Rb-sr ages of chondrules and carbonaceous chondrites

Rubidium-strontium and potassium-strontium isotope composition of carbonaceous chondrites and chondrules - age of carbonaceous meteorite

Vibration analysis of rotor blades with an attached concentrated mass

The effect of an attached concentrated mass on the dynamics of helicopter rotor blades is determined. The point transmission matrix method was used to define, through three completely automated computer programs, the natural vibrational characteristics (natural frequencies and mode shapes) of rotor blades. The problems of coupled flapwise bending, chordwise bending, and torsional vibration of a twisted nonuniform blade and its special subcase pure torsional vibration are discussed. The orthogonality relations that exist between the natural modes of rotor blades with an attached concentrated mass are derived. The effect of pitch, rotation, and point mass parameters on the collective, cyclic, scissor, and pure torsional modes of a seesaw rotor blade is determined

A Fermion-like description of condensed Bosons in a trap

A Bose-Einstein condensate of atoms, trapped in an axially symmetric harmonic potential, is considered. By averaging the spatial density along the symmetry direction over a length that preserves the aspect ratio, the system may be mapped on to a zero temperature noninteracting Fermi-like gas. The ``mock fermions'' have a state occupancy factor $(>>1)$ proportional to the ratio of the coherance length to the ``hard-core'' radius of the atom. The mapping reproduces the ground state properties of the condensate, and is used to estimate the vortex excitation energy analytically. The ``mock-fermion'' description predicts some novel collective excitation in the condensed phase.Comment: 11 pages, REVTE

Sensitivity analysis and approximation methods for general eigenvalue problems

Optimization of dynamic systems involving complex non-hermitian matrices is often computationally expensive. Major contributors to the computational expense are the sensitivity analysis and reanalysis of a modified design. The present work seeks to alleviate this computational burden by identifying efficient sensitivity analysis and approximate reanalysis methods. For the algebraic eigenvalue problem involving non-hermitian matrices, algorithms for sensitivity analysis and approximate reanalysis are classified, compared and evaluated for efficiency and accuracy. Proper eigenvector normalization is discussed. An improved method for calculating derivatives of eigenvectors is proposed based on a more rational normalization condition and taking advantage of matrix sparsity. Important numerical aspects of this method are also discussed. To alleviate the problem of reanalysis, various approximation methods for eigenvalues are proposed and evaluated. Linear and quadratic approximations are based directly on the Taylor series. Several approximation methods are developed based on the generalized Rayleigh quotient for the eigenvalue problem. Approximation methods based on trace theorem give high accuracy without needing any derivatives. Operation counts for the computation of the approximations are given. General recommendations are made for the selection of appropriate approximation technique as a function of the matrix size, number of design variables, number of eigenvalues of interest and the number of design points at which approximation is sought

Dynamic characteristics of rotor blades with pendulum absorbers

The point transmission matrix for a vertical plane pendulum on a rotating blade undergoing combined flapwise bending, and chordwise bending and torsion is derived. The equilibrium equation of the pendulum is linearized for small oscillations about the steady state. A FORTRAN program was written for the case of a vertical plane pendulum attached to a uniform blade with flapwise bending degree of freedom for cantilever boundary conditions. The frequency has a singular value right at the uncoupled pendulum natural frequency and thus introduces two frequencies corresponding to the nearest natural frequency of the blade without pendulum. In both of these modes it was observed that the pendulum deflection is large. One frequency can be thought of as a coupled pendulum frequency and the other as a coupled bending and pendulum frequency

Optimization of cascade blade mistuning under flutter and forced response constraints

In the development of modern turbomachinery, problems of flutter instabilities and excessive forced response of a cascade of blades that were encountered have often turned out to be extremely difficult to eliminate. The study of these instabilities and the forced response is complicated by the presence of mistuning; that is, small differences among the individual blades. The theory of mistuned cascade behavior shows that mistuning can have a beneficial effect on the stability of the rotor. This beneficial effect is produced by the coupling between the more stable and less stable flutter modes introduced by mistuning. The effect of mistuning on the forced response can be either beneficial or adverse. Kaza and Kielb have studied the effects of two types of mistuning on the flutter and forced response: alternate mistuning where alternte blades are identical and random mistuning. The objective is to investigate other patterns of mistuning which maximize the beneficial effects on the flutter and forced response of the cascade. Numerical optimization techniques are employed to obtain optimal mistuning patterns. The optimization program seeks to minimize the amount of mistuning required to satisfy constraints on flutter speed and forced response

Haldane Exclusion Statistics and the Boltzmann Equation

We generalize the collision term in the one-dimensional Boltzmann-Nordheim transport equation for quasiparticles that obey the Haldane exclusion statistics. For the equilibrium situation, this leads to the ``golden rule'' factor for quantum transitions. As an application of this, we calculate the density response function of a one-dimensional electron gas in a periodic potential, assuming that the particle-hole excitations are quasiparticles obeying the new statistics. We also calculate the relaxation time of a nuclear spin in a metal using the modified golden rule.Comment: version accepted for publication in J. of Stat. Phy