On invariant sets in Lagrangian graphs

In this exposition, we show that a Hamiltonian is always constant on a compact invariant connected subset which lies in a Lagrangian graph provided that the Hamiltonian and the graph are smooth enough. We also provide some counterexamples for the case that the Hamiltonians are not smooth enough.Comment: 4 page

Meeting report: Thunderstorms

Copyright @ 2007 Royal Meteorological Societ

Interferometer

A high resolution interferometer is described. The interferometer is insensitive to slight misalignment of its elements, avoids channeling in the spectrum, generates a maximum equal path fringe contrast, produces an even two sided interferogram without critical matching of the wedge angles of the beamsplitter and compensator wedges, and is optically phase tunable. The interferometer includes a mirror along the path of each beam component produced by the beamsplitter, for reflecting the beam component from the beamsplitter, for reflecting the beam component from the beamsplitter to a corresponding retroreflector and for reflecting the beam returned by the retroreflector back to the beamsplitter. A wedge located along each beam component path, is large enough to cover the retroreflector, so that each beam component passes through the wedge during movement towards the retroreflector and away therefrom

How much more can sunspots tell us about the solar dynamo?

Sunspot observations inspired solar dynamo theory and continue to do so. Simply counting them established the sunspot cycle and its period. Latitudinal distributions introduced the tough constraint that the source of sunspots moves equator-ward as the cycle progresses. Observations of Hale's polarity law mandated hemispheric asymmetry. How much more can sunspots tell us about the solar dynamo? We draw attention to a few outstanding questions raised by inherent sunspot properties. Namely, how to explain sunspot rotation rates, the incoherence of follower spots, the longitudinal spacing of sunspot groups, and brightness trends within a given sunspot cycle. After reviewing the first several topics, we then present new results on the brightness of sunspots in Cycle 24 as observed with the Helioseismic Magnetic Imager (HMI). We compare these results to the sunspot brightness observed in Cycle 23 with the Michelson Doppler Imager (MDI). Next, we compare the minimum intensities of five sunspots simultaneously observed by the Hinode Solar Optical Telescope Spectropolarimeter (SOT-SP) and HMI to verify that the minimum brightness of sunspot umbrae correlates well to the maximum field strength. We then examine 90 and 52 sunspots in the north and south hemisphere, respectively, from 2010 - 2012. Finally, we conclude that the average maximum field strengths of umbra 40 Carrington Rotations into Cycle 24 are 2690 Gauss, virtually indistinguishable from the 2660 Gauss value observed at a similar time in Cycle 23 with MDI

Comment on ``Superconducting PrBa_2Cu_3O_x''

Recently, Zou et al. (Phys. Rev. Lett. 80, 1074, 1998) reported the observation of bulk superconductivity (SC) for a PrBa_2Cu_3O_x (Pr123) single crystal grown by the traveling-solvent floating zone (TSFZ) method. The aim of this Comment is to show the inconsistency of the value of effective magnetic moment \mu_{eff} reported by Zou et al. (2.92\mu_B) with their magnetic susceptibility data. The estimation made directly from their data points gives a considerably smaller value of \mu_{eff}=2.09\mu_B. At the same time the values of mu_{eff}=2.9\mu_B and 3.1\mu_B were obtained for our Pr123 single crystals grown by flux method for H||ab-plane and H||c-axis, respectively. This suggests that Pr occupies only about a half of the RE sites in TSFZ crystal. The other half of the RE sites is occupied most probably by the nonmagnetic Ba. Noteworthy, SC with T_c=43 K was observed earlier for Pr_{0.5}Ca_{0.5}Ba_2Cu_3O_{7-y} thin films. Ba^{2+} has a larger ionic radius than Pr^{3+} and so the substitution of Ba for Pr could give a natural explanation not only for the SC in TSFZ Pr123 but also for the elongation of the distance between the CuO_2 planes observed by Zou et al.Comment: Slightly extended version of Comment accepted to Phys. Rev. Lett. (v.81, N24, 1998), tentatevely to be publ. 14Dec98. 1 page, REVTex; 1 EPS fi

Einstein equations in the null quasi-spherical gauge III: numerical algorithms

We describe numerical techniques used in the construction of our 4th order evolution for the full Einstein equations, and assess the accuracy of representative solutions. The code is based on a null gauge with a quasi-spherical radial coordinate, and simulates the interaction of a single black hole with gravitational radiation. Techniques used include spherical harmonic representations, convolution spline interpolation and filtering, and an RK4 "method of lines" evolution. For sample initial data of "intermediate" size (gravitational field with 19% of the black hole mass), the code is accurate to 1 part in 10^5, until null time z=55 when the coordinate condition breaks down.Comment: Latex, 38 pages, 29 figures (360Kb compressed

Tile drainage for increased production

Organized drainage districts in Iowa include approximately 6 million acres of land, representing an original investment of over $75,000,000. There are 18,519 miles of public drainage improvements (ditches, tile lines and levees). There is no record of the immense amount of private drainage work which has been done in Iowa, but it probably is far greater in extent and is more evenly spread over the state than the public drainage improvement. In spite of this, many thousands of acres of crops were lost or badly damaged in 1942 and 1943 because of inadequate drainage. Production of food can be increased by bringing into production much low, level and fertile Iowa land which is not being farmed because it is too wet. Efficiency in production also can be increased. Countless seepy hillsides in the rolling sections of the state are unproductive and interfere greatly with field operation of equipment

Pulsations and orbital modulation of the intermediate polar 1WGA J1958.2+3232

We present optical photometry, spectroscopy and photopolarimetry, as well as ASCA X-ray observations, of the recently discovered intermediate polar 1WGA J1958.2+3232. Through the first detection of an optical beat frequency, we confirm the previously tentative suggestion that the spin period of the white dwarf is twice the X-ray and optical pulsation period, which we also confirm in each case. We detect an orbital modulation in each of the U, B, V, R and I bands for the first time, and suggest that the true orbital period is the -1d alias of that previously suggested. We also confirm the presence of circular polarization in this system, detecting a variable polarization which has opposite signs in each of the B and R bands. The double peaked pulse profile and oppositely signed polarization pulses suggest that 1WGA J1958.2+3232 accretes onto both magnetic poles via a disc which is truncated relatively close to the white dwarf.Comment: All figures now included as postscrip