnet in a Magnetic Field

The spin dynamics of a canted antiferromagnet with a quadratic spin-wave dispersion near \vq =0 is shown to possess a unique signature. When the anisotropy gap is negligible, the spin-wave stiffness \dsw (\vq, B) = (\omega_{\vq}-B)/q^2 depends on whether the limit of zero field or zero wavevector is taken first. Consequently, \dsw is a strong function of magnetic field at a fixed wavevector. Even in the presence of a sizeable anisotropy gap, the field dependence of both \dsw and the gap energy distinguishes a canted antiferromagnet from a phase-separated mixture containing both ferromagnetic and antiferromagnetic regions.Comment: 10 pages, 3 figure

Effect of noise for two interacting particles in a random potential

We investigated the effect of noise on propagation of two interacting particles pairs in a quasi one--dimensional random potential. It is shown that pair diffusion is strongly enhanced by short range interaction comparing with the non--interacting case.Comment: 8 Latex pages + 3 postscript figures uu- compressed submitted to Europhysics Letter