9,050 research outputs found
Adaptive BDDC algorithms for the system arising from plane wave discretization of Helmholtz equations
Balancing domain decomposition by constraints (BDDC) algorithms with adaptive
primal constraints are developed in a concise variational framework for the
weighted plane wave least-squares (PWLS) discritization of Helmholtz equations
with high and various wave numbers. The unknowns to be solved in this
preconditioned system are defined on elements rather than vertices or edges,
which are different from the well-known discritizations such as the classical
finite element method. Through choosing suitable "interface" and appropriate
primal constraints with complex coefficients and introducing some local
techniques, we developed a two-level adaptive BDDC algorithm for the PWLS
discretization, and the condition number of the preconditioned system is proved
to be bounded above by a user-defined tolerance and a constant which is only
dependent on the maximum number of interfaces per subdomain. A multilevel
algorithm is also attempted to resolve the bottleneck in large scale coarse
problem. Numerical results are carried out to confirm the theoretical results
and illustrate the efficiency of the proposed algorithms
Stochastic Linear Quadratic Stackelberg Differential Game with Overlapping Information
This paper is concerned with the stochastic linear quadratic Stackelberg
differential game with overlapping information, where the diffusion terms
contain the control and state variables. Here the term "overlapping" means that
there are common part between the follower's and the leader's information,
while they have no inclusion relation. Optimal controls of the follower and the
leader are obtained by the stochastic maximum principle, the direct calculation
of the derivative of the cost functional and stochastic filtering. A new system
of Riccati equations is introduced to represent the state estimate feedback of
the Stackelberg equilibrium strategy. A special solvable case is then studied
and is applied to the continuous-time principal-agent problem.Comment: 43 page
Leader-Follower Stochastic Differential Game with Asymmetric Information and Applications
This paper is concerned with a leader-follower stochastic differential game
with asymmetric information, where the information available to the follower is
based on some sub--algebra of that available to the leader. Such kind
of game problem has wide applications in finance, economics and management
engineering such as newsvendor problems, cooperative advertising and pricing
problems. Stochastic maximum principles and verification theorems with partial
information are obtained, to represent the Stackelberg equilibrium. As
applications, a linear-quadratic leader-follower stochastic differential game
with asymmetric information is studied. It is shown that the open-loop
Stackelberg equilibrium admits a state feedback representation if some system
of Riccati equations is solvable.Comment: 20 pages. The main content of this paper is presented by the first
author in IMS-China International Conference on Statistics and Probability,
Kunming, P.R. China, June 201
Anomalous magnetohydrodynamics with longitudinal boost invariance and chiral magnetic effect
We study relativistic magnetohydrodynamics with longitudinal boost invariance
in the presence of chiral magnetic effects and finite electric conductivity.
With initial magnetic fields parallel or anti-parallel to electric fields, we
derive the analytic solutions of electromagnetic fields and the chiral number
and energy density in an expansion of several parameters determined by initial
conditions. The numerical solutions show that such analytic solutions work well
in weak fields or large chiral fluctuations. We also discuss the properties of
electromagnetic fields in the laboratory frame.Comment: 27 pages, 5 figure
Randomized Consensus based Distributed Kalman Filtering over Wireless Sensor Networks
This paper is concerned with developing a novel distributed Kalman filtering
algorithm over wireless sensor networks based on randomized consensus strategy.
Compared with the centralized algorithm, distributed filtering techniques
require less computation per sensor and lead to more robust estimation since
they simply use the information from the neighboring nodes in the network.
However, poor local sensor estimation caused by limited observability and
network topology changes which interfere the global consensus are challenging
issues. Motivated by this observation, we propose a novel randomized
gossip-based distributed Kalman filtering algorithm. Information exchange and
computation in the proposed algorithm can be carried out in an arbitrarily
connected network of nodes. In addition, the computational burden can be
distributed for a sensor which communicates with a stochastically selected
neighbor at each clock step under schemes of gossip algorithm. In this case,
the error covariance matrix changes stochastically at every clock step, thus
the convergence is considered in a probabilistic sense. We provide the mean
square convergence analysis of the proposed algorithm. Under a sufficient
condition, we show that the proposed algorithm is quite appealing as it
achieves better mean square error performance theoretically than the
noncooperative decentralized Kalman filtering algorithm. Besides, considering
the limited computation, communication, and energy resources in the wireless
sensor networks, we propose an optimization problem which minimizes the average
expected state estimation error based on the proposed algorithm. To solve the
proposed problem efficiently, we transform it into a convex optimization
problem. And a sub-optimal solution is attained. Examples and simulations are
provided to illustrate the theoretical results
Morita Equivalence and Interpolation of The Dirac-Born-infeld Theory on the Non-Commutative Torus
In the noncommutative Dirac-Born-Infeld action with Chern-Simons term, an
interpolation field is used in both DBI action and Chern-Simons term.
The Morita equivalence is discussed in both the lagrangian and the Hamiltonian
formalisms, which is more transparent in this treatment.Comment: 6 pages, latex, no figure
Computing optimal interfacial structure of ordered phases
We propose a general framework of computing interfacial structure. If an
ordered phase is involved, the interfacial structure can be obtained by simply
minimizing the free energy with compatible boundary conditions. The framework
is applied to Landau- Brazovskii model and works efficiently
Exact solutions to the three-dimensional Gross-Pitaevskii equation with modulated radial nonlinearity
We study the Bose-Einstein condensate trapped in a three-dimensional
spherically symmetrical potential. Exact solutions to the stationary
Gross-Pitaevskii equation are obtained for properly modulated radial
nonlinearity. The solutions contain vortices with different winding numbers and
exhibit the shell-soliton feature in the radial distributions.Comment: 5 figure
Computing optimal interfacial structure of modulated phases
We propose a general framework of computing interfacial structures between
two modulated phases. Specifically we propose to use a computational box
consisting of two half spaces, each occupied by a modulated phase with given
position and orientation. The boundary conditions and basis functions are
chosen to be commensurate with the bulk structures. It is observed that the
ordered nature of modulated structures stabilizes the interface, which enables
us to obtain optimal interfacial structures by searching local minima of the
free energy landscape. The framework is applied to the Landau-Brazovskii model
to investigate interfaces between modulated phases with different relative
positions and orientations. Several types of novel complex interfacial
structures are obtained from the calculations.Comment: 15 pages, 7 figures. arXiv admin note: substantial text overlap with
arXiv:1511.0362
Inheritance Study on the Culture of Traditional Music in Middle and Primary Education: Taking South Korean Music Curriculum as an Example
âMusicâ and âeducationâ are the organic components of culture. South Korea show great solicitude for the succeeding of traditional culture in middle and primary education. During the instant, pluralistic and open globalization period, it gives consideration to the ultimate value pursuit of both the times and its own laws, forming a distinctive music curriculum. This paper clarifies the feasibility and necessity of the succeeding of such sort of culture. On the basis of actively elaborating the concept and curriculum content, this paper does propose a whole string of inheritance trajectory of this kind of culture, which has important reference significance for further coming true the succeeding of traditional culture in studentsâ education
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