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Properties of the GEM problem Reconnected flux. We define magnetic reconnection to be the loss of magnetic flux through the vertical axis into the first quadrant. Using Faraday’s law, ∂tB + ∇ × E = 0, one can show that the rate of reconnection is minus the value of the out-of-plane component of the electric field at the origin (i.e. the X-point) [8]. Ohm’s law at the origin. Since the electric field at the origin is the rate of reconnection, we are lead to study the terms of Ohm’s law for the electric field at the origin. Since the problem is symmetric under 180 degree rotational symmetry about the origin, only the out-of-plane component of vectors is nonzero at the origin. In Ohm’s law only the out-of-plane components of the resistive, pressure, and inertial terms survive. As a proxy for Ohm’s law5 , we select a species and write the momentum equation solved for the electric field: � � −Ri dt(reconnected flux) = E3 � = + origin eni ∇ · Pi + eni mi e ∂tui � � � � � . 3� origin In a perfectly collisionless, gyrotropic plasma, the resistive term and pressure divergence vanish, and reconnected flux should exactly track with species velocity (a proxy for the current) at the origin. Results We simulated the GEM magnetic reconnection challenge problem for pair plasmas, varying the mesh resolution and varying the rate of isotropization from zero to instantaneous. We plotted the contribution of proxy Ohm’s law terms to the reconnected flux. We find that for a broad intermediate range of isotropization rates reconnection is fast and that the pressure term makes the dominant contribution to reconnected flux. When isotropization is very slow or absent, there is oscillatory exchange between the inertial term and the pressure term at roughly a typical gyrofrequency, and reconnection proceeds at a slow to moderate rate (our simulations for the case of no isotropization are not sufficiently resolved). For a broad intermediate range of isotropization, there is little oscillation and, in agreement with PIC simulations (see [1, 2]), the pressure divergence dominates and provides for faster reconnection. As the rate of isotropization becomes very fast, however, the pressure divergence is forced to vanish and the inertial term is the only remaining term in the equation that can provide for reconnected flux. This forces the current at the origin to ramp up in track with reconnected flux. The system seems unable to sustain this ramp-up in current, however, and numerical instability kicks in, as evidenced by the sudden appearance of strong, very rapid oscillatory exchange (less evident in the accumulation integrals shown) between the inertial term and the residual. The numerical 5 Ohm’s law involves the approximating assumption of quasineutrality, whereas the momentum equation holds exactly and the inertial term reduces to a simpler form at the origin. 16
esidual displaces the inertial term, allowing the the current to peak and then decay while the reconnected flux maintains the same smooth, rapid ascent seen for intermediate isotropization rates, as if unconcerned whether pressure, inertia, numerical resistivity – or even anomalous resistivity, as our cursory investigations suggest – provides for its determined course. We can conclude that fast reconnection at least commences in an isotropic pair plasma model, and we conjecture that the numerical instability we see corresponds to some physical (perhaps streaming?) instability that provides for an effective anomalous resistivity (whose functional form we have not analyzed). As expected, the five-moment simulations show agreement with instantaneous relaxation of the ten-moment system to isotropy. Acknowledgements I thank the Wisconsin Space Grant Consortium for their support. In addition to my advisor, James Rossmanith, I also thank Nick Murphy, Ellen Zweibel, and Ping Zhu for helpful conversations. References [1] N. Bessho and A. Bhattacharjee. Collisionless reconnection in an electron-positron plasma. Phys. Rev. Letters, 95:245001, December 2005. [2] N. Bessho and A. Bhattacharjee. Fast collisionless reconnection in electron-positron plasmas. Physics of Plasmas, 14:056503, 2007. [3] J. Birn, J.F. Drake, M.A. Shay, B.N. Rogers, R.E. Denton, M. Hesse, M. Kuznetsova, Z.W. Ma, A. Bhattacharjee, A. Otto, and P.L. Pritchett. Geospace environmental modeling (GEM) magnetic reconnection challenge. Journal of Geophysical Research – Space Physics, 106:3715–3719, 2001. [4] L. Chacon, Andrei N. Simakov, V.S. Lukin, and A. Zocco. Fast reconnection in nonrelativistic 2D electron-positron plasmas. Phys. Rev. Letters, 101:025003, July 2008. [5] A. Hakim, J. Loverich, and U. Shumlak. A high-resolution wave propagation scheme for ideal two-fluid plasma equations. J. Comp. Phys., 219:418–442, 2006. [6] A.H. Hakim. Extended MHD modelling with the ten-moment equations. J. Fusion Energy, 27(1–2):36–43, June 2007. [7] M. Hesse, M. Kuznetsova, and J. Birn. The role of electron heat flux in guide-field magnetic reconnection. Physics of Plasmas, 11(12):5387–5397, 2004. [8] E.A. Johnson and J.A. Rossmanith. Collisionless magnetic reconnection in a five-moment two-fluid electron-positron plasma. submitted, 2008. [9] C. David Levermore. Kinetic theory, Gaussian moment closures, and fluid approximations. Presented at IPAM KT2009 Culminating Retreat, Lake Arrowhead, California, June 2009. [10] S. Zenitani, M. Hesse, and A. Klimas. Two-fluid magnetohydrodynamic simulations of relativistic magnetic reconnection. The Astrophysical Journal, 696:1385–1401, May 2009. 17
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Space Grant Consortium wisconsin UN
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THE CASSINI ENCOUNTER WITH THE GEM
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Th he proceedinngs of our 199th Ann
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Wisconsin Space Grant Consortium Un
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Part 3: NASA Reduced Gravity Progra
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EAA Women Soar - You Soar, Lee Siud
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Elijah High Altitude Balloon Projec
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Our experience with the HALO II lau
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which had been a problem in the pas
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Figure 6: 3-D GPS Generated Track o
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Results The seeds tested in the lab
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hour as we assumed the flight in th
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Experimental Results There are two
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A series of tests were done in a co
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380 360 340 320 23.3 Temp. (Celsius
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First Place, Non-Engineering: Schmi
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of the basis for fin designs came f
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ejection charge from the motor fire
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using rip-stop nylon cloth. To atta
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Post-flight recovery. A field searc
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Thus, it is believed that the main
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[2] Public Missiles Ltd. Frequently
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Design Features The chief requireme
