scholarly journals The diffractive wave trace on manifolds with conic singularities

2017 ◽  
Vol 304 ◽  
pp. 1330-1385 ◽  
Author(s):  
G. Austin Ford ◽  
Jared Wunsch
Keyword(s):  
Wave Trace

Evaluating Possibility of Registering Scattered Gravitational Radiation on Wormholes

2020 ◽  
pp. 89-102
Author(s):  
A.A. Kirillov ◽  
D.P. Krichevskiy
Keyword(s):  
Numerical Simulation ◽  
Gravitational Wave ◽  
Cross Section ◽  
Gravitational Radiation ◽  
Wave Amplitude ◽  
Spherically Symmetric ◽  
Curved Space ◽  
Klein Gordon ◽  
Wave Trace ◽  
Limiting Case

Possibility of experimental registration of gravitational radiation scattered on wormholes was evaluated. Scattered radiation registration could become the experimental evidence of the wormhole gas theory explaining the dark matter nature. The simplest model of the traversable static spherically symmetric wormhole was used, which is the limiting case for the Bronnikov --- Ellis wormhole. Equations for gravitational wave against the background of non-empty curved space--time were obtained in the gauge, where the trace of a gravitational wave is not equal to zero. It is shown that equation on the trace is reduced to the Klein --- Gordon --- Fock equation. Explicit expressions were obtained for the gravitational wave trace scattering cross section on a wormhole. It was assumed that the gravitational wave amplitude order was equal to its trace order, numerical simulation was carried out, and scattered gravitational radiation intensity and amplitude from wormholes on Earth were estimated. In the multiverse case, when the wormhole throat was leading to another universe, conclusion was made that it was currently impossible to register radiation scattered by wormholes taking into account the LIGO/VIRGO detector sensitivity

The Tian–Yau–Zelditch Theorem and Toeplitz Operators

2011 ◽  
Vol 10 (3) ◽  
pp. 449-461 ◽  
Author(s):  
Daniel Burns ◽  
Victor Guillemin
Keyword(s):  
Trace Formula ◽  
Toeplitz Operators ◽  
Asymptotic Properties ◽  
Holomorphic Functions ◽  
Pseudoconvex Domains ◽  
Wave Trace

AbstractZelditch's proof of the Tian–Yau–Zelditch Theorem makes use of the Boutet de Monvel–Sjöstrand results on the asymptotic properties of Szegö projectors for strictly pseudoconvex domains. However, as we will show below, the theorem is also closely related to another theorem of Boutet de Monvel's, namely his wave trace formula for Toeplitz operators. Finally, we will derive, for the pseudoconvex manifolds considered by Zelditch in his proof of the Tian–Yau–Zelditch Theorem, an analogue of another result of Boutet de Monvel's, the extendability theorem of Berndtsson for holomorphic functions on Grauert tubes.

scholarly journals Singularities of the wave trace for the Friedlander model

2017 ◽  
Vol 133 (1) ◽  
pp. 1-25
Author(s):  
Yves Colin de Verdière ◽  
Victor Guillemin ◽  
David Jerison
Keyword(s):  
Wave Trace

scholarly journals Trace singularities in obstacle scattering and the Poisson relation for the relative trace

2021 ◽  
Author(s):  
Yan-Long Fang ◽  
Alexander Strohmaier
Keyword(s):  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Trace Class ◽  
Spectral Shift ◽  
Dirichlet Boundary Conditions ◽  
Shift Function ◽  
Relative Trace Formula ◽  
Casimir Interactions ◽  
Wave Trace ◽  
Obstacle Scattering

AbstractWe consider the case of scattering by several obstacles in $${\mathbb {R}}^d$$ R d , $$d \ge 2$$ d ≥ 2 for the Laplace operator $$\Delta $$ Δ with Dirichlet boundary conditions imposed on the obstacles. In the case of two obstacles, we have the Laplace operators $$\Delta _1$$ Δ 1 and $$\Delta _2$$ Δ 2 obtained by imposing Dirichlet boundary conditions only on one of the objects. The relative operator $$g(\Delta ) - g(\Delta _1) - g(\Delta _2) + g(\Delta _0)$$ g ( Δ ) - g ( Δ 1 ) - g ( Δ 2 ) + g ( Δ 0 ) was introduced in Hanisch, Waters and one of the authors in (A relative trace formula for obstacle scattering. arXiv:2002.07291, 2020) and shown to be trace-class for a large class of functions g, including certain functions of polynomial growth. When g is sufficiently regular at zero and fast decaying at infinity then, by the Birman–Krein formula, this trace can be computed from the relative spectral shift function $$\xi _\mathrm {rel}(\lambda ) = -\frac{1}{\pi } {\text {Im}}(\Xi (\lambda ))$$ ξ rel ( λ ) = - 1 π Im ( Ξ ( λ ) ) , where $$\Xi (\lambda )$$ Ξ ( λ ) is holomorphic in the upper half-plane and fast decaying. In this paper we study the wave-trace contributions to the singularities of the Fourier transform of $$\xi _\mathrm {rel}$$ ξ rel . In particular we prove that $${\hat{\xi }}_\mathrm {rel}$$ ξ ^ rel is real-analytic near zero and we relate the decay of $$\Xi (\lambda )$$ Ξ ( λ ) along the imaginary axis to the first wave-trace invariant of the shortest bouncing ball orbit between the obstacles. The function $$\Xi (\lambda )$$ Ξ ( λ ) is important in the physics of quantum fields as it determines the Casimir interactions between the objects.

