For
s
,
t
,
u
∈
C
, we show rapidly (or globally) convergent series representations of the Tornheim double zeta function
T
(
s, t, u
) and (desingularized) symmetric Tornheim double zeta functions. ...As a corollary, we give a new proof of known results on the values of
T
(
s, s, s
) at non-positive integers and the location of the poles of
T
(
s, s, s
). Furthermore, we prove that
T
(
s, s, s
) can not be written by a polynomial in the form of
∑
k
=
1
j
c
k
∏
r
=
1
q
ζ
d
kr
(
a
kr
s
+
b
kr
)
, where
a
kr
,
b
kr
,
c
k
∈
C
and
d
kr
∈
Z
≥
0
.
Magnetic reconnection is believed to be the main driver to transport solar wind into the Earth's magnetosphere when the magnetopause features a large magnetic shear. However, even when the magnetic ...shear is too small for spontaneous reconnection, the Kelvin-Helmholtz instability driven by a super-Alfvénic velocity shear is expected to facilitate the transport. Although previous kinetic simulations have demonstrated that the non-linear vortex flows from the Kelvin-Helmholtz instability gives rise to vortex-induced reconnection and resulting plasma transport, the system sizes of these simulations were too small to allow the reconnection to evolve much beyond the electron scale as recently observed by the Magnetospheric Multiscale (MMS) spacecraft. Here, based on a large-scale kinetic simulation and its comparison with MMS observations, we show for the first time that ion-scale jets from vortex-induced reconnection rapidly decay through self-generated turbulence, leading to a mass transfer rate nearly one order higher than previous expectations for the Kelvin-Helmholtz instability.
Abstract
Coalescence of multiple magnetic islands is recognized as an effective process to energize particles during magnetic reconnection, while its energy conversion process still remains unclear. ...Here, a two-dimensional fully kinetic simulation of multiple island coalescence with a small reconnection guide field is studied. In the analysis of energy conversion within a magnetic island, the dot product of
V
e
·
j
×
B
=
w
1
is a useful quantity to compare with
j
·
E
=
w
2
, since the average work done by the Lorentz force on the circulating particles is negligible in the island and
w
2
−
w
1
=
j
·
E
+
V
e
×
B
=
j
·
E
′
=
w
3
. A bipolar pattern of
w
1
is found at a secondary island when the electrons are in circular motion inside the island. Significant energy dynamo (
w
3
< 0) resulting from
j
∥
E
∥
is found at the secondary island, which has not been reported before, where the parallel electric field
E
∥
is highly correlated with
w
3
. Moreover, significant energy dissipation (
w
3
> 0) due to
j
⊥
·
E
⊥
′
is seen in the merging region between two coalescing islands. Both types of energy conversions are accompanied by enhancements in
j
∥
and the parallel electron temperature
T
e
∥
. Three ion-scale magnetic islands (FR1, FR2, and FR3) observed by the Magnetospheric Multiscale spacecraft are compared favorably with the simulated signatures of energy dynamo and dissipation of an evolving secondary island. In particular, FR1 displayed a similar energy dynamo signature as that simulated in an early stage of the secondary island. FR2 and FR3 showed a dominant
j
⊥
·
E
⊥
′
energy conversion similar to that obtained in a later stage of the secondary island.
The pathological processes of neurodegenerative disorders such as Alzheimer's and Parkinson's diseases engender synaptic and neuronal cell damage. While mild oxidative and nitrosative (nitric oxide ...(NO)-related) stress mediates normal neuronal signaling, excessive accumulation of these free radicals is linked to neuronal cell injury or death. In neurons, N-methyl-D-aspartate (NMDA) receptor (NMDAR) activation and subsequent Ca(2+) influx can induce the generation of NO via neuronal NO synthase. Emerging evidence has demonstrated that S-nitrosylation, representing covalent reaction of an NO group with a critical protein thiol, mediates the vast majority of NO signaling. Analogous to phosphorylation and other posttranslational modifications, S-nitrosylation can regulate the biological activity of many proteins. Here, we discuss recent studies that implicate neuropathogenic roles of S-nitrosylation in protein misfolding, mitochondrial dysfunction, synaptic injury, and eventual neuronal loss. Among a growing number of S-nitrosylated proteins that contribute to disease pathogenesis, in this review we focus on S-nitrosylated protein-disulfide isomerase (forming SNO-PDI) and dynamin-related protein 1 (forming SNO-Drp1). Furthermore, we describe drugs, such as memantine and newer derivatives of this compound that can prevent both hyperactivation of extrasynaptic NMDARs as well as downstream pathways that lead to nitrosative stress, synaptic damage, and neuronal loss.
