Weak solutions of the three-dimensional vorticity equation with vortex singularities

The use of a modified scheme for the dynamics of vortex singularities is shown to lead to a weak solution of the three-dimensional inviscid incompressible vorticity equation

Application of numerical methods to planetary radiowave scattering

Existing numerical techniques for the solution of scattering problems were investigated to determine those which might be applicable to planetary surface studies, with the goal of improving the interpretation of radar data from Venus, Mars, the Moon, and icy satellites. The general characteristics of the models are described along with computational concerns. In particular, the Numerical Electrogmatics Code (NEC) developed at the Lawrence Livermore Laboratory is discussed. Though not developed for random rough surfaces, the NEC contains elements which may be generalized and which could be valuable in the study of scattering by planetary surfaces

Subcentimeter-size particle distribution functions in planetary rings from Voyager radio and photopolarimeter occultation data

Analysis of measurements of the scattered and direct components of Voyager 1 radio occultation signals at 3.5 and 13 cm wavelengths yield estimates of the distribution functions of supracentimeter-size particles and thickness of relatively broad regions in Saturn's rings. If mearurements of signal amplitude at a shorter wavelength are combined with the previously analyzed data, the shape of the distribution functions characterizing the smaller particles can be constrained. If size distributions of arbitrary form were considered, many solutions are found that are consistent with the three available observations of signal amplitude. The best-fit power law was calculated to the three observations at three wavelengths for several of the embedded Saturn ringlets. Mie scattering theory predicts that the measured phase of the radio occultation signal is highly sensitive to particles ranging from 0.1 to 1.0 wavelengths in size, thus additional constraints on the subcentimeter-size distribution functions for both the Saturn and Uranus rings can in principle be derived from radio phase measurements

Real-time decoding of question-and-answer speech dialogue using human cortical activity.

Natural communication often occurs in dialogue, differentially engaging auditory and sensorimotor brain regions during listening and speaking. However, previous attempts to decode speech directly from the human brain typically consider listening or speaking tasks in isolation. Here, human participants listened to questions and responded aloud with answers while we used high-density electrocorticography (ECoG) recordings to detect when they heard or said an utterance and to then decode the utterance's identity. Because certain answers were only plausible responses to certain questions, we could dynamically update the prior probabilities of each answer using the decoded question likelihoods as context. We decode produced and perceived utterances with accuracy rates as high as 61% and 76%, respectively (chance is 7% and 20%). Contextual integration of decoded question likelihoods significantly improves answer decoding. These results demonstrate real-time decoding of speech in an interactive, conversational setting, which has important implications for patients who are unable to communicate

Optical polarimetric monitoring of the type II-plateau SN 2005af

Aims. Core-collapse supernovae may show significant polarization that implies non-spherically symmetric explosions. We observed the type II-plateau SN 2005af using optical polarimetry in order to verify whether any asphericity is present in the supernova temporal evolution. Methods. We used the IAGPOL imaging polarimeter to obtain optical linear polarization measurements in R (five epochs) and V (one epoch) broadbands. Interstellar polarization was estimated from the field stars in the CCD frames. The optical polarimetric monitoring began around one month after the explosion and lasted ~30 days, between the plateau and the early nebular phase. Results. The weighted mean observed polarization in R band was [1.89 +/- 0.03]% at position angle (PA) 54 deg. After foreground subtraction, the level of the average intrinsic polarization for SN 2005af was ~0.5% with a slight enhancement during the plateau phase and a decline at early nebular phase. A rotation in PA on a time scale of days was also observed. The polarimetric evolution of SN 2005af in the observed epochs is consistent with an overall asphericity of ~20% and an inclination of ~30 deg. Evidence for a more complex, evolving asphericity, possibly involving clumps in the SN 2005af envelope, is found.Comment: 6 pages, 5 figures, to be published A&

Green's functions for multidimensional neutron transport in a slab

The integral form of the one-speed, steady-state Boltzmann transport equation is solved for a point source in a homogeneous, isotropically scattering slab. In addition, solutions are obtained for line sources and plane sources in the slab, both normal and parallel to the slab faces. Using Fuorier and Laplace transforms, the problem is reduced to that of solving a 1-dimensional integral equation with a difference kernel. This equation is transformed into a singular integral equation which is solved using standard methods. The Green's functions are subsequently obtained as generalized eigenfunction expansions over the spectrum of the 1-dimensional integral operator. This form yields a simple solution far from the source, and alternate expressions are obtained to facilitate evaluation near the source. In a thick slab the exact solutions are shown to reduce to simple closed expressions plus correction terms that decrease exponentially as the slab thickness increases. Most of the work previously done in multidimensional transport in slabs is shown to be easily reproduced using this theory in the thick-slab approximation. Also, virtually all other problems of this type can be solved using the theory presented here. In particular, the density from a pencil beam of particles normally incident to the slab is obtained

Satin Spar from Dubuque

Located less than six miles south of Dubuque and one and three-fourth miles due west of Massey station on the Chicago, Milwaukee & St. Paul Railroad are some curious spar caves as they are appropriately called. In these caverns are some occurrences of satin spar that are very unusual and of much interest. It is doubtful whether there is another locality where such peculiar forms of calcite are found, two varieties being associated together in the stalactites. The latter have also undergone a change in structure since first formed

Occurrence of Zinc in Northeastern Iowa

In the Upper Mississippi Valley for a considerable period after the mines began to be operated much more lead than zinc was produced. It was not until 1860 that the latter metal came into market. Since then the zinc production has rapidly increased. During the ten years previous to 1882 the output of zinc more than doubled that of lead, while in 1889, according to the last federal census report the proportion between the two was as 18 to 1 for the entire region