87,287 research outputs found
On the B-twisted topological sigma model and Calabi-Yau geometry
We provide a rigorous perturbative quantization of the B-twisted topological
sigma model via a first order quantum field theory on derived mapping space in
the formal neighborhood of constant maps. We prove that the first Chern class
of the target manifold is the obstruction to the quantization via
Batalin-Vilkovisky formalism. When the first Chern class vanishes, i.e. on
Calabi-Yau manifolds, the factorization algebra of observables gives rise to
the expected topological correlation functions in the B-model. We explain a
twisting procedure to generalize to the Landau-Ginzburg case, and show that the
resulting topological correlations coincide with Vafa's residue formula.Comment: 73 pages. Comments welcom
Implicit Asymptotic Preserving Method for Linear Transport Equations
The computation of the radiative transfer equation is expensive mainly due to
two stiff terms: the transport term and the collision operator. The stiffness
in the former comes from the fact that particles (such as photons) travels at
the speed of light, while that in the latter is due to the strong scattering in
the diffusive regime. We study the fully implicit scheme for this equation to
account for the stiffness. The main challenge in the implicit treatment is the
coupling between the spacial and velocity coordinates that requires the large
size of the to-be-inverted matrix, which is also ill-conditioned and not
necessarily symmetric. Our main idea is to utilize the spectral structure of
the ill-conditioned matrix to construct a pre-conditioner, which, along with an
exquisite split of the spatial and angular dependence, significantly improve
the condition number and allows matrix-free treatment. We also design a fast
solver to compute this pre-conditioner explicitly in advance. Meanwhile, we
reformulate the system via an even-odd parity, which results in a symmetric and
positive definite matrix that can be inverted using conjugate gradient method.
This idea can also be implemented to the original non-symmetric system whose
inversion is solved by GMRES. A qualitative comparison with the conventional
methods, including Krylov iterative method pre-conditioned with diffusive
synthetic acceleration and asymptotic preserving scheme via even-odd
decomposition, is also discussed
On the Number of Zeros and Poles of Dirichlet Series
This paper investigates lower bounds on the number of zeros and poles of a
general Dirichlet series in a disk of radius and gives, as a consequence,
an affirmative answer to an open problem of Bombieri and Perelli on the bound.
Applications will also be given to Picard type theorems, global estimates on
the symmetric difference of zeros, and uniqueness problems for Dirichlet
series.Comment: 24 page
Second Stop and Sbottom Searches with a Stealth Stop
The top squarks (stops) may be the most wanted particles after the Higgs
boson discovery. The searches for the lightest stop have put strong constraints
on its mass. However, there is still a search gap in the low mass region if the
spectrum of the stop and the lightest neutralino is compressed. In that case,
it may be easier to look for the second stop since naturalness requires both
stops to be close to the weak scale. The current experimental searches for the
second stop are based on the simplified model approach with the decay modes
and . However,
in a realistic supersymmetric spectrum there is always a sbottom lighter than
the second stop, hence the decay patterns are usually more complicated than the
simplified model assumptions. In particular, there are often large branching
ratios of the decays and as long as they are open. The decay chains can be even more
complex if there are intermediate states of additional charginos and
neutralinos in the decays. By studying several MSSM benchmark models at the 14
TeV LHC, we point out the importance of the multi- final states in the
second stop and the sbottom searches, such as the same-sign dilepton and
multilepton signals, aside from the traditional search modes. The observed
same-sign dilepton excesses at LHC Run 1 and Run 2 may be explained by some of
our benchmark models. We also suggest that the vector boson tagging and a new
kinematic variable may help to suppress the backgrounds and increase the signal
significance for some search channels. Due to the complex decay patterns and
lack of the dominant decay channels, the best reaches likely require a
combination of various search channels at the LHC for the second stop and the
lightest sbottom.Comment: 46 pages, 9 figures, updated experimental constraints and benchmark
points after the ICHEP2016 data, published in JHE
Response to "Reply to comment on 'Divergent and Ultrahigh Thermal Conductivity in Millimeter-Long Nanotubes'"
More than one year ago, Prof. Chih-Wei Chang and the co-authors published
"Divergent and Ultrahigh Thermal Conductivity in Millimeter-Long Nanotubes" in
PRL and we submitted a comment. After some while we received Prof. Chang et
al.'s reply, which is almost the same as their arXiv preprint, and responded to
the reply promptly. On the request of some readers, I personally post here the
detailed response to "Reply to comment on 'Divergent and Ultrahigh Thermal
Conductivity in Millimeter-Long Nanotubes'"
A characterization of rational functions
