11,978 research outputs found
The mass of unimodular lattices
The purpose of this paper is to show how to obtain the mass of a unimodular
lattice from the point of view of the Bruhat-Tits theory. This is achieved by
relating the local stabilizer of the lattice to a maximal parahoric subgroup of
the special orthogonal group, and appealing to an explicit mass formula for
parahoric subgroups developed by Gan, Hanke and Yu.
Of course, the exact mass formula for positive defined unimodular lattices is
well-known. Moreover, the exact formula for lattices of signature (1,n) (which
give rise to hyperbolic orbifolds) was obtained by Ratcliffe and Tschantz,
starting from the fundamental work of Siegel. Our approach works uniformly for
the lattices of arbitrary signature (r,s) and hopefully gives a more conceptual
way of deriving the above known results.Comment: 15 pages, to appear in J. Number Theor
Electron acceleration by cascading reconnection in the solar corona I Magnetic gradient and curvature effects
Aims: We investigate the electron acceleration in convective electric fields
of cascading magnetic reconnection in a flaring solar corona and show the
resulting hard X-ray (HXR) radiation spectra caused by Bremsstrahlung for the
coronal source. Methods: We perform test particle calculation of electron
motions in the framework of a guiding center approximation. The electromagnetic
fields and their derivatives along electron trajectories are obtained by
linearly interpolating the results of high-resolution adaptive mesh refinement
(AMR) MHD simulations of cascading magnetic reconnection. Hard X-ray (HXR)
spectra are calculated using an optically thin Bremsstrahlung model. Results:
Magnetic gradients and curvatures in cascading reconnection current sheet
accelerate electrons: trapped in magnetic islands, precipitating to the
chromosphere and ejected into the interplanetary space. The final location of
an electron is determined by its initial position, pitch angle and velocity.
These initial conditions also influence electron acceleration efficiency. Most
of electrons have enhanced perpendicular energy. Trapped electrons are
considered to cause the observed bright spots along coronal mass ejection
CME-trailing current sheets as well as the flare loop-top HXR emissions.Comment: submitted to A&
Morphological evolution of a 3D CME cloud reconstructed from three viewpoints
The propagation properties of coronal mass ejections (CMEs) are crucial to
predict its geomagnetic effect. A newly developed three dimensional (3D) mask
fitting reconstruction method using coronagraph images from three viewpoints
has been described and applied to the CME ejected on August 7, 2010. The CME's
3D localisation, real shape and morphological evolution are presented. Due to
its interaction with the ambient solar wind, the morphology of this CME changed
significantly in the early phase of evolution. Two hours after its initiation,
it was expanding almost self-similarly. CME's 3D localisation is quite helpful
to link remote sensing observations to in situ measurements. The investigated
CME was propagating to Venus with its flank just touching STEREO B. Its
corresponding ICME in the interplanetary space shows a possible signature of a
magnetic cloud with a preceding shock in VEX observations, while from STEREO B
only a shock is observed. We have calculated three principle axes for the
reconstructed 3D CME cloud. The orientation of the major axis is in general
consistent with the orientation of a filament (polarity inversion line)
observed by SDO/AIA and SDO/HMI. The flux rope axis derived by the MVA analysis
from VEX indicates a radial-directed axis orientation. It might be that locally
only the leg of the flux rope passed through VEX. The height and speed profiles
from the Sun to Venus are obtained. We find that the CME speed possibly had
been adjusted to the speed of the ambient solar wind flow after leaving COR2
field of view and before arriving Venus. A southward deflection of the CME from
the source region is found from the trajectory of the CME geometric center. We
attribute it to the influence of the coronal hole where the fast solar wind
emanated from.Comment: ApJ, accepte
Relativistic Harmonic Oscillator
We study the semirelativistic Hamiltonian operator composed of the
relativistic kinetic energy and a static harmonic-oscillator potential in three
spatial dimensions and construct, for bound states with vanishing orbital
angular momentum, its eigenfunctions in compact form, i. e., as power series,
with expansion coefficients determined by an explicitly given recurrence
relation. The corresponding eigenvalues are fixed by the requirement of
normalizability of the solutions.Comment: 14 pages, extended discussion of result
Restingâstate fMRI detects the effects of learning in short term: A visual search training study
Can resting-state functional connectivity (rs-FC) detect the impact of learning on the brain inthe short term? To test this possibility, we have combined task-FC and rs-FC tested before andafter a 30-min visual search training. Forty-two healthy adults (20 men) divided into no-contactcontrol and trained groups completed the study. We studied the connectivity between fourdifferent regions of the brain involved in visual search: the primary visual area, the right poste-rior parietal cortex (rPPC), the right dorsolateral prefrontal cortex (rDLPFC), and the dorsalanterior cingulate cortex (dACC). Task-FC showed increased connectivity between the rPPCand rDLPFC and between the dACC and rDLPFC from pretraining to posttraining for boththe control group and the trained group, suggesting that connectivity between these areasincreased with task repetition. In rs-FC, we found enhanced connectivity between theseregions in the trained group after training, especially in those with better learning. Whole brainindependent component analyses did not reveal any change in main networks after training.These results imply that rs-FC may not only predict individual differences in task performance,but rs-FC might also serve to monitor the impact of learning on the brain after short periodsof cognitive training, localizing them in brain areas specifically involved in training
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