On the number of trees with n terminal nodes

Number of trees with arbitrary number of terminal node

Characterization of low-energy magnetic excitations in chromium

The low-energy excitations of Cr, i.e. the Fincher-Burke (FB) modes, have been investigated in the transversely polarized spin-density-wave phase by inelastic neutron scattering using a single-(Q+-) crystal with a propagation vector (Q+-) parallel to [0,0,1]. The constant-momentum-transfer scans show that the energy spectra consist of two components, namely dispersive FB modes and an almost energy-independent cross section. Most remarkably, we find that the spectrum of the FB modes exhibits one peak at 140 K near Q = (0,0,0.98) and two peaks near Q = (0,0,1.02), respectively. This is surprising because Cr crystallizes in a centro-symmetric bcc structure. The asymmetry of those energy spectra decreases with increasing temperature. In addition, the observed magnetic peak intensity is independent of Q suggesting a transfer of spectral-weight between the upper and lower FB modes. The energy-independent cross section is localized only between the incommensurate peaks and develops rapidly with increasing temperature.Comment: 6 pages, 8 figure

Spin Dynamics of Double-Exchange Manganites with Magnetic Frustration

This work examines the effects of magnetic frustration due to competing ferromagnetic and antiferromagnetic Heisenberg interactions on the spin dynamics of the double-exchange model. When the local moments are non-colinear, a charge-density wave forms because the electrons prefer to sit on lines of sites that are coupled ferromagnetically. With increasing hopping energy, the local spins become aligned and the average spin-wave stiffness increases. Phase separation is found only within a narrow range of hopping energies. Results of this work are applied to the field-induced jump in the spin-wave stiffness observed in the manganite Pr$_{1-x}$Ca$_x$MnO$_3$ with $0.3 \le x \le 0.4$.Comment: 10 pages, 3 figure

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

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

Bibliography and KWIC index on mechanical theorem proving and its application

Double Exchange in a Magnetically Frustrated System

This work examines the magnetic order and spin dynamics of a double-exchange model with competing ferromagnetic and antiferromagnetic Heisenberg interactions between the local moments. The Heisenberg interactions are periodically arranged in a Villain configuration in two dimensions with nearest-neighbor, ferromagnetic coupling $J$ and antiferromagnetic coupling $-\eta J$. This model is solved at zero temperature by performing a $1/\sqrt{S}$ expansion in the rotated reference frame of each local moment. When $\eta$ exceeds a critical value, the ground state is a magnetically frustrated, canted antiferromagnet. With increasing hopping energy $t$ or magnetic field $B$, the local moments become aligned and the ferromagnetic phase is stabilized above critical values of $t$ or $B$. In the canted phase, a charge-density wave forms because the electrons prefer to sit on lines of sites that are coupled ferromagnetically. Due to a change in the topology of the Fermi surface from closed to open, phase separation occurs in a narrow range of parameters in the canted phase. In zero field, the long-wavelength spin waves are isotropic in the region of phase separation. Whereas the average spin-wave stiffness in the canted phase increases with $t$ or $\eta$, it exhibits a more complicated dependence on field. This work strongly suggests that the jump in the spin-wave stiffness observed in Pr$_{1-x}$Ca$_x$MnO$_3$ with $0.3 \le x \le 0.4$ at a field of 3 T is caused by the delocalization of the electrons rather than by the alignment of the antiferromagnetic regions.Comment: 28 pages, 12 figure

The value of improved (ERS) information based on domestic distribution effects of U.S. agriculture crops

The value of improving information for forecasting future crop harvests was investigated. Emphasis was placed upon establishing practical evaluation procedures firmly based in economic theory. The analysis was applied to the case of U.S. domestic wheat consumption. Estimates for a cost of storage function and a demand function for wheat were calculated. A model of market determinations of wheat inventories was developed for inventory adjustment. The carry-over horizon is computed by the solution of a nonlinear programming problem, and related variables such as spot and future price at each stage are determined. The model is adaptable to other markets. Results are shown to depend critically on the accuracy of current and proposed measurement techniques. The quantitative results are presented parametrically, in terms of various possible values of current and future accuracies

Polymers for spacecraft hardware materials specifications and engineering information Monthly technical progress report no. 18, Nov. 10 - Dec. 9, 1965

Chemical test procedures for analyzing potting compound bases for spacecraft construction material