How Accurately Can We Measure the Reconnection Rate E M for the MMS Diffusion Region Event of 11 July 2017?

We investigate the accuracy with which the reconnection electric field E M can be determined from in situ plasma data. We study the magnetotail electron diffusion region observed by National Aeronautics and Space Administration's Magnetospheric Multiscale (MMS) on 11 July 2017 at 22:34 UT and focus on the very large errors in E M that result from errors in an L M N boundary normal coordinate system. We determine several L M N coordinates for this MMS event using several different methods. We use these M axes to estimate E M. We find some consensus that the reconnection rate was roughly E M = 3.2 ± 0.6 mV/m, which corresponds to a normalized reconnection rate of 0.18 ± 0.035. Minimum variance analysis of the electron velocity (MVA-v e), MVA of E, minimization of Faraday residue, and an adjusted version of the maximum directional derivative of the magnetic field (MDD-B) technique all produce reasonably similar coordinate axes. We use virtual MMS data from a particle-in-cell simulation of this event to estimate the errors in the coordinate axes and reconnection rate associated with MVA-v e and MDD-B. The L and M directions are most reliably determined by MVA-v e when the spacecraft observes a clear electron jet reversal. When the magnetic field data have errors as small as 0.5% of the background field strength, the M direction obtained by MDD-B technique may be off by as much as 35°. The normal direction is most accurately obtained by MDD-B. Overall, we find that these techniques were able to identify E M from the virtual data within error bars ≥20%

Towards Verifying Nonlinear Integer Arithmetic

We eliminate a key roadblock to efficient verification of nonlinear integer arithmetic using CDCL SAT solvers, by showing how to construct short resolution proofs for many properties of the most widely used multiplier circuits. Such short proofs were conjectured not to exist. More precisely, we give n^{O(1)} size regular resolution proofs for arbitrary degree 2 identities on array, diagonal, and Booth multipliers and quasipolynomial- n^{O(\log n)} size proofs for these identities on Wallace tree multipliers.Comment: Expanded and simplified with improved result

Electron-Scale Quadrants of the Hall Magnetic Field Observed by the Magnetospheric Multiscale spacecraft during Asymmetric Reconnection

An in situ measurement at the magnetopause shows that the quadrupole pattern of the Hall magnetic field, which is commonly observed in a symmetric reconnection, is still evident in an asymmetric component reconnection, but the two quadrants adjacent to the magnetosphere are strongly compressed into the electron scale and the widths of the remaining two quadrants are still ion scale. The bipolar Hall electric field pattern generally created in a symmetric reconnection is replaced by a unipolar electric field within the electron-scale quadrants. Furthermore, it is concluded that the spacecraft directly passed through the inner electron diffusion region based on the violation of the electron frozen-in condition, the energy dissipation, and the slippage between the electron flow and the magnetic field. Within the inner electron diffusion region, magnetic energy was released and accumulated simultaneously, and it was accumulated in the perpendicular directions while dissipated in the parallel direction. The localized thinning of the current sheet accounts for the energy accumulation in a reconnection

MMS observations of electron-scale filamentary currents in the reconnection exhaust and near the X line

© 2016. American Geophysical Union. All Rights Reserved.We report Magnetospheric Multiscale observations of macroscopic and electron-scale current layers in asymmetric reconnection. By intercomparing plasma, magnetic, and electric field data at multiple crossings of a reconnecting magnetopause on 22 October 2015, when the average interspacecraft separation was ~10km, we demonstrate that the ion and electron moments are sufficiently accurate to provide reliable current density measurements at 30ms cadence. These measurements, which resolve current layers narrower than the interspacecraft separation, reveal electron-scale filamentary Hall currents and electron vorticity within the reconnection exhaust far downstream of the X line and even in the magnetosheath. Slightly downstream of the X line, intense (up to 3μA/m2) electron currents, a super-Alfvénic outflowing electron jet, and nongyrotropic crescent shape electron distributions were observed deep inside the ion-scale magnetopause current sheet and embedded in the ion diffusion region. These characteristics are similar to those attributed to the electron dissipation/diffusion region around the X line

Counterexamples Revisited: Principles, Algorithms, Applications

Abstract. Algorithmic counterexample generation is a central feature of model checking which sets the method apart from other approaches such as theorem proving. The practical value of counterexamples to the verification engineer is evident, and for many years, counterexam-ple generation algorithms have been employed in model checking sys-tems, even though they had not been subject to an adequate fundamen-tal investigation. Recent advances in model checking technology such as counterexample-guided abstraction refinement have put strong em-phasis on counterexamples, and have lead to renewed interest both in fundamental and pragmatic aspects of counterexample generation. In this paper, we survey several key contributions to the subject includ-ing symbolic algorithms, results about the graph-theoretic structure of counterexamples, and applications to automated abstraction as well as software verification. Irrefutability is not a virtue of a theory (as people often think) but a vice

Treatment of Canine Osseous Tumors with Photodynamic Therapy: A Pilot Study

Photodynamic therapy uses nonthermal coherent light delivered via fiber optic cable to locally activate a photosensitive chemotherapeutic agent that ablates tumor tissue. Owing to the limitations of light penetration, it is unknown whether photodynamic therapy can treat large osseous tumors. We determined whether photodynamic therapy can induce necrosis in large osseous tumors, and if so, to quantify the volume of treated tissue. In a pilot study we treated seven dogs with spontaneous osteosarcomas of the distal radius. Tumors were imaged with MRI before and 48 hours after treatment, and the volumes of hypointense regions were compared. The treated limbs were amputated immediately after imaging at 48 hours and sectioned corresponding to the MR axial images. We identified tumor necrosis histologically; the regions of necrosis corresponded anatomically to hypointense tissue on MRI. The mean volume of necrotic tissue seen on MRI after photodynamic therapy was 21,305 mm3 compared with a pretreatment volume of 6108 mm3. These pilot data suggest photodynamic therapy penetrates relatively large canine osseous tumors and may be a useful adjunct for treatment of bone tumors

Reconnection Inside a Dipolarization Front of a Diverging Earthward Fast Flow

We examine a Dipolarization Front (DF) event with an embedded electron diffusion region (EDR), observed by the Magnetospheric Multiscale (MMS) spacecraft on 08 September 2018 at 14:51:30 UT in the Earth's magnetotail by applying multi-scale multipoint analysis methods. In order to study the large-scale context of this DF, we use conjunction observations of the Cluster spacecraft together with MMS. A polynomial magnetic field reconstruction technique is applied to MMS data to characterize the embedded electron current sheet including its velocity and the X-line exhaust opening angle. Our results show that the MMS and Cluster spacecraft were located in two counter-rotating vortex flows, and such flows may distort a flux tube in a way that the local magnetic shear angle is increased and localized magnetic reconnection may be triggered. Using multi-point data from MMS we further show that the local normalized reconnection rate is in the range of R ∼ 0.16 to 0.18. We find a highly asymmetric electron in- and outflow structure, consistent with previous simulations on strong guide-field reconnection events. This study shows that magnetic reconnection may not only take place at large-scale stable magnetopause or magnetotail current sheets but also in transient localized current sheets, produced as a consequence of the interaction between the fast Earthward flows and the Earth's dipole field