Search

The magnetohydrodynamics (MHD) problem is most often studied in a framework where Dirichlet type boundary conditions on the velocity field is imposed. In this Note, we study the (MHD) system with pressure boundary condition, together with zero tangential trace for the velocity and the magnetic field. In a three-dimensional bounded possibly multiply connected domain, we first prove the existence of weak solutions in the Hilbert case, and later, the regularity in $W^{1,p}(\Omega)$ for $p\geq 2$ and in $W^{2,p}(\Omega)$ for $p\geq 6/5$ using the regularity results for some Stokes and elliptic problems with this type of boundary conditions. Furthermore, under the condition of small data, we obtain the existence and uniqueness of solutions in $W^{1,p}(\Omega)$ for $3/2

We show that the motion of the neutral masses in an accretion disk orbiting a black hole creates a general-relativistic magnetic-like (gravitomagnetic) field that vertically accelerates neutral particles near the accretion disk upward and then inward toward the axis of the accretion disk. Even though this gravitomagnetic field alone does not achieve collimated jets, it is a novel means to identify one general relativistic effect from a much more complicated problem. In addition, as the accelerated material above or below the accretion disk nears the axis with a nearly vertical direction, a frame-dragging effect twists the trajectories around the axis thus contributing to the formation of collimated bipolar jets., Comment: 7 pages, 4 figures, typos corrected

GRAND is an array of position sensitive proportional wire chambers (PWCs) located at 86.2 degrees W, 41.7 degrees N at an elevation of 220 m adjacent to the campus of the University of Notre Dame with 82 square meters of total muon detector area. The geometry of the PWCs allows the angles of the charged secondary muon tracks to be measured to +/- 0.3 deg in each of two orthogonal planes. Muons are 99% differentiated from electrons by means of a 51 mm steel plate in each detector., Comment: 4 pages. For 2007 ICRC in Merida, Mexico

Project GRAND, a proportional wire chamber array, is used to examine the decreased counting rate of ground level muons during the Forbush decrease event of September 11, 2005. Data are presented and compared to that of other cosmic ray monitors. A directional study of the Forbush decrease was undertaken and precursor anisotropies to this geomagnetic storm were studied utilizing GRAND's angular resolution., Comment: 4 pages. For 2007 ICRC in Merida, Mexico

On October 28, 2003 an earthward-directed coronal mass ejection (CME) was observed from SOHO/LASCO imagery in conjunction with an X17 solar flare. The CME, traveling at nearly 2000 km/s, impacted the Earth on October 29, 2003 causing ground-based particle detectors to register a counting rate drop known as a Forbush decrease. In addition to affecting the rate of cosmic rays, the CME was also responsible for causing anisotropies in the direction of incidence. Data from Project GRAND, an array of proportional wire chambers, are presented during the time of this Forbush decrease. A simple model for CME propagation is proposed and we present an argument based on gyroradius that shows that a magnetic field of the radius calculated for the ejecta is sufficient to deflect energetic charged particles of an energy detectable by GRAND.

Project GRAND, a proportional wire chamber array, is used to examine the increased counting rate of single muons during the solar Ground Level Event (GLE) of April 15, 2001. Data are presented and compared to our background rates and to that of neutron monitor stations. This GLE is seen with a statistical significance of 6.1 sigma., Comment: To be presented at the XXVIII International Cosmic Ray Conference, Tsukuba, Japan

Project GRAND is a 100m x 100m air shower array of position sensitive proportional wire chambers (PWCs) located at 41.7 degrees North and 86.2 degrees West at an elevation of 220m above sea level. Its convenient location adjacent to the campus of the University of Notre Dame makes it a good training ground for students. There are 64 stations each with eight 1.29 m^2 PWCs. The geometry of the stations allows for the angles of charged secondaries to be determined to within 0.26 degrees in each of two orthogonal planes; muons are differentiated from electrons and hadrons by means of a steel plate. Two triggers are run simultaneously: a multiple hit coincidence trigger, rich in extensive air showers, and a single track trigger, rich in secondary muon tracks. The former trigger is sensitive to primary energies greater than ~100 TeV, the latter to energies greater than ~10 GeV., Comment: To be presented at the XXVIII International Cosmic Ray Conference, Tsukuba, Japan

