Corrigendum: Solitary wave-based strain measurements in one-dimensional granular crystals

A method is outlined that allows the determination of one-dimensional stress gradients at length scales greater than 0.2 mm. By using standard four-circle X-ray diffractometer equipment and simple aperture components, length resolutions down to 0.05 mm in one direction can be achieved through constant orientation of a narrow, line-shaped beam spot. Angle calculations are given for the adjustment of goniometer angles, and for the effective azimuth and tilt of the scattering vector for general angle settings in a four-circle goniometer. The latter is necessary for the computation of stresses from lattice strain measurements.

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Statistical mechanics of one-dimensional solitary-wave-bearing scalar fields: Exact results and ideal-gas phenomenology

Physical Review B ◽

10.1103/physrevb.22.477 ◽

1980 ◽

Vol 22 (2) ◽

pp. 477-496 ◽

Cited By ~ 458

Author(s):

J. F. Currie ◽

J. A. Krumhansl ◽

A. R. Bishop ◽

S. E. Trullinger

Keyword(s):

Solitary Wave ◽

Statistical Mechanics ◽

Scalar Fields ◽

Ideal Gas ◽

Exact Results ◽

One Dimensional

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Frequency- and Amplitude-Dependent Transmission of Stress Waves in Curved One-Dimensional Granular Crystals Composed of Diatomic Particles

Experimental Mechanics ◽

10.1007/s11340-012-9652-y ◽

2012 ◽

Vol 53 (3) ◽

pp. 469-483 ◽

Cited By ~ 16

Author(s):

Jinkyu Yang ◽

Chiara Daraio

Keyword(s):

Stress Waves ◽

One Dimensional ◽

Granular Crystals

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Tunable topological interface states in one-dimensional extended granular crystals

International Journal of Mechanical Sciences ◽

10.1016/j.ijmecsci.2020.105549 ◽

2020 ◽

Vol 176 ◽

pp. 105549 ◽

Cited By ~ 4

Author(s):

Hongfa Wang ◽

Dongying Liu ◽

Wenbo Fang ◽

Siqi Lin ◽

Yijie Liu ◽

...

Keyword(s):

Interface States ◽

One Dimensional ◽

Granular Crystals

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Phase shift of solitary wave in a one-dimensional granular chain

International Journal of Modern Physics B ◽

10.1142/s0217979219500851 ◽

2019 ◽

Vol 33 (10) ◽

pp. 1950085

Author(s):

Xian-Qing Yang ◽

Yao Yang ◽

Yang Jiao ◽

Wei Zhang

Keyword(s):

Phase Shift ◽

Solitary Wave ◽

Numerical Scheme ◽

Binary Collision ◽

One Dimensional ◽

Binary Collision Approximation ◽

Fifth Order ◽

The Waves ◽

Theoretical Results ◽

Collision Approximation

In this paper, both the fifth-order Runge–Kutta numerical scheme and binary collision approximation are used to study the phase shift. Both numerical and theoretical results are shown that the solitary wave after head-on collision propagates along the chain behind the reference wave in both even and odd numbers of grain chains. It is the well-known feature of the appearance of the phase shift. Those results are in agreement with the experimental results. Furthermore, it is found that the phase shift is not only related to the collision position of the waves, but also to the position where the time is measured. The value of phase shift increases nonmonotonously with increasing the velocity of the opposite propagation of the wave. Binary collision approximation is applied to analyze the phase shift, and it is found that theoretical results agree well with numerical results, especially in the case of phase shift in odd chain.

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