We give an elementary characterization of rational functions among
meromorphic functions in the complex plane
Constraining the Compressed Top Squark and Chargino along the W Corridor
Studying superpartner production together with a hard initial state radiation
(ISR) jet has been a useful strategy for searches of supersymmetry with a
compressed spectrum at the Large Hadron Collider (LHC). In the case of the top
squark (stop), the ratio of the missing transverse momentum from the lightest
neutralinos and the ISR momentum, defined as , turns out to be an
effective variable to distinguish the signal from the backgrounds. It has
helped to exclude the stop mass below 590 GeV along the top corridor where
. On the other hand, the
current experimental limit is still rather weak in the corridor where
. In this work we extend
this strategy to the parameter region around the corridor by considering
the one lepton final state. In this case the kinematic constraints are
insufficient to completely determine the neutrino momentum which is required to
calculate . However, the minimum value of consistent
with the kinematic constraints still provides a useful discriminating variable,
allowing the exclusion reach of the stop mass to be extended to GeV
based on the current 36 fb LHC data. The same method can also be applied
to the chargino search with because the analysis does not rely on jets. If no excess is
present in the current data, a chargino mass of 300 GeV along the corridor
can be excluded, beyond the limit obtained from the multilepton search.Comment: 29 pages,8 figure
A new numerical approach to inverse transport equation with error analysis
The inverse radiative transfer problem finds broad applications in medical
imaging, atmospheric science, astronomy, and many other areas. This problem
intends to recover the optical properties, denoted as absorption and scattering
coefficient of the media, through the source-measurement pairs. A typical
computational approach is to form the inverse problem as a PDE-constraint
optimization, with the minimizer being the to-be-recovered coefficients. The
method is tested to be efficient in practice, but lacks analytical
justification: there is no guarantee of the existence or uniqueness of the
minimizer, and the error is hard to quantify. In this paper, we provide a
different algorithm by levering the ideas from singular decomposition analysis.
Our approach is to decompose the measurements into three components, two out of
which encode the information of the two coefficients respectively. We then
split the optimization problem into two subproblems and use those two
components to recover the absorption and scattering coefficients separately. In
this regard, we prove the well-posedness of the new optimization, and the error
could be quantified with better precision. In the end, we incorporate the
diffusive scaling and show that the error is harder to control in the diffusive
limit
Stability of Stationary Inverse Transport Equation in Diffusion Scaling
We consider the inverse problem of reconstructing the optical parameters for
stationary radiative transfer equation (RTE) from velocity-averaged
measurement. The RTE often contains multiple scales characterized by the
magnitude of a dimensionless parameter---the Knudsen number (). In the
diffusive scaling (), the stationary RTE is well approximated by an
elliptic equation in the forward setting. However, the inverse problem for the
elliptic equation is acknowledged to be severely ill-posed as compared to the
well-posedness of inverse transport equation, which raises the question of how
uniqueness being lost as . We tackle this problem by
examining the stability of inverse problem with varying . We show that,
the discrepancy in two measurements is amplified in the reconstructed
parameters at the order of , and as a result lead
to ill-posedness in the zero limit of . Our results apply to both
continuous and discrete settings. Some numerical tests are performed in the end
to validate these theoretical findings
Transport Protocols in Cognitive Radio Networks: A Survey
Cognitive radio networks (CRNs) have emerged as a promising solution to
enhance spectrum utilization by using unused or less used spectrum in radio
environments. The basic idea of CRNs is to allow secondary users (SUs) access
to licensed spectrum, under the condition that the interference perceived by
the primary users (PUs) is minimal. In CRNs, the channel availability is
uncertainty due to the existence of PUs, resulting in intermittent
communication. Transmission control protocol (TCP) performance may
significantly degrade in such conditions. To address the challenges, some
transport protocols have been proposed for reliable transmission in CRNs. In
this paper we survey the state-of-the-art transport protocols for CRNs. We
firstly highlight the unique aspects of CRNs, and describe the challenges of
transport protocols in terms of PU behavior, spectrum sensing, spectrum
changing and TCP mechanism itself over CRNs. Then, we provide a summary and
comparison of existing transport protocols for CRNs. Finally, we discuss
several open issues and research challenges. To the best of our knowledge, our
work is the first survey on transport protocols for CRNs.Comment: to appear in KSII Transactions on Internet and Information System
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