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The joint between the dart and the
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Area dramatically influenced by flo
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Altitude [ft] 6000 5000 4000 3000 2
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though a strong crosswind was prese
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Our Design Our rocket uses the basi
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e easily recovered. Bong recreation
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Performance Characteristics of Pred
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Background and Context: Student Roc
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The Rocky Mountain Miners’ compet
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19th Annual Conference Part Three N
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The angle of repose of a granular m
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Experiment Design The experiment co
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on the ground and in the Weightless
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measurements for the 1 − g data.
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[ImageJ, 2008] Image Analysis Softw
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Dynamics Characterization of the El
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Figure 1 - A calibration equation f
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Wire A secondary investigation into
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[1] Taminger, K. M. B.; and Hafley,
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Introduction The analysis of wake v
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Figure 2: Screen I mage o f G UI. T
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References ¹ Burnham, D.C., and Ha
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Validation of Novel Rigid Body Fric
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forces is implemented in the popula
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Figure 2. CAD representation of a t
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Results Figure 5. Assembled hydraul
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References Anitescu, M. (2006). "Op
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Multi-stage Joule-Thomson cycles ar
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significant change in total compres
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The enthalpy (h3) of the 2 nd stage
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educed, the temperature range that
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7. Lemmon, E. W.; Huber, M. L.; McL
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Throughout each of the run cycles,
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and heater adjusted to accommodate
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Phaeton Mast Dynamics Mechanical Sy
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exposure to the FEMAP with NASTRAN
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The irregularity in the plots above
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inversion of a particular matrix, t
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clarified. Additionally, the PMD ki
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A. Abstract For hardware to be flig
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should be performed at the JWST obs
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B. Attenuation and Uncertainty Shoc
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Detector Array and ROIC SCA Mount L
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Detector Shock Environment The leve
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Orbiter (MRO), Moon Mineralogy Mapp
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4. NASA JPL. MIRI FOCAL PLANE SYSTE
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Is Lake Superior a significant sour
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each grid cell at daily resolution.
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Figure 3. (a) Seasonal cycle of lak
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Figure 5. Model pCO2 at the surface
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Marshall, J., A. Adcroft, C. Hill,
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numerical weather prediction (NWP)
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High Resolution Radiometer (AVHRR)
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On the morning of 26 May 2008, ther
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eneficiation reagents. Ionic liquid
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Figure 3: Current versus voltage da
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Abstract New Initiatives in the Pro
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was noticed above the gel. A discol
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delicate structures (hairs). N o fu
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and A. Y. Rozanov, Eds., SPIE, Vol.
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Combining Writing Across the Curric
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But the study also reported a consi
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Educators’ Aerospace Workshop for
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2008-2009 Evaluation Educators’ A
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Some comments from participants 200
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The cost of a one credit graduate c
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EAA WOMEN SOAR - YOU SOAR Dr. Lee J
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� Incorporated the technology res
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Evaluation Results: At the conclusi
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Educational Standards: The National
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curriculum development, to provide
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and applications of GIS technology
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• A significant new outcome for t
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The design of this project and appl
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Activities at the workshop involved
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to give our students a series of PR
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In the past we have not focused on
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Providing High School Students with
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that th e current generations of s
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instruction a s pa rt o f t heir ow
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Wisconsin Space Grant Consortium &
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11:45-1:00 pm Lunch *** Concurrent
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Moderator: David B lock, A ssociate
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Second Place, E ngineering, Drew an
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Wisconsin Space Grant Consortium
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