Abstract
At the Earth's magnetopause, the Kelvin‐Helmholtz (KH) instability, driven by the persistent velocity shear between the magnetosheath and the magnetosphere, has been frequently observed ...during northward interplanetary magnetic field periods and considered as one of the most important candidates for transporting and mixing plasmas across the magnetopause. However, how this process interacts with magnetic field fluctuations, which persistently exist near the magnetopause, has been less discussed. Here we perform a series of 2‐D fully kinetic simulations of the KH instability at the magnetopause considering a power law spectrum of initial fluctuations in the magnetic field. The simulations demonstrate that when the amplitude level of the initial fluctuations is sufficiently large, the KH instability evolves faster, leading to a more efficient plasma mixing within the vortex layer. In addition, when the spectral index of the initial fluctuations is sufficiently small, the modes whose wavelength is longer than the theoretical fastest growing mode grow dominantly. The fluctuating magnetic field also results in the formation of the well‐matured turbulent spectrum with a −5/3 index within the vortex layer even in the early nonlinear growth phase of the KH instability. The obtained spectral features in the simulations are in reasonable agreement with the features in KH waves events at the magnetopause observed by the Magnetospheric Multiscale mission and conjunctively by the Geotail and Cluster spacecraft. These results indicate that the magnetic field fluctuations may really contribute to enhancing the wave activities especially for longer wavelength modes and the associated mixing at the magnetopause.
Key Points
The 2‐D fully kinetic simulations of magnetopause Kelvin‐Helmholtz instability initially imposing power law field fluctuations are performed
The growth of the instability especially for long wavelength modes is enhanced by the fluctuating field, leading to more efficient mixing
Spectral features obtained from the simulations are in reasonable agreement with past spacecraft observations at the Earth's magnetopause
We investigate the accuracy with which the reconnection electric field EM 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 EM that result from errors in an LMN boundary normal coordinate system. We determine several LMN coordinates for this MMS event using several different methods. We use these M axes to estimate EM. We find some consensus that the reconnection rate was roughly EM = 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‐ve), 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‐ve and MDD‐B. The L and M directions are most reliably determined by MVA‐ve 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 EM from the virtual data within error bars ≥20%.
Key Points
The reconnection rate EM is estimated for one event using several techniques to find an M direction
The error bars in EM and the LMN coordinate directions are estimated from virtual data
The reconnection rate is likely EM = 3.2 mV/m ± 0.6 mV/m, which corresponds to a normalized rate of 0.18 ± 0.035
In the Earth's magnetotail, magnetic reconnection releases stored magnetic energy and drives magnetospheric convection. The rate at which magnetic flux is transferred from the reconnection inflow to ...outflow regions is determined by the reconnection electric field Er, which is often referred to as the unnormalized reconnection rate. To better quantify the efficiency of reconnection, this electric field Er is often normalized by the characteristic Alfvén speed and the reconnecting magnetic field. This parameter is generally called the normalized or dimensionless reconnection rate R. In this paper, we employ a two‐dimensional fully kinetic simulation to model a magnetotail reconnection event with weak geomagnetic activity (<200 nT of the AE index) observed by the Magnetospheric Multiscale (MMS) mission on 11 July 2017. We obtain R and Er from direct measurements in the diffusion region and indirect measurements of the rate at the separatrix using a recently proposed remote sensing technique. The measured normalized rate for this MMS event is R ∼0.15–0.2, consistent with theoretical and simulation models of fast collisionless reconnection. This corresponds to an unnormalized rate of Er ∼2–3 mV/m. Based on quantitative consistencies between the simulation and the MMS observations, we conclude that our estimates of the reconnection rates are reasonably accurate. Given that past studies have found Er of the order ∼10 mV/m during strong geomagnetic substorms, these results indicate that the local Er in magnetotail reconnection may be an important parameter controlling the amplitude of geomagnetic disturbances.
Key Points
Reliable reconnection rates are obtained based on virtual observations in a fully kinetic simulation of an MMS tail reconnection event
The normalized rates obtained from the simulation and MMS data are 0.15–0.2, indicating the occurrence of fast reconnection
The observed unnormalized rate is 2–3 mV/m, while higher rates were observed in other events with stronger geomagnetic activities
IVIM MR imaging provides perfusion and diffusion information with a single diffusion-weighted MR image. We determined whether PP and D differ among various types of head and neck tumors.
The study ...cohort included 123 head and neck tumors: 30 SCCs, 28 benign and 20 malignant SG tumors, 36 lymphomas, and 9 schwannomas. The D and PP values were determined by using b-values of 0, 500, and 1000 s/mm(2) based on the IVIM model.
The PP values (lymphomas, 0.09 ± 0.04; SCCs, 0.15 ± 0.04; and malignant SG tumors, 0.22 ± 0.07) and D values (0.47 ± 0.07 × 10(-3) mm(2)/s, 0.82 ± 0.17 × 10(-3) mm(2)/s, and 1.03 ± 0.16 × 10(-3) mm(2)/s, respectively) were significantly different among the malignant tumors (P < .01). These values were also significantly different between pleomorphic adenomas (0.13 ± 0.02 and 1.44 ± 0.39 × 10(-3) mm(2)/s) and Warthin tumors (0.19 ± 0.04 and 0.73 ± 0.22 × 10(-3) mm(2)/s) (P < .001). The PP values of malignant SG tumors were significantly different from those of pleomorphic adenomas (P = .001) and the D values of the malignant SG tumors were significantly different from those of pleomorphic adenomas (P = .002) and Warthin tumors (P = .007). Schwannomas had large PP (0.23 ± 0.08) and D values (1.26 ± 0.20 × 10(-3) mm(2)/s), greatly overlapping those of some SG tumor types.
Head and neck tumors had distinctive PP and D values by using IVIM MR imaging.
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