Non-linear Theory of Wave-front Propagation

Varley, E.; Cumberbatch, E.

doi:10.1093/imamat/1.2.101

Cited by 99 publications

(24 citation statements)

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“…It is known that in general rays are not orthogonal to wavefronts: this is guaranteed only if the speed of propagation c does not depends on n. Since all the quantities are evaluated at u = u 0 , this is an ordinary differential equation in (t, x) [5]. For any matrix or vector B(t, x, u) we use the following notation:…”

Section: General Resultsmentioning

confidence: 99%

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Generation of axisymmetric magnetosonic shock waves: Applications to static equilibria and accretion disks

Núñez

2016

International Journal of Non-Linear Mechanics

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Section: General Resultsmentioning

confidence: 99%

“…Both sound and MHD waves have been studied in simple special configurations from a long time ago [5][6][7][8], but never including the case of axisymmetric equilibria.…”

Section: Introductionmentioning

confidence: 99%

Generation of axisymmetric magnetosonic shock waves: Applications to static equilibria and accretion disks

Núñez

2016

International Journal of Non-Linear Mechanics

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“…The following derivation fills a gap in [3] and generalizes [9] where the evolution of discontinuities in first derivatives of the dependent variables is studied. Choose a root of the characteristic equation,…”

Section: Appendix Amentioning

confidence: 96%

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McCarthy

Sarıoğlu

2000

International Journal of Theoretical Physics

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We present the shock-free wave propagation requirements for massless fields. First, we briefly argue how the "completely exceptional" approach, originally developed to study the characteristics of hyperbolic systems in 1+1 dimensions, can be generalized to higher dimensions and used to describe propagation without emerging shocks, with characteristic flow remaining parallel along the waves. We then study the resulting requirements for scalar, vector, vectorscalar and gravity models and characterize physically acceptable actions in each case.

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“…Unlike the propagation of an acceleration wave in which the growth or decay of the discontinuity in acceleration depends on quantities known on the singular surface (see [1,2], for example), the growth or decay of a shock wave depends also on the motion ahead of the shock wave and an unknown quantity qb-behind the shock wave. This unknown quantity ~-is a scalar, regardless whether the shock wave is a one-dimensional or three-dimensional wave.…”

Section: Introductionmentioning

confidence: 99%

Eulerian formulation of transport equations for three-dimensional shock waves in simple elastic solids

Ting

Yong-chi

1983

J Elasticity

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The propagation of a three-dimensional shock wave in an elastic solid is studied. The material is assumed to be a simple elastic solid in which the Cauchy stress depends on the deformation gradient only. It is shown that the growth or decay of a discontinuity i/, depends on (i) an unknown quantity ~-behind the shock wave, (ii) the two principal curvatures of the shock surface, (iii) the gradient on the shock surface of the shock wave speeds and (iv) the inhomogeneous term which depends on the motion ahead of the shock surface and vanishes when the motion ahead of the shock surface is uniform. If a proper choice is made of the propagation vector b along which the growth or decay of the discontinuity is measured, the dependence on item (iii) can be avoided. However, b assumes different directions depending on the choice of discontinuity ~k with which one is concerned and the unknown quantity 4)-behind the shock wave on which one chooses to depend. As in the case of one-dimensional shock waves, the growth (or decay) of one discontinuity may not be accompanied by the growth (or decay) of other discontinuities. A universal equation relating the growth or decay of discontinuities in the normal stress, normal velocity and specific volume is also presented.

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Non-linear Theory of Wave-front Propagation

Cited by 99 publications

References 0 publications

Generation of axisymmetric magnetosonic shock waves: Applications to static equilibria and accretion disks

Generation of axisymmetric magnetosonic shock waves: Applications to static equilibria and accretion disks

Untitled

Eulerian formulation of transport equations for three-dimensional shock waves in simple elastic solids

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