Project GRAND is a 100m x 100m air shower array of proportional wire chambers (PWCs). There are 64 stations each with eight 1.29 m^2 PWC planes arranged in four orthogonal pairs placed vertically above one another to geometrically measure the angles of charged secondaries. A steel plate above the bottom pair of PWCs differentiates muons (which pass undeflected through the steel) from non-penetrating particles. FLUKA Monte Carlo studies show that a TeV gamma ray striking the atmosphere at normal incidence produces 0.23 muons which reach ground level where their angles and identities are measured. Thus, paradoxically, secondary muons are used as a signature for gamma ray primaries. The data are examined for possible angular and time coincidences with eight gamma ray bursts (GRBs) detected by BATSE. Seven of the GRBs were selected because of their good acceptance by GRAND and high BATSE Fluence. The eighth GRB was added due to its possible coincident detection by Milagrito. For each of the eight candidate GRBs, the number of excess counts during the BATSE T90 time interval and within plus or minus five degrees of BATSE's direction was obtained. The highest statistical significance reported in this paper (2.7 sigma) is for the event that was predicted to be the most likely to be observed (GRB 971110)., Comment: To be presented at the XXVIII International Cosmic Ray Conference, Tsukuba, Japan

The counting rate of single muon tracks from the Project GRAND proportional wire chamber array is examined during the Ground Level Event (GLE) of April 15, 2001. The GLE was seen by neutron monitor stations shortly after the time of the solar X-ray flare. GRAND's single muon data are presented and compared with neutron monitor data from Climax, Newark, and Oulu. The single muon data have mean primary hadron energies higher than those of these neutron monitor stations and so contain information about higher energy hadrons. For the single muon data for Project GRAND, the GLE is detected at a statistical significance of 6.1-sigma., Comment: 9 pages, 6 figures

We explore several models which might be proposed to explain recent possible detections of high-energy (TeV) gamma rays in association with low-energy gamma-ray bursts (GRBs). Likely values (and/or upper limits) for the source energies in low- and high-energy gamma rays and hadrons are deduced for the burst sources associated with possible TeV gamma-ray detections by the Project GRAND array. Possible spectra for energetic gammas are deduced for three models: 1) inverse-Compton scattering of ambient photons from relativistic electrons; 2) proton-synchrotron emission; and 3) inelastic scattering of relativistic protons from ambient photons creating high-energy neutral pions, which decay into high-energy photons. These models rely on some basic assumptions about the GRB properties, e.g. that: the low- and high-energy gamma rays are produced at the same location; the time variability of the high-energy component can be estimated from the FWHM of the highest peak in the low-energy gamma ray light curve; and the variability-luminosity relation of Fenimore & Ramirez-Ruiz (2000) gives a reliable estimate of the redshifts of these bursts. We also explore the impact of each of these assumptions upon our models. We conclude that the energetic requirements are difficult to satisfy for any of these models unless, perhaps, either the photon beaming angle is much narrower for the high-energy component than for the low-energy GRB or the bursts occur at very low redshifts (z<0.01). Nevertheless, we find that the energetic requirements are most easily satisfied if TeV gamma rays are produced predominantly by inverse-Compton scattering with a magnetic field strength well below equipartition or by proton-synchrotron emission with a magnetic field strength near equipartition., Comment: 39 pages, 7 figures, accepted for publication in Astroparticle Physics

Project GRAND is an array of proportional wire chambers composed of 64 stations with each station containing eight proportional wire planes and a 50 mm steel plate. The proportional wire planes together with the steel absorber allow a measurement of the angle and identity of single muon tracks. Of the two data-taking triggers, one is for single tracks. Since the rate of single muon tracks at sea level above the muon energy threshold of the experiment (0.1 GeV) is substantial, good statistics are available by accumulating several years of data. A map in sidereal right ascension and declination is obtained as well as one in a sun-centered coordinate system in order to study the sidereal and solar effects separately., Comment: 4 pages; 27th ICRC, p. 4103

