14,361 research outputs found
Umbilic hypersurfaces of constant sigma-k curvature in the Heisenberg group
We study immersed, connected, umbilic hypersurfaces in the Heisenberg group
with We show that such a hypersurface, if closed, must
be rotationally invariant up to a Heisenberg translation. Moreover, we prove
that, among others, Pansu spheres are the only such spheres with positive
constant sigma-k curvature up to Heisenberg translations.Comment: 28 pages, 6 figure
Umbilicity and characterization of Pansu spheres in the Heisenberg group
For we define a notion of umbilicity for hypersurfaces in the
Heisenberg group . We classify umbilic hypersurfaces in some cases, and
prove that Pansu spheres are the only umbilic spheres with positive constant
(or horizontal)-mean curvature in up to Heisenberg translations.Comment: 32 pages, 2 figures; in Crelle's journal, 201
A Codazzi-like equation and the singular set for smooth surfaces in the Heisenberg group
In this paper, we study the structure of the singular set for a
smooth surface in the -dimensional Heisenberg group . We
discover a Codazzi-like equation for the -area element along the
characteristic curves on the surface. Information obtained from this ordinary
differential equation helps us to analyze the local configuration of the
singular set and the characteristic curves. In particular, we can estimate the
size and obtain the regularity of the singular set. We understand the global
structure of the singular set through a Hopf-type index theorem. We also
justify that Codazzi-like equation by proving a fundamental theorem for local
surfaces in .Comment: 64 pages, 17 figure
Bidirectional outflows as evidence of magnetic reconnection leading to a solar microflare
Magnetic reconnection is a rapid energy release process that is believed to
be responsible for flares on the Sun and stars. Nevertheless, such
flare-related reconnection is mostly detected to occur in the corona, while
there have been few studies concerning the reconnection in the chromosphere or
photosphere. Here we present both spectroscopic and imaging observations of
magnetic reconnection in the chromosphere leading to a microflare. During the
flare peak time, chromospheric line profiles show significant
blueshifted/redshifted components on the two sides of the flaring site,
corresponding to upflows and downflows with velocities of (70--80) km
s, comparable with the local Alfv\'{e}n speed as expected by the
reconnection in the chromosphere. The three-dimensional nonlinear force-free
field configuration further discloses twisted field lines (a flux rope) at a
low altitude, cospatial with the dark threads in He I 10830 \r{A} images. The
instability of the flux rope may initiate the flare-related reconnection. These
observations provide clear evidence of magnetic reconnection in the
chromosphere and show the similar mechanisms of a microflare to those of major
flares.Comment: 16 pages, 5 figures, accepted for publication in ApJ
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Rapid (<5 min) identification of pathogen in human blood by electrokinetic concentration and surface-enhanced Raman spectroscopy.
This study reports a novel microfluidic platform for rapid and long-ranged concentration of rare-pathogen from human blood for subsequent on-chip surface-enhanced Raman spectroscopy (SERS) identification/discrimination of bacteria based on their detected fingerprints. Using a hybrid electrokinetic mechanism, bacteria can be concentrated at the stagnation area on the SERS-active roughened electrode, while blood cells were excluded away from this region at the center of concentric circular electrodes. This electrokinetic approach performs isolation and concentration of bacteria in about three minutes; the density factor is increased approximately a thousand fold in a local area of ~5000 μm(2) from a low bacteria concentration of 5 × 10(3) CFU/ml. Besides, three genera of bacteria, S. aureus, E. coli, and P. aeruginosa that are found in most of the isolated infections in bacteremia were successfully identified in less than one minute on-chip without the use of any antibody/chemical immobilization and reaction processes
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