67 research outputs found
On the accuracy of solving confluent Prony systems
In this paper we consider several nonlinear systems of algebraic equations
which can be called "Prony-type". These systems arise in various reconstruction
problems in several branches of theoretical and applied mathematics, such as
frequency estimation and nonlinear Fourier inversion. Consequently, the
question of stability of solution with respect to errors in the right-hand side
becomes critical for the success of any particular application. We investigate
the question of "maximal possible accuracy" of solving Prony-type systems,
putting stress on the "local" behavior which approximates situations with low
absolute measurement error. The accuracy estimates are formulated in very
simple geometric terms, shedding some light on the structure of the problem.
Numerical tests suggest that "global" solution techniques such as Prony's
algorithm and ESPRIT method are suboptimal when compared to this theoretical
"best local" behavior
Fractal Weyl law for chaotic microcavities: Fresnel's laws imply multifractal scattering
We demonstrate that the harmonic inversion technique is a powerful tool to
analyze the spectral properties of optical microcavities. As an interesting
example we study the statistical properties of complex frequencies of the fully
chaotic microstadium. We show that the conjectured fractal Weyl law for open
chaotic systems [W. T. Lu, S. Sridhar, and M. Zworski, Phys. Rev. Lett. 91,
154101 (2003)] is valid for dielectric microcavities only if the concept of the
chaotic repeller is extended to a multifractal by incorporating Fresnel's laws.Comment: 8 pages, 12 figure
Eigenvectors in the Superintegrable Model II: Ground State Sector
In 1993, Baxter gave eigenvalues of the transfer matrix of the
-state superintegrable chiral Potts model with spin-translation quantum
number , where . In our previous paper we
studied the Q=0 ground state sector, when the size of the transfer matrix
is chosen to be a multiple of . It was shown that the corresponding
matrix has a degenerate eigenspace generated by the generators of
simple algebras. These results enable us to express the transfer matrix
in the subspace in terms of these generators and for
. Moreover, the corresponding eigenvectors of the transfer
matrix are expressed in terms of rotated eigenvectors of .Comment: LaTeX 2E document, using iopart.cls with iopams packages. 17 pages,
uses eufb10 and eurm10 fonts. Typeset twice! vs2: Many changes and additions,
adding 7 pages. vs3: minor corrections. vs4 minor improvement
Excited-State Effective Masses in Lattice QCD
We apply black-box methods, i.e. where the performance of the method does not
depend upon initial guesses, to extract excited-state energies from
Euclidean-time hadron correlation functions. In particular, we extend the
widely used effective-mass method to incorporate multiple correlation functions
and produce effective mass estimates for multiple excited states. In general,
these excited-state effective masses will be determined by finding the roots of
some polynomial. We demonstrate the method using sample lattice data to
determine excited-state energies of the nucleon and compare the results to
other energy-level finding techniques.Comment: 18 pages, 6 figure
Development of the Bélanger Equation and Backwater Equation by Jean-Baptiste Bélanger (1828)
A hydraulic jump is the sudden transition from a high-velocity to a low-velocity open channel flow. The application of the momentum principle to the hydraulic jump is commonly called the Bélanger equation, but few know that Bélanger's (1828) treatise was focused on the study of gradually varied open channel flows. Further, although Bélanger understood the rapidly-varied nature of the jump flow, he applied incorrectly the Bernoulli principle in 1828, and corrected his approach 10 years later. In 1828, his true originality lay in the successful development of the backwater equation for steady, one-dimensional gradually-varied flows in an open channel, together with the introduction of the step method, distance calculated from depth, and the concept of critical flow conditions
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