Project GRAND is an extensive air shower array of proportional wire chambers. It has 64 stations in a 100m x 100m area; each station has eight planes of proportional wire chambers with a 50 mm steel absorber plate above the bottom two planes. This arrangement of planes, each 1.25 square meters of area, allow an angular measurement for each track to 0.25 degrees in each of two projections. The steel absorber plate allows a measurement of the identity of each muon track to 96% accuracy. Two data-taking triggers allow data to be simultaneously taken for a) extensive air showers (multiple coincidence station hits) at about 1 Hz and b) single muons (single tracks of identified muons) at 2000 Hz. Eight on-line computers pre-analyze the single track data and store the results on magnetic tape in compacted form with a minimum of computer dead-time. One additional computer reads data from the shower triggers and records this raw data on a separate magnetic tape with no pre-analysis., Comment: 4 pages; 27th ICRC, p. 607

The Ground-Level Event (GLE) associated with the X5.7 solar flare of July 14, 2000 is studied by the Project GRAND proportional wire chamber array. Results are compared to those obtained by the Climax Neutron Monitor experiment which detects secondary neutrons. The Climax monitor, located in Climax, Colorado, is operated by the University of Chicago. The time of the GLE signal of the Climax station is examined for a possible coincident signal in the data of Project GRAND. Project GRAND is an array of 64 proportional wire chamber stations. The stations are sensitive to secondary muons with energies greater than 0.1 GeV. The mean energy of primaries which produce these ground level muons depends on the spectral index of the primary spectrum. For a differential spectral index of 2.4, the most probable primary energy is 10 GeV falling rapidly below this energy and falling slowly above this energy., Comment: 3 pages; 27th ICRC, p. 3557 (no significant observation)

Project GRAND observes small variations in the number of incident muons when plotted versus local solar time. The total accumulated number of muons by GRAND over four years' time is ~140 billion. The data obtained by Project GRAND are compared with data from neutron monitor stations at Climax and at Newark which detect secondary neutrons. Project GRAND is an array of 64 proportional wire chamber stations which are sensitive to secondary muons at energies greater than 0.1 GeV. The mean energy of cosmic ray primaries which produce these muons depends on the spectral index. For a differential spectral index of 2.4, the most probable gamma ray primary energy is about 10 GeV, the response falling steeply below this energy and slowly above this energy; this most probably energy varies only slowly with spectral index., Comment: 4 pages; 27th ICRC, p. 4114

Project GRAND has the capability of measuring the angle and identity of single tracks of secondary muons at ground level. The array is comprised of 64 stations each containing eight proportional wire planes with a 50 mm steel absorber plate placed above the bottom two planes in each station. The added steel absorber plate allows muon tracks to be separated from the less massive electrons. Over 100 billion identified muon angles have been measured. With the high statistics available, it is possible to obtain muon angular asymmetries with low systematics by subtracting west from east (and separately, south from north) angles; the subtraction eliminates most of the systematic errors while still retaining adequately small statistical errors on the differences. A preliminary analysis is performed as a function of solar time to obtain the effects on the muon rate due to effects of the sun., Comment: 7 pages; 27th ICRC, p. 4410

The FLUKA Monte Carlo program is used to predict the distributions of the muons which originate from primary cosmic gamma rays and reach sea level. The main result is the angular distribution of muons produced by vertical gamma rays which is necessary to predict the inherent angular resolution of any instrument utilizing muons to infer properties of gamma ray primaries. Furthermore, various physical effects are discussed which affect these distributions in differing proportions., Comment: 36 pages, 13 figures, minor revision, new layout

The theoretical calculations of the production of neutrinos via cosmic rays incident upon the earth's atmosphere (Barr et al., 1989; Becker-Szendy et al., 1992; Bugaev & Naumov, 1989; Gaisser et al, 1988; Honda et al., 1995) are examined. These calculations use a one-dimensional approximation in the production, transport, and decay of the produced particles. Examined are various additional effects of the earth's magnetic field and the three-dimensional nature of the problem which have the effect of decreasing the calulated ratio of muon neutrinos to electron neutrinos., Comment: 4 pages. 26th ICRC, vol 2, 253 (1999)

