45,574 research outputs found
A toral diffeomorphism with a non-polygonal rotation set
We construct a diffeomorphism of the two-dimensional torus which is isotopic
to the identity and whose rotation set is not a polygon
Density of non-residues in Burgess-type intervals and applications
We show that for any fixed \eps>0, there are numbers and with the following property: for every prime and every integer
such that p^{1/(4\sqrt{e})+\eps}\le N\le p, the sequence
contains at least quadratic non-residues modulo . We use this
result to obtain strong upper bounds on the sizes of the least quadratic
non-residues in Beatty and Piatetski--Shapiro sequences.Comment: In the new version we use an idea of Roger Heath-Brown (who is now a
co-author) to simply the proof and improve the main results of the previous
version, 14 page
Effect of pulsed power on particle matter in diesel engine exhaust using a DBD plasma reactor
Nonthermal plasma (NTP) treatment of exhaust gas is a promising technology for both nitrogen oxides (NOX) and particulate matter (PM) reduction by introducing plasma into the exhaust gases. This paper considers the effect of NTP on PM mass reduction, PM size distribution, and PM removal efficiency. The experiments are performed on real exhaust gases from a diesel engine. The NTP is generated by applying high-voltage pulses using a pulsed power supply across a dielectric barrier discharge (DBD) reactor. The effects of the applied high-voltage pulses up to 19.44 kVpp with repetition rate of 10 kHz are investigated. In this paper, it is shown that the PM removal and PM size distribution need to be considered both together, as it is possible to achieve high PM removal efficiency with undesirable increase in the number of small particles. Regarding these two important factors, in this paper, 17 kVpp voltage level is determined to be an optimum point for the given configuration. Moreover, particles deposition on the surface of the DBD reactor is found to be a significant phenomenon, which should be considered in all plasma PM removal tests
Lattice dynamics and electron-phonon coupling in Sr2RuO4
The lattice dynamics in SrRuO has been studied by inelastic neutron
scattering combined with shell-model calculations. The in-plane bond-stretching
modes in SrRuO exhibit a normal dispersion in contrast to all
electronically doped perovskites studied so far. Evidence for strong electron
phonon coupling is found for c-polarized phonons suggesting a close connection
with the anomalous c-axis charge transport in SrRuO.Comment: 11 pages, 8 figures 2 table
Resolvent Estimates in L^p for the Stokes Operator in Lipschitz Domains
We establish the resolvent estimates for the Stokes operator in
Lipschitz domains in , for . The result, in particular, implies that the Stokes operator in a
three-dimensional Lipschitz domain generates a bounded analytic semigroup in
for (3/2)-\varep < p< 3+\epsilon. This gives an affirmative answer to a
conjecture of M. Taylor.Comment: 28 page. Minor revision was made regarding the definition of the
Stokes operator in Lipschitz domain
Probing the Crust of the Neutron Star in EXO 0748-676
X-ray observations of quiescent X-ray binaries have the potential to provide
insight into the structure and the composition of neutron stars. EXO 0748-676
had been actively accreting for over 24 yr before its outburst ceased in late
2008. Subsequent X-ray monitoring revealed a gradual decay of the quiescent
thermal emission that can be attributed to cooling of the accretion-heated
neutron star crust. In this work, we report on new Chandra and Swift
observations that extend the quiescent monitoring to ~5 yr post-outburst. We
find that the neutron star temperature remained at ~117 eV between 2009 and
2011, but had decreased to ~110 eV in 2013. This suggests that the crust has
not fully cooled yet, which is supported by the lower temperature of ~95 eV
that was measured ~4 yr prior to the accretion phase in 1980. Comparing the
data to thermal evolution simulations reveals that the apparent lack of cooling
between 2009 and 2011 could possibly be a signature of convection driven by
phase separation of light and heavy nuclei in the outer layers of the neutron
star.Comment: 9 pages, 4 tables, 3 figures. Minor revisions according to referee
report. Accepted to Ap
Generalized Unitarity and Six-Dimensional Helicity
