8,618 research outputs found
Simultaneous Deformations of Lie Algebroids and Lie Subalgebroids
The -algebra is an algebraic structure suitable for describing
deformation problems. In this paper we construct one -algebra, which
turns out to be a differential graded Lie algebra, to control the deformations
of Lie algebroids and a second one to control the deformations of Lie
subalgebroids. We also combine these two -algebras into one to
control the simultaneous deformations of a Lie algebroid and its Lie
subalgebroids. The results generalize the deformation theory of Lie algebra and
Lie subalgebras. Applications of our results include deformations of
foliations, deformations of complex structures and deformations of
homomorphisms of Lie algebroids
Deformations of Courant Algebroids and Dirac Structures via Blended Structures
Deformations of a Courant Algebroid E and its Dirac subbundle A have been
widely considered under the assumption that the pseudo-Euclidean metric is
fixed. In this paper, we attack the same problem in a setting that allows the
pseudo-Euclidean metric to deform. Thanks to Roytenberg, a Courant algebroid is
equivalent to a symplectic graded Q-manifold of degree 2. From this viewpoint,
we extend the notions of graded Q-manifold, DGLA and L_\infty-algebra all to
"blended" version so that Poisson manifold, Lie algebroid and Courant algebroid
are unified as blended Q-manifolds; and define a submaniold A of "coisotropic
type" which naturally generalizes the concepts of coisotropic submanifolds, Lie
subalgebroids and Dirac subbundles. It turns out the deformations a blended
homological vector field Q is controlled by a blended DGLA, and the
deformations of A is controlled by a blended L_\infty-algebra. The results
apply to the deformations of a Courant algebroid and its Dirac structures, the
deformations of a Poisson manifold and its coisotropic submanifold, the
deformations of a Lie algebroid and its Lie subalgebroid
The scattering outcomes of Kepler circumbinary planets: planet mass ratio
Recent studies reveal that the free eccentricities of Kepler-34b and
Kepler-413b are much larger than their forced eccentricities, implying that the
scattering events may take place in their formation. The observed orbital
configuration of Kepler-34b cannot be well reproduced in disk-driven migration
models, whereas a two-planet scattering scenario can play a significant role of
shaping the planetary configuration. These studies indicate that circumbinary
planets discovered by Kepler may have experienced scattering process. In this
work, we extensively investigate the scattering outcomes of circumbinary
planets focusing on the effects of planet mass ratio. We find that the
planetary mass ratio and the the initial relative locations of planets act as
two important parameters which affect the eccentricity distribution of the
surviving planets. As an application of our model, we discuss the observed
orbital configurations of Kepler-34b and Kepler-413b. We first adopt the
results from the disk-driven models as the initial conditions, then simulate
the scattering process occurred in the late evolution stage of circumbinary
planets. We show that the present orbital configurations of Kepler-34b and
Kepler-413b can be well reproduced when considering two unequal-mass planet
ejection model. Our work further suggests that some of the currently discovered
circumbinary single-planet systems may be the survivals of original
multiple-planet systems. The disk-driven migration and the scattering events
occurring in the late stage both play an irreplaceable role in sculpting the
final systems.Comment: 18 pages, 9 figures, accepted for publication in A
Formation of S-type planets in close binaries: scattering induced tidal capture of circumbinary planets
Although several S-type and P-type planets in binary systems were discovered
in past years, S-type planets have not yet been found in close binaries with an
orbital separation not more than 5 au. Recent studies suggest that S-type
planets in close binaries may be detected through high-accuracy observations.
However, nowadays planet formation theories imply that it is difficult for
S-type planets in close binaries systems to form in situ. In this work, we
extensively perform numerical simulations to explore scenarios of planet-planet
scattering among circumbinary planets and subsequent tidal capture in various
binary configurations, to examine whether the mechanism can play a part in
producing such kind of planets. Our results show that this mechanism is robust.
