Composing and Factoring Generalized Green's Operators and Ordinary Boundary Problems

We consider solution operators of linear ordinary boundary problems with "too many" boundary conditions, which are not always solvable. These generalized Green's operators are a certain kind of generalized inverses of differential operators. We answer the question when the product of two generalized Green's operators is again a generalized Green's operator for the product of the corresponding differential operators and which boundary problem it solves. Moreover, we show that---provided a factorization of the underlying differential operator---a generalized boundary problem can be factored into lower order problems corresponding to a factorization of the respective Green's operators. We illustrate our results by examples using the Maple package IntDiffOp, where the presented algorithms are implemented.Comment: 19 page

Ising pyrochlore magnets: Low temperature properties, ice rules and beyond

Pyrochlore magnets are candidates for spin-ice behavior. We present theoretical simulations of relevance for the pyrochlore family R2Ti2O7 (R= rare earth) supported by magnetothermal measurements on selected systems. By considering long ranged dipole-dipole as well as short-ranged superexchange interactions we get three distinct behaviours: (i) an ordered doubly degenerate state, (ii) a highly disordered state with a broad transition to paramagnetism, (iii) a partially ordered state with a sharp transition to paramagnetism. Thus these competing interactions can induce behaviour very different from conventional ``spin ice''. Closely corresponding behaviour is seen in the real compounds---in particular Ho2Ti2O7 corresponds to case (iii) which has not been discussed before, rather than (ii) as suggested earlier.Comment: 5 pages revtex, 4 figures; some revisions, additional data, additional co-authors and a changed title. Basic ideas of paper remain the same but those who downloaded the original version are requested to get this more complete versio

High-spatial-resolution passive microwave sounding systems

During this period the emphasis was on the following: (1) further design, construction, and testing of the improved 54-GHz portion of the 54-118 GHz microwave temperature sounder (MTS) aircraft radiometer system in preparation for ER-2 observations in July 1991; and (2) final analysis and documentation of procedures for detecting and analyzing thermal waves in our 118-GHz MTS imagery. In addition, we have new unpublished measurements of dry-air attenuation at frequencies of 54 to 66 GHz and over a temperature range of 280K to 326K; these measurements should enable us to improve further our atmospheric transmittance models. It was further noted that the proposed SSMIS conical-scanning microwave spectrometer on the military DMSP Block 5D-3 spacecraft designed to measure stratospheric and mesospheric temperature profiles will be observing the Zeeman-split oxygen lines with sufficient spectral resolution that the changing Doppler shifts with view angle will substantially degrade the potential system performance unless remedied; this was briefly studied and documented

Destroying coherence in high temperature superconductors with current flow

The loss of single-particle coherence going from the superconducting state to the normal state in underdoped cuprates is a dramatic effect that has yet to be understood. Here, we address this issue by performing angle resolved photoemission spectroscopy (ARPES) measurements in the presence of a transport current. We find that the loss of coherence is associated with the development of an onset in the resistance, in that well before the midpoint of the transition is reached, the sharp peaks in the ARPES spectra are completely suppressed. Since the resistance onset is a signature of phase fluctuations, this implies that the loss of single-particle coherence is connected with the loss of long-range phase coherence.Comment: 7 pages, 7 figure