116 research outputs found
The Sylvester equation and integrable equations: I. The Korteweg-de Vries system and sine-Gordon equation
The paper is to reveal the direct links between the well known Sylvester
equation in matrix theory and some integrable systems. Using the Sylvester
equation we introduce a scalar
function
which is defined as same as in discrete case. satisfy some
recurrence relations which can be viewed as discrete equations and play
indispensable roles in deriving continuous integrable equations. By imposing
dispersion relations on and , we find the
Korteweg-de Vries equation, modified Korteweg-de Vries equation, Schwarzian
Korteweg-de Vries equation and sine-Gordon equation can be expressed by some
discrete equations of defined on certain points. Some special
matrices are used to solve the Sylvester equation and prove symmetry property
. The solution provides function
by . We hope our results can not only
unify the Cauchy matrix approach in both continuous and discrete cases, but
also bring more links for integrable systems and variety of areas where the
Sylvester equation appears frequently.Comment: 23 page
Testing of high current transformer by non-uniform equivalent magnetomotive force method
Peer Reviewe
Design of the Tsinghua Tabletop Kibble Balance
The Kibble balance is a precision instrument for realizing the mass unit, the
kilogram, in the new international system of units (SI). In recent years, an
important trend for Kibble balance experiments is to go tabletop, in which the
instrument's size is notably reduced while retaining a measurement accuracy of
. In this paper, we report a new design of a tabletop Kibble balance
to be built at Tsinghua University. The Tsinghua Kibble balance aims to deliver
a compact instrument for robust mass calibrations from 10 g to 1 kg with a
targeted measurement accuracy of 50 g or less. Some major features of the
Tsinghua Kibble balance system, including the design of a new magnet, one-mode
measurement scheme, the spring-compensated magnet moving mechanism, and
magnetic shielding considerations, are discussed.Comment: 8 pages, 9 figure
Multi-helical Lamb Wave Imaging for Pipe-like Structures Based on a Probabilistic Reconstruction Approach
The special form of pipe-like structure provides the helical route for ultrasonic guided wave. Considering the pipe as a flattened plate but with periodical replications, the helical wave becomes intuitional and a corresponding imaging algorithm can be constructed. This work proposes the multihelical Lamb wave imaging method by utilizing the multiple arrival wavepackets which are denoted as different orders. The helical wave signal model is presented and the constant group velocity point is illustrated. The probabilistic reconstruction algorithm is combined with the separation and fusion of different helical routes. To verify the proposed scheme, finite element simulations and corresponding experiments are conducted. The cases of single-defect simulation and two-defect simulation indicate the successful and robust implementation of the imaging algorithm. The test on actual pipe damage is also investigated to show its capability in imaging an irregular defect. The comparison with imaging results from only first arrival demonstrates the advantage of multihelical wave imaging, including the better imaging resolution and higher localization accuracy
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