We combine the unitarity method with the six-dimensional helicity formalism
of Cheung and O'Connell to construct loop-level scattering amplitudes. As a
first example, we construct dimensionally regularized QCD one-loop four-point
amplitudes. As a nontrivial multiloop example, we confirm that the recently
constructed four-loop four-point amplitude of N=4 super-Yang-Mills theory,
including nonplanar contributions, is valid for dimensions less than or equal
to six. We comment on the connection of our approach to the recently discussed
Higgs infrared regulator and on dual conformal properties in six dimensions.Comment: 38 pages, 7 figures, typos correcte
Rectification from Radially-Distorted Scales
This paper introduces the first minimal solvers that jointly estimate lens
distortion and affine rectification from repetitions of rigidly transformed
coplanar local features. The proposed solvers incorporate lens distortion into
the camera model and extend accurate rectification to wide-angle images that
contain nearly any type of coplanar repeated content. We demonstrate a
principled approach to generating stable minimal solvers by the Grobner basis
method, which is accomplished by sampling feasible monomial bases to maximize
numerical stability. Synthetic and real-image experiments confirm that the
solvers give accurate rectifications from noisy measurements when used in a
RANSAC-based estimator. The proposed solvers demonstrate superior robustness to
noise compared to the state-of-the-art. The solvers work on scenes without
straight lines and, in general, relax the strong assumptions on scene content
made by the state-of-the-art. Accurate rectifications on imagery that was taken
with narrow focal length to near fish-eye lenses demonstrate the wide
applicability of the proposed method. The method is fully automated, and the
code is publicly available at https://github.com/prittjam/repeats.Comment: pre-prin
Combinatorial stress responses: direct coupling of two major stress responses in Escherichia coli
Nitrogen is an essential element for all life, and this is no different for the bacterial cell. Numerous cellular macromolecules contain nitrogen, including proteins, nucleic acids and cell wall components. In Escherichia coli and related bacteria, the nitrogen stress (Ntr) response allows cells to rapidly sense and adapt to nitrogen limitation by scavenging for alternative nitrogen sources through the transcriptional activation of transport systems and catabolic and biosynthetic operons by the global transcriptional regulator NtrC. Nitrogen-starved bacterial cells also synthesize the (p)ppGpp effector molecules of a second global bacterial stress response - the stringent response. Recently, we showed that the transcription of relA, the gene which encodes the major (p)ppGpp synthetase in E. coli, is activated by NtrC during nitrogen starvation. Our results revealed that in E. coli and related bacteria, NtrC functions in combinatorial stress and serves to couple two major stress responses, the Ntr response and stringent response
Inviscid dynamical structures near Couette flow
Consider inviscid fluids in a channel {-1<y<1}. For the Couette flow
v_0=(y,0), the vertical velocity of solutions to the linearized Euler equation
at v_0 decays in time. At the nonlinear level, such inviscid damping has not
been proved. First, we show that in any (vorticity) H^{s}(s<(3/2)) neighborhood
of Couette flow, there exist non-parallel steady flows with arbitrary minimal
horizontal period. This implies that nonlinear inviscid damping is not true in
any (vorticity) H^{s}(s<(3/2)) neighborhood of Couette flow and for any
horizontal period. Indeed, the long time behavior in such neighborhoods are
very rich, including nontrivial steady flows, stable and unstable manifolds of
nearby unstable shears. Second, in the (vorticity) H^{s}(s>(3/2)) neighborhood
of Couette, we show that there exist no non-parallel steadily travelling flows
v(x-ct,y), and no unstable shears. This suggests that the long time dynamics in
H^{s}(s>(3/2)) neighborhoods of Couette might be much simpler. Such contrasting
dynamics in H^{s} spaces with the critical power s=(3/2) is a truly nonlinear
phenomena, since the linear inviscid damping near Couette is true for any
initial vorticity in L^2
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