Faster-than-light group velocities and causality violation

1970 ◽  
Vol 316 (1527) ◽  
pp. 515-524 ◽  
Keyword(s):  
Wave Equations ◽  
Signal Propagation ◽  
Necessary Condition ◽  
Speed Of Light ◽  
Frequency Range ◽  
Classical Analysis ◽  
Causality Violation ◽  
Light Group ◽  
Group Velocities ◽  
Faster Than Light

The classical analysis of Brillouin and Sommerfeld has shown that the appearance, in some frequency range, of group velocities in excess of the speed of light does not imply causality violation. The group velocity is not always identical with the velocity of signal propagation. We show that a necessary condition for causality violation is that the infinite- frequency limit of the phase velocity shall exceed the speed of light. Application of the theorem leads to the conclusions ( a ) that all Lorentz-invariant wave equations (and in particular the Feinberg ‘tachyon’) are causal, and ( b ) that the quasi-acoustic branch of the Bludman-Ruderman model is causal.

scholarly journals Do Faster-than-Light Group Velocities imply Violation of Causality?

Nature ◽  
1969 ◽  
Vol 223 (5206) ◽  
pp. 597-597 ◽  
Author(s):  
R. FOX ◽  
C. G. KUPER ◽  
S. G. LIPSON
Keyword(s):  
Light Group ◽  
Group Velocities ◽  
Faster Than Light

Numerical Simulation of Lamb Wave Propagation in Isotropic Materials with Different Plate Thicknesses

2015 ◽  
Vol 1094 ◽  
pp. 500-504
Author(s):  
Hamada M. Elgamal ◽  
Zai Lin Yang ◽  
Jian Wei Zhang
Keyword(s):  
Lamb Wave ◽  
Wave Equations ◽  
Lamb Waves ◽  
Propagation Characteristics ◽  
Frequency Range ◽  
Health Monitoring System ◽  
Phase Group ◽  
Lamb Wave Propagation ◽  
Al 2024 ◽  
Group Velocities

Understanding the characteristics of Lamb waves is very important for developing a structural health monitoring system. The propagation characteristics of Lamb waves are described in the form of dispersion curves, which are plots of phase/group velocities versus the product offrequency-thicknessgenerated by solving the Lamb wave equations. This paper presents a numerical modeling of Lamb waves’ amplitude behaviors for isotropic aluminum plate (Al 2024-T3). The numerical simulations were carried out using ANSYS by exciting the Lamb wave at the plate end in the frequency range of 150-200 kHz for different plate thicknesses.

scholarly journals Generalized approximate boundary synchronization for a coupled system of wave equations

2020 ◽  
Author(s):  
Yanyan Wang
Keyword(s):  
Wave Equations ◽  
Dirichlet Boundary ◽  
Coupled System ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Exact Boundary ◽  
Boundary Controls ◽  
The Relationship ◽  
Exact Boundary Synchronization ◽  
Dirichlet Boundary Controls

In this paper, we consider the generalized approximate boundary synchronization for a coupled system of wave equations with Dirichlet boundary controls. We analyse the relationship between the generalized approximate boundary synchronization and the generalized exact boundary synchronization, give a sufficient condition to realize the generalized approximate boundary synchronization and a necessary condition in terms of Kalman’s matrix, and show the meaning of the number of total controls. Besides, by the generalized synchronization decomposition, we define the generalized approximately synchronizable state, and obtain its properties and a sufficient condition for it to be independent of applied boundary controls.

scholarly journals The duality principle and new forms of the inverse Laplace transform for the analysis of signal propagation in inhomogeneous media with dispersion

2019 ◽  
Vol 489 (6) ◽  
pp. 558-563
Author(s):  
A. G. Pavelyev ◽  
A. A. Pavelyev
Keyword(s):  
Laplace Transform ◽  
Impulse Response ◽  
Angular Spectrum ◽  
Signal Propagation ◽  
Inhomogeneous Media ◽  
Inverse Laplace Transform ◽  
Duality Principle ◽  
Causality Principle ◽  
Speed Of Light ◽  
Laplace Transform Inversion

New equations for Laplace transform inversion are obtained. The equations satisfy the causality principle. The impulse response of a channel is determined in order to analyze dispersion distortions in inhomogeneous media. The impulse response excludes the possibility that the signal exceeds the speed of light in the medium. The transmission bandwidth, the angular spectrum, and the Doppler shift in the ionosphere are computed.

