Negative group velocity in solids

Tamm, Kert; Peets, Tanel; Engelbrecht, Jüri; Kartofelev, Dmitri

doi:10.1016/j.wavemoti.2016.04.010

Cited by 16 publications

(5 citation statements)

References 34 publications

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“…This is common to many cases of multi-valued dispersion reported in literature. Hence 'negative group-velocity' is a term frequently used to name this phenomenon and has made it into the title of several papers (Negishi 1987;Wolf et al 1988;Tamm et al 2017;Nishimiya et al 2007). This term is misleading and might appear like a violation of accepted physics, where group velocity in non-dissipative media equals velocity of energy transport (Carcione et al 2010).…”

Section: Group Slownessmentioning

confidence: 99%

A single Rayleigh mode may exist with multiple values of phase-velocity at one frequency

Forbriger

Gao

Malischewsky

et al. 2020

Geophysical Journal International

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SUMMARY Other than commonly assumed in seismology, the phase velocity of Rayleigh waves is not necessarily a single-valued function of frequency. In fact, a single Rayleigh mode can exist with three different values of phase velocity at one frequency. We demonstrate this for the first higher mode on a realistic shallow seismic structure of a homogeneous layer of unconsolidated sediments on top of a half-space of solid rock (LOH). In the case of LOH a significant contrast to the half-space is required to produce the phenomenon. In a simpler structure of a homogeneous layer with fixed (rigid) bottom (LFB) the phenomenon exists for values of Poisson’s ratio between 0.19 and 0.5 and is most pronounced for P-wave velocity being three times S-wave velocity (Poisson’s ratio of 0.4375). A pavement-like structure (PAV) of two layers on top of a half-space produces the multivaluedness for the fundamental mode. Programs for the computation of synthetic dispersion curves are prone to trouble in such cases. Many of them use mode-follower algorithms which loose track of the dispersion curve and miss the multivalued section. We show results for well established programs. Their inability to properly handle these cases might be one reason why the phenomenon of multivaluedness went unnoticed in seismological Rayleigh wave research for so long. For the very same reason methods of dispersion analysis must fail if they imply wave number kl(ω) for the lth Rayleigh mode to be a single-valued function of frequency ω. This applies in particular to deconvolution methods like phase-matched filters. We demonstrate that a slant-stack analysis fails in the multivalued section, while a Fourier–Bessel transformation captures the complete Rayleigh-wave signal. Waves of finite bandwidth in the multivalued section propagate with positive group-velocity and negative phase-velocity. Their eigenfunctions appear conventional and contain no conspicuous feature.

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Section: Group Slownessmentioning

confidence: 99%

A single Rayleigh mode may exist with multiple values of phase-velocity at one frequency

Forbriger

Gao

Malischewsky

et al. 2020

Geophysical Journal International

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“…Such higher-order gradient terms permit the prediction of size-dependent response as well as dispersive wave propagation, and indeed the length scale parameters that accompany these higher-order gradients can typically be linked to microstructural properties. Thus, gradient-enriched elasticity theories have been used successfully to analyse a range of phenomena including buckling, vibration and wave propagation [8,9,10,11,12,13]. Furthermore, new gradientenriched elasticity models, such as complete anisotropic strain-gradient elasticity [14,15], spatial-temporal nonlocal homogenisation models [16,17] and dispersive gradient elasticity with multiple micro-inertia terms [18,19], have increased the versatility of the gradient elasticity modelling framework.…”

Section: Introductionmentioning

confidence: 99%

Mono-scale and multi-scale formulations of gradient-enriched dynamic piezomagnetics

Askes

Gitman

2019

Wave Motion

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“…3 the spectral composition [58] of a typical bell-shaped pulse is shown where it can be seen that while the bulk of the signal is contained in lower harmonics, there is a sufficient number of higher harmonics whose wavelengths can be of the same order of magnitude as nodes of Ranvier as the wavelength of harmonics decreases rapidly for the higher harmonics. Since the myelinated axon can be viewed as a microstructured material then inspiration can be drawn from the Mindlin-type model for materials with double microstructure [16,50,65]:…”

Section: Model Formulationmentioning

confidence: 99%

Mechanical waves in myelinated axon wall

Tamm,

Peets,

Engelbrecht

2021

Preprint

Self Cite

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The propagation of an action potential is accompanied by mechanical and thermal effects. Several mathematical models explain the deformation of the unmyelinated axon wall. In this paper, the deformation of the myelinated axon wall is studied. The mathematical model is inspired by the mechanics of microstructured materials. The model involves the improved Heimburg-Jackson equation together with another equation of wave motion that describes the process in the myelin sheath. The dispersion analysis of such a model explains the behaviour of group and phase velocities. In addition, it is shown how dissipative effects may influence the process. Numerical calculations demonstrate the changes in velocities and wave profiles in the myelinated axon wall.

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Negative group velocity in solids

Cited by 16 publications

References 34 publications

A single Rayleigh mode may exist with multiple values of phase-velocity at one frequency

A single Rayleigh mode may exist with multiple values of phase-velocity at one frequency

Mono-scale and multi-scale formulations of gradient-enriched dynamic piezomagnetics

Mechanical waves in myelinated axon wall

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