Properties of ℛ-Sausages

This paper is concerned with the Steiner ratio. A number of properties about the structure of the flat sausage and -Sausage convex polytopes yielding the best Steiner ratio in two- and three-dimensional Euclidean space, and the topology of the Steiner Minimal Tree for the corresponding vertex sets, are presented.     

Waves in interplanetary shocks: a wind/WAVES study

We describe results from the first statistical study of waveform capture data during 67 interplanetary (IP) shocks with Mach numbers ranging from approximately 1-6. Most of the waveform captures and nearly 100% of the large amplitude waves were in the ramp region. Although solitary waves, Langmuir waves, and ion acoustic waves (IAWs) are all observed in the ramp region of the IP shocks, large amplitude IAWs dominate. The wave amplitude is correlated with the fast mode Mach number and with the shock strength. The observed waves produced anomalous resistivities from approximately 1-856 Omega.m (approximately 10(7) times greater than classical estimates.) The results are consistent with theory suggesting IAWs provide the primary dissipation for low Mach number shocks.     

New methods for the acquisition of ultra-wideline solid-state NMR spectra of spin-1/2 nuclides

The Wideband Uniform Rate Smooth Truncation - Carr-Purcell Meiboom-Gill (WURST-CPMG) pulse sequence was recently introduced as a new method of acquiring ultra-wideline solid-state NMR (SSNMR) patterns of quadrupolar nuclei (Chem. Phys. Lett. 464 (2008) 97). Herein, we describe the application of the WURST-CPMG pulse sequence to stationary samples (i.e., non-spinning or "static" samples) of various spin-1/2 nuclides ((119)Sn, (207)Pb, (199)Hg and (195)Pt) in order to examine its effectiveness for acquiring ultra-wideline SSNMR patterns. WURST-CPMG is compared to the CPMG and Cross Polarization (CP)-CPMG pulse sequences in select cases ((119)Sn and (207)Pb, respectively), and its usefulness in obtaining ultra-wideline SSNMR spectra in a piecewise fashion is explored. In addition, a preliminary investigation of pulses generated using optimal control theory (OCT) for the purpose of wideline excitation is presented; spectra acquired using these pulses are compared with standard, rectangular pulses of similar pulse powers. Both methods show much promise for acquiring high quality wideline patterns dominated by chemical shift anisotropy, with minimal distortions and significantly reduced experimental times.