scholarly journals Gravitational waves in modified Gauss–Bonnet gravity

2020 ◽  
Vol 29 (10) ◽  
pp. 2050072
Author(s):  
Tomohiro Inagaki ◽  
Masahiko Taniguchi
Keyword(s):  
General Relativity ◽  
Gravitational Waves ◽  
Wave Equations ◽  
Massive Scalar ◽  
Speed Of Light ◽  
Bonnet Gravity ◽  
Cosmological Background ◽  
Background Curvature ◽  
Scalar Mode ◽  
Metric Perturbation

We study the gravitational waves (GWs) in modified Gauss–Bonnet gravity. Applying the metric perturbation around a cosmological background, we obtain explicit expressions for the wave equations. It is shown that the speed of the traceless mode is equal to the speed of light. An additional massive scalar mode appears in the propagation of the GWs. To find phenomena beyond the general relativity, the scalar mode mass is calculated as a function of the background curvature in some typical models.

Differential equations for long-period gravity waves on fluid of rapidly varying depth

1977 ◽  
Vol 83 (2) ◽  
pp. 289-310 ◽  
Author(s):  
James Hamilton
Keyword(s):  
Gravity Waves ◽  
Wave Equations ◽  
Velocity Potential ◽  
Taylor Series Expansion ◽  
Finite Amplitude ◽  
Necessary Condition ◽  
Exact Equation ◽  
Rapid Convergence ◽  
Long Period ◽  
Long Wave

The conventional long-wave equations for waves propagating over fluid of variable depth depend for their formal derivation on a Taylor series expansion of the velocity potential about the bottom. The expansion, however, is not possible if the depth is not an analytic function of the horizontal co-ordinates and it is a necessary condition for its rapid convergence that the depth is also slowly varying. We show that if in the case of two-dimensional motions the undisturbed fluid is first mapped conformally onto a uniform strip, before the Taylor expansion is made, the analytic condition is removed and the approximations implied in the lowest-order equations are much improved.In the limit of infinitesimal waves of very long period, consideration of the form of the error suggests that by modifying the coefficients of the reformulated equation we may find an equation exact for arbitrary depth profiles. We are thus able to calculate the reflexion coefficients for long-period waves incident on a step change in depth and a half-depth barrier. The forms of the coefficients of the exact equation are not simple; however, for these particular cases, comparison with the coefficients of the reformulated long-wave equation suggests that in most cases the latter may be adequate. This opens up the possibility of beginning to study finite amplitude and frequency effects on regions of rapidly varying depth.

scholarly journals Signal Propagation Model for Microcells at 900 MHz Frequency Range

2015 ◽  
Vol 21 (4) ◽  
Author(s):  
Saulius Japertas ◽  
Karolis Pilipavičius ◽  
Dilip Janarthanan
Keyword(s):  
Signal Propagation ◽  
Propagation Model ◽  
Frequency Range ◽  
Signal Propagation Model

scholarly journals Atmospheric Propagation Of SubTHz Waves And Space, 6G & 7G Communications

2021 ◽  
Vol 2015 (1) ◽  
pp. 012084
Author(s):  
Lesnov Ilya ◽  
Vdovin Vyacheslav
Keyword(s):  
High Capacity ◽  
Signal Propagation ◽  
Low Noise ◽  
High Signal ◽  
Atmospheric Conditions ◽  
Frequency Range ◽  
Actual Problem ◽  
Atmospheric Propagation ◽  
Data Rates ◽  
Wireless Telecommunication

Abstract The work is devoted to the actual problem of data rate of wireless telecommunication channels. Presented analysis of the telecommunication channel subterahertz (subTHz) frequency range - as the most promising band for the implementation of wireless telecommunications for space links and terrestrial cellular communications of high capacity. A channel considered as a combination of high effective transponder / transmitter duplex together with an open high dissipative atmospheric line. The means to achieve a high signal / noise ratio is usage of low-noise cryogenic receivers. The theoretical analysis of data rates for various atmospheric conditions and technical implementations of communication channels demonstrated reasonable limits of cooling of receivers, providing a weighty increase channel capacity, while deeper cooling is impractical due to weather restrictions in certain ranges and conditions of signal propagation, including altitude and seasonal features.

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