Chebyshev-Type Rational Approximations of the One-Way Helmholtz Equation for Solving a Class of Wave Propagation Problems

2021 ◽  
pp. 422-435
Author(s):  
Mikhail S. Lytaev
Keyword(s):  
Wave Propagation ◽  
Helmholtz Equation ◽  
Rational Approximations ◽  
The One

The effect of boundaries on wave propagation in a liquid-filled porous solid: VI. Love waves in a double surface layer

1964 ◽  
Vol 54 (1) ◽  
pp. 417-423
Author(s):  
H. Deresiewicz
Keyword(s):  
Wave Propagation ◽  
Surface Layer ◽  
Dispersion Relation ◽  
Energy Loss ◽  
Classical Solution ◽  
Specific Energy ◽  
Classical Case ◽  
Specific Energy Loss ◽  
Double Surface ◽  
The One

abstract The classical solution of Stoneley and Tillotson is generalized by considering the outer one of the pair of layers to be porous. Although the dispersion relation turns out, for practical purposes, to be identical with the one governing the classical case, the motion in the present instance is shown to be dissipative and the expression is exhibited for the specific energy loss.

scholarly journals Thin-layer solutions of the Helmholtz equation

2020 ◽  
pp. 1-15
Author(s):  
J. R. OCKENDON ◽  
R. H. TEW
Keyword(s):  
Wave Propagation ◽  
Thin Layer ◽  
Helmholtz Equation ◽  
Open Problem ◽  
High Frequency ◽  
Mathematical Structure ◽  
Mathematical Physics ◽  
Thin Layers ◽  
Frequency Wave ◽  
High Frequency Wave

This paper gives a brief overview of some configurations in which high-frequency wave propagation modelled by Helmholtz equation gives rise to solutions that vary rapidly across thin layers. The configurations are grouped according to their mathematical structure and tractability and one of them concerns a famous open problem of mathematical physics.

scholarly journals The THz Spectrum of Density Fluctuations of Water: The Viscoelastic Regime

2015 ◽  
Vol 2015 ◽  
pp. 1-24 ◽  
Author(s):  
Alessandro Cunsolo
Keyword(s):  
Wave Propagation ◽  
Viscoelastic Properties ◽  
Sound Absorption ◽  
Supercooled Water ◽  
Density Fluctuations ◽  
Water Dynamics ◽  
Relaxation Phenomena ◽  
X Ray ◽  
X Ray Scattering ◽  
The One

Relevant advances in the knowledge of the water dynamics at mesoscopic scales are reviewed, while mainly focusing on the contribution provided by high resolution inelastic X-ray scattering (IXS). In particular it is discussed how the use of IXS has improved our understanding of viscoelastic properties of water at THz frequencies. This specifically involves some solid-like features such as the onset of shear wave propagation, a sound velocity surprisingly similar to the one of ice, and an anomalously low sound absorption coefficient. All these properties can be explained by assuming the coupling of THz density fluctuations with a structural relaxation process connected to the breaking and forming of hydrogen bonds (HBs). This review also includes more recent IXS results demonstrating that, upon approaching supercritical conditions, relaxation phenomena in water gradually lose their structural character becoming essentially collisional in character. Furthermore, GHz spectroscopy results on supercooled water, suggesting the occurrence of a structural arrest, are discussed. An overview of the new opportunities offered by next generation IXS spectrometers finally concludes this review.

VALIDITY OF ONE-WAY MODELS IN THE WEAK RANGE DEPENDENCE LIMIT

2004 ◽  
Vol 12 (01) ◽  
pp. 55-66 ◽  
Author(s):  
JIANXIN ZHU ◽  
YA YAN LU
Keyword(s):  
Helmholtz Equation ◽  
Numerical Solutions ◽  
Underwater Acoustics ◽  
Square Root ◽  
Orthogonal Transform ◽  
The Difference ◽  
The One ◽  
Dirichlet To Neumann Map ◽  
Root Operator ◽  
Marching Method

Numerical solutions of the Helmholtz equation and the one-way Helmholtz equation are compared in the weak range dependence limit, where the overall range distance is increased while the range dependence is weakened. It is observed that the difference between the solutions of these two equations persists in this limit. The one-way Helmholtz equation involves a square root operator and it can be further approximated by various one-way models used in underwater acoustics. An operator marching method based on the Dirichlet-to-Neumann map and a local orthogonal transform is used to solve the Helmholtz equation.

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