The maximum capture probability is , which can be comparable to the
tidal capture probability of hot Jupiters in single star systems. The capture
probability is related to binary configurations, where a smaller eccentricity
or a low mass ratio of the binary will lead to a larger probability of capture,
and vice versa. Furthermore, we find that S-type planets with retrograde orbits
can be naturally produced via capture process. These planets on retrograde
orbits can help us distinguish in situ formation and post-capture origin for
S-type planet in close binaries systems. The forthcoming missions (PLATO) will
provide the opportunity and feasibility to detect such planets. Our work
provides several suggestions for selecting target binaries in search for S-type
planets in the near future.Comment: 12 pages, 6 figures, accepted for publication in MNRA
Terrestrial Planets Formation around Circumbinary Habitable Zone: Inward Migration in the Planetesimal Swarm
According to the core accretion theory, circumbinary embryos can form only
beyond a critical semimajor axis (CSMA). However, due to the relatively high
density of solid materials in the inner disk, significant amount of small
planetesimals must exist in the inner zone when embryos were forming outside
this CSMA. So embryos migration induced by the planetesimal swarm is possible
after the gas disk depletion. Through numerical simulations, we found (i) the
scattering-driven inward migration of embryos is robust, planets can form in
the habitable zone if we adopt a mass distribution of MMSN-like disk; (ii) the
total mass of the planetesimals in the inner region and continuous
embryo-embryo scattering are two key factors that cause significant embryo
migrations; (iii) the scattering-driven migration of embryos is a natural
water-deliver mechanism. We propose that planet detections should focus on the
close binary with its habitable zone near CSMA.Comment: Accepted for publication at ApJ
Anti-rumor dynamics and emergence of the timing threshold on complex network
Anti-rumor dynamics is proposed on the basis of rumor dynamics and the
characteristics of anti-rumor dynamics are explored by both mean-field
equations and numerical simulations on complex network. The main metrics we
study are the timing effect of combating rumor and the identification of
influential nodes, which are what an efficient strategy against rumor may
concern about. The results indicate that, there exists robust time dependence
of anti-rumor dynamics and the timing threshold emerges as a consequence of
launching the anti-rumor at different delay time after the beginning of rumor
spreading. The timing threshold as a critical feature is further verified on a
series of Barabasi-Albert scale-free networks (BA networks), where anti-rumor
dynamics arises explicitly. The timing threshold is a network-dependent
quantity and its value decreases as the average degree of the BA network
increases until close to zero. Meanwhile, coreness also constitutes a better
topological descriptor to identify hubs. Our results will hopefully be useful
for the understanding of spreading behaviors of rumor and anti-rumor and
suggest a possible avenue for further study of interplays of multiple pieces of
information on complex network.Comment: 11 pages, 5 figures, Physica A: Statistical Mechanics and its
Applications (2014
The theory of superstring with flux on non-Kahler manifolds and the complex Monge-Ampere equation
The purpose of this paper is to solve a problem posed by Strominger in
constructing smooth models of superstring theory with flux. These are given by
non-Kahler manifolds with torsion
Existence of Supersymmetric Hermitian Metrics with Torsion on Non-Kaehler Manifolds
We proved the existence of supersymmetric Hermitian metrics with torsion on a
class of non-Kaehler manifolds.Comment: 48 page
Cache-aided Interference Management Using Hypercube Combinatorial Cache Designs
We consider a cache-aided interference network which consists of a library of
files, transmitters and receivers (users), each equipped with a
local cache of size and files respectively, and connected via a
discrete-time additive white Gaussian noise channel. Each receiver requests an
arbitrary file from the library. The objective is to design a cache placement
without knowing the receivers' requests and a communication scheme such that
the sum Degrees of Freedom (sum-DoF) of the delivery is maximized. This network
model has been investigated by Naderializadeh {\em et al.}, who proposed a
prefetching and a delivery schemes that achieves a sum-DoF of
. One of biggest limitations of this
scheme is the requirement of high subpacketization level. This paper is the
first attempt in the literature (according to our knowledge) to reduce the file
subpacketization in such a network. In particular, we propose a new approach
for both prefetching and linear delivery schemes based on a combinatorial
design called {\em hypercube}. We show that required number of packets per file
can be exponentially reduced compared to the state of the art scheme proposed
by Naderializadeh {\em et al.}, or the NMA scheme. When , the achievable one-shot sum-DoF using this approach is
, which shows that 1) the one-shot sum-DoF scales
linearly with the aggregate cache size in the network and 2) it is within a
factor of to the information-theoretic optimum. Surprisingly, the identical
and near optimal sum-DoF performance can be achieved using the hypercube
approach with a much less file subpacketization.Comment: 6 pages, 4 figures, accepted by ICC 201
Synchronized output regulation of nonlinear multi-agent systems
This paper considers the synchronized output regulation (SOR) problem of
nonlinear multi-agent systems with switching graph. The SOR means that all
agents regulate their outputs to synchronize on the output of a predefined
common exosystem. Each agent constructs its local exosystem with the same
dynamics as that of the common exosystem and exchanges the state information of
the local exosystem. It is shown that the SOR is solvable under the assumptions
same as that for nonlinear output regulation of a single agent, if the
switching graph satisfies the bounded interconnectivity times condition. Both
state feedback and output feedback are addressed. A numerical simulation is
made to show the efficacy of the analytic results.Comment: 20 pages, 2 figures, submitted to International Journal of Contro
- …