Barnes Hospital Record

https://digitalcommons.wustl.edu/bjc_barnes_record/1053/thumbnail.jp

The Singularity in Generic Gravitational Collapse Is Spacelike, Local, and Oscillatory

A longstanding conjecture by Belinskii, Khalatnikov, and Lifshitz that the singularity in generic gravitational collapse is spacelike, local, and oscillatory is explored analytically and numerically in spatially inhomogeneous cosmological spacetimes. With a convenient choice of variables, it can be seen analytically how nonlinear terms in Einstein's equations control the approach to the singularity and cause oscillatory behavior. The analytic picture requires the drastic assumption that each spatial point evolves toward the singularity as an independent spatially homogeneous universe. In every case, detailed numerical simulations of the full Einstein evolution equations support this assumption.Comment: 7 pages includes 4 figures. Uses Revtex and psfig. Received "honorable mention" in 1998 Gravity Research Foundation essay contest. Submitted to Mod. Phys. Lett.

The topological description of coronal magnetic fields

Determining the structure and behavior of solar coronal magnetic fields is a central problem in solar physics. At the photosphere, the field is believed to be strongly localized into discrete flux tubes. After providing a rigorous definition of field topology, how the topology of a finite collection of flux tubes may be classified is discussed

Solving the Tower of Hanoi with Random Moves

We prove the exact formulae for the expected number of moves to solve several variants of the Tower of Hanoi puzzle with 3 pegs and n disks, when each move is chosen uniformly randomly from the set of all valid moves. We further present an alternative proof for one of the formulae that couples a theorem about expected commute times of random walks on graphs with the delta-to-wye transformation used in the analysis of three-phase AC systems for electrical power distribution

Strategic Planning: A Review of Grantee Practices

Provides an analysis of the strategic planning process of nonprofit organizations funded by the foundation, including the process of organizational change. Includes recommendations

A Modified Version of the Waxman Algorithm

The iterative algorithm recently proposed by Waxman for solving eigenvalue problems, which relies on the method of moments, has been modified to improve its convergence considerably without sacrificing its benefits or elegance. The suggested modification is based on methods to calculate low-lying eigenpairs of large bounded hermitian operators or matrices

Domain - wall - induced magnetoresistance in pseudo spin-valve/superconductor hybrid structures

We have studied the interaction between magnetism and superconductivity in a pseudo-spin-valve structure consisting of a Co/Cu/Py/Nb layer sequence. We are able to control the magnetization reversal process and monitor it by means of the giant magnetoresistance effect during transport measurements. By placing the superconducting Nb-film on the top of the permalloy (Py) electrode instead of putting it in between the two ferromagnets, we minimize the influence of spin scattering or spin accumulation onto the transport properties of Nb. Magnetotransport data reveal clear evidence that the stray fields of domain walls (DWs) in the pseudo-spin-valve influence the emerging superconductivity close to the transition temperature by the occurrence of peak-like features in the magneto-resistance characteristic. Direct comparison with magnetometry data shows that the resistance peaks occur exactly at the magnetization reversal fields of the Co and Py layers, where DWs are generated. For temperatures near the superconducting transition the amplitude of the DW-induced magnetoresistance increases with decreasing temperature, reaching values far beyond the size of the giant magnetoresistive response of our structure in the normal state.Comment: 20 pages, 4 figure

Automatic adaptive grid refinement for the Euler equations

A method of adaptive grid refinement for the solution of the steady Euler equations for transonic flow is presented. Algorithm automatically decides where the coarse grid accuracy is insufficient, and creates locally uniform refined grids in these regions. This typically occurs at the leading and trailing edges. The solution is then integrated to steady state using the same integrator (FLO52) in the interior of each grid. The boundary conditions needed on the fine grids are examined and the importance of treating the fine/coarse grid inerface conservatively is discussed. Numerical results are presented