The theoretical Monte Carlo calculations of the production of neutrinos via cosmic rays incident upon the earth's atmosphere are examined. The calculations are sensitive to the assumed ratio of pi+ / pi- production cross sections; this ratio appears to be underestimated in the theory relative to the experimentally measured ratio. Since the neutrino detection cross section is three times larger than that for the antineutrino, the theoretical predicted detection ratio (nu_mu / nu_e) is correspondingly too large., Comment: 4 pages. HE.3.2.26 in 26th ICRC, 2, 147 (1999)

An increased data sample of identified secondary muons is collected at detection level. Project GRAND identifies secondary cosmic ray muons from electrons utilizing a thin steel absorber and tracking (PWC) chambers. The resulting angular resolution for the primary is about +/- 5 degrees. Since there is a 1.5% probability that a 100 GeV gamma primary will produce a single muon track at ground level, the high statistics allows a search for angular enhancements due to gammas. More than 100 billion muons are identified and analyzed. A table of stellar sources is examined., Comment: 4 pgs; includes 1 fig. and 2 tables. HE.3.2.10 in 26th ICRC, 2, 104, (1999)

The FLUKA Monte Carlo program is used to calculate the effects of hadroproduction by primary gamma rays incident upon the earth's atmosphere; for the results presented in this paper, only primary angles at 0 degrees from zenith are considered. The FLUKA code is believed to be quite accurate in reproducing experimental photon hadroproduction data in the 1 GeV to 10 TeV energy range studied. The charged pions which are so produced can decay to muons with sufficient energy to reach ground level. The number of these muons and their radial and energy distribution are studied for incident gamma ray energies from 1 GeV to 10 TeV. The number of these muons is not negligible; they can, in certain circumstances, be used to study potential sources of gamma rays like gamma ray bursts. It is found, for example, that a 10 TeV incident primary gamma ray produces, on average, 3.4 muons which reach ground level; the gamma ray energy which produces the maximum number of muons at ground level depends on the spectral index of the primary gamma spectrum, a constant which describes how the primary gamma flux rises with decreasing primary energy. An example: for a differential spectral index of 2.7, there is a broad maximum number of muons coming from ~ 30 GeV primary gamma ray energy., Comment: 10 pages, 5 figures. Updated and expanded version of 26th ICRC vol 2, 127 (1999); HE.3.2.20

The high energy gamma ray sources provided by experiment EGRET on the Compton Gamma Ray Observatory are examined, testing Project GRAND's ability to detect primary gamma rays by means of studying secondary muons. There is ~1.5% chance that a 100 GeV primary cosmic gamma ray will produce a muon at detection level (Fasso & Poirier, 1999), a probability which increases with increasing gamma energy. Project GRAND has 80 square meters of muon detector which identifies secondary muons >0.1 GeV and measures their angles to 0.26 deg (projected angle in the XZ and YZ planes). Data taken during the last two years are analyzed. A table of EGRET's gamma ray sources is examined (The Third EGRET Catalog of High Energy Gamma Ray Sources (EGRET webpage, 1999). EGRET's flux (>0.1 GeV), angular information, and spectral index were extrapolated to GRAND's energy region (>30 GeV). Then the geometrical acceptance was calculated for each of these events. Thus, GRAND's sensitivity to each of EGRET's sources was predicted. A product of extrapolated flux and GRAND's detection sensitivity yields an overall parameter indicating GRAND's relative sensitivity to each source, assuming an energy dependence given by EGRET's spectral index. The 14 sources with the best extrapolated detection efficiency were selected to be examined with the data., Comment: 4 pages