Development of ball surface acoustic wave trace moisture analyzer using burst waveform undersampling circuit

2018 ◽  
Vol 89 (5) ◽  
pp. 055006 ◽  
Author(s):  
Toshihiro Tsuji ◽  
Toru Oizumi ◽  
Hideyuki Fukushi ◽  
Nobuo Takeda ◽  
Shingo Akao ◽  
...  
Keyword(s):  
Acoustic Wave ◽  
Surface Acoustic Wave ◽  
Trace Moisture ◽  
Ball Surface ◽  
Wave Trace

Plane-wave orthogonal polynomial transform for amplitude-preserving noise attenuation

2020 ◽  
Vol 222 (3) ◽  
pp. 1789-1804
Author(s):  
Yangkang Chen ◽  
Weilin Huang ◽  
Yatong Zhou ◽  
Wei Liu ◽  
Dong Zhang
Keyword(s):  
Plane Wave ◽  
Orthogonal Polynomial ◽  
Seismic Data ◽  
Random Noise ◽  
Seismic Energy ◽  
Noise Attenuation ◽  
Amplitude Variation ◽  
Slope Estimation ◽  
Polynomial Transform ◽  
Wave Trace

SUMMARY Amplitude-preserving data processing is an important and challenging topic in many scientific fields. The amplitude-variation details in seismic data are especially important because the amplitude variation is directly related with the subsurface wave impedance and fluid characteristics. We propose a novel seismic noise attenuation approach that is based on local plane-wave assumption of seismic events and the amplitude preserving capability of the orthogonal polynomial transform (OPT). The OPT is a way for representing spatially correlative seismic data as a superposition of polynomial basis functions, by which the random noise is distinguished from the useful energy by the high orthogonal polynomial coefficients. The seismic energy is the most correlative along the structural direction and thus the OPT is optimally performed in a flattened gather. We introduce in detail the flattening operator for creating the flattened dimension, where the OPT can be applied subsequently. The flattening operator is created by deriving a plane-wave trace continuation relation following the plane-wave equation. We demonstrate that both plane-wave trace continuation and OPT can well preserve the strong amplitude variation existing in seismic data. In order to obtain a robust slope estimation performance in the presence of noise, a robust slope estimation approach is introduced to substitute the traditional method. A group of synthetic, pre-stack and post-stack field seismic data are used to demonstrate the potential of the proposed framework in realistic applications.

A NOVEL IONOSPHERIC CYCLOTRON RESONANCE PHENOMENON OBSERVED ON ALOUETTE I DATA

1966 ◽  
Vol 44 (5) ◽  
pp. 925-939 ◽  
Author(s):  
D. B. Muldrew ◽  
E. L. Hagg
Keyword(s):  
Magnetic Field ◽  
Time Delay ◽  
Cyclotron Resonance ◽  
Electron Cyclotron Resonance ◽  
Extraordinary Wave ◽  
Resonance Phenomenon ◽  
Resonant Region ◽  
Electron Gyrofrequency ◽  
Wave Trace ◽  
Good Agreement

Characteristics of an extraordinary wave trace recently identified on Alouette I topside ionograms, and called the remote resonance trace by Hagg (1966), are discussed in detail. From the observations it has been deduced that the radio energy associated with the production of this trace propagates along an ionospheric magnetic field-aligned wave guide. The electric field of an h.f. wave propagating along such a guide would have a gradient normal to the earth's magnetic field, and because of this gradient the wave could excite an electron–cyclotron resonance in a region of the ionosphere that includes the height where the wave frequency is equal to twice the electron gyrofrequency. At some time delay after the wave has passed through the resonant region, the resonating electrons generate an extraordinary wave, which propagates upward along the guide and is subsequently received by the satellite. This wave is responsible for the production of the remote resonance trace. The equation for the time delay is given and the resonance trace computed, using this equation, is shown to be in good agreement with the observed resonance trace for a specific ionogram.

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