Project GRAND presents the results of a search for coincident high-energy gamma ray events in the direction and at the time of nine Gamma Ray Bursts (GRBs) detected by BATSE. A gamma ray has a non-negligible hadron production cross section; for each gamma ray of energy of 100 GeV, there are 0.015 muons which reach detection level (Fasso & Poirier, 1999). These muons are identified and their angles are measured in stations of eight planes of proportional wire chambers (PWCs). A 50 mm steel plate above the bottom pair of planes is used to distinguish muons from electrons. The mean angular resolution is 0.26 degrees over a +/- 61 degree range in the XZ and YZ planes. The BATSE GRB catalogue is examined for bursts which are near zenith for Project GRAND. The geometrical acceptance is calculated for each of these events. The product is then taken of the GRB flux and GRAND's geometrical acceptance. The nine sources with the best combination of detection efficiency and BATSE's intensity are selected to be examined in the data. The most significant detection of these nine sources is at a statistical significance of +3.7 sigma; this is also the GRB with the highest product of GRB flux and geometrical acceptance., Comment: 4 pages. Superseded by astro-ph/0004379

Project GRAND presents results on the atomic composition of primary cosmic rays. This is accomplished by determining the average height of primary particles that cause extensive air showers detected by Project GRAND. Particles with a larger cross sectional area, such as iron nuclei, are likely to start an extensive air shower higher in the atmosphere whereas protons, with a smaller cross section, would pass through more air before interacting and thus start showers at lower heights. Such heights can be determined by extrapolating identified muon tracks backward (upward) to determine their height of origin (Gress et al., 1997). Since muons are from the top, hadronic part of the shower, they are a good estimator for the beginning of the shower. The data for this study were taken during the previous year with 20 million shower events., Comment: 4 pages including 1 table and 4 figures. OG.3.1.12 in 26th ICRC, 4, 172 (1999)

Project GRAND is an extensive air shower array utilizing position sensitive detectors of proportional wire chambers. The 64 detectors deployed in a field 100 m x 100 m are located at 86.2 deg W and 41.7 deg N, at 220 m above sea level. The project was completed about two years ago and has been taking data, simultaneously on two triggers: 1) multiple-hit coincidence triggers which collect data on extensive air showers, and 2) 200 Hz triggers which collect the single tracks stored in each station during the last 5 msec., Comment: 4 pages, 4 figures. Appeared in 26th ICRC, vol 5, 304 (1999), OG.4.4.02

Project GRAND preents a map in right ascension and declination for single cosmic secondary tracks which have been identified as muons. These muons are measured in stations of proportional wire chambers (PWCs) which have a mean angular resolution of 0.26 deg. A 50 mm steel plate interspersed with the PWCs is used to distinguish muons from electrons. Two years of data are accumulated in a map of right ascension and declination which covers all of the northern hemisphere and a small portion of the southern hemisphere. The total number of muon tracks in this data sample are 40 billion. Significant large angular structure is found in this map; the deviations from average are small compared to the average, but because of the high statistics, the deviations from average are statistically significant to many standard deviations. Systematic effects in the data are minimized by averaging over this two year period. These results are similar to those obtained in previous data., Comment: 4 pages, 3 figures

Project GRAND measures the asymmetries of secondary cosmic muons by calculating the differences between the muons from the east and the muons from the west for complete solar days. A similar north-south difference is also presented. These muons are identified in single track data taken with the 64 stations of Project GRAND; the data cover a two year span with a total muon sample of 30 billion muons., Comment: 4 pages, 2 figures

We report on a study of sub-TeV ($E_\gamma > 10$ GeV) gamma-ray-induced muon secondaries in coincidence with BATSE gamma ray bursts (GRBs). Each TeV gamma ray striking the atmosphere produces $\approx$0.2 muons whose identity and angle can be measured by the Project GRAND array. Eight GRB candidates were studied; seven were selected based upon the optimum product of (detected BATSE fluence) $\times$ (GRAND's acceptance). One candidate was added because it was reported as a detection by the Milagrito collaboration. Seven candidates show a positive, though not statistically significant, muon excess. The most significant possible coincidence shows an excess of $466 \pm 171$ muons during the BATSE T90 time interval. It is also of interest that the event with the second most significant signal to noise (1.2$\sigma$) is the Milagrito event. If our most significant event is real, the implied fluence of energetic ($> 10$ GeV) gammas necessary to account for the observed muon excess would require that most of the GRB fluence arrived in the form of energetic gammas., Comment: 7 pages, including 3 figures and 1 table. Revised as per Referees' suggestions. Accepted for publication in Physical Review D