Peierls-Nabarro potential for a confined chain of hard spheres under compression

Mughal, Adil; Weaire, D.; Hutzler, Stefan

doi:10.1209/0295-5075/ac1a24

Cited by 5 publications

(2 citation statements)

References 24 publications

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“…10: 230293 direction. These discrete equations have been solved numerically using the shooting method [1,[22][23][24][25], and the solutions produce the angle profiles, θ n .…”

Section: Differential Equationmentioning

confidence: 99%

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A continuum description of the buckling of a line of spheres in a transverse harmonic confining potential

et al. 2023

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A line of contacting hard spheres, placed in a transverse confining potential, buckles under compression or when tilted away from the horizontal, once a critical tilt angle is exceeded. This interesting nonlinear problem is enriched by the combined application of both compression and tilt. In a continuous formulation, the profile of transverse sphere displacement is well described by numerical solutions of a second-order differential equation (provided that buckling is not of large amplitude). Here we provide a detailed discussion of these solutions, which are approximated by analytic expressions in terms of Jacobi, Whittaker and Airy functions. The analysis in terms of Whittaker functions yields an exact result for the critical tilt for buckling without compression.

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“…10: 230293 direction. These discrete equations have been solved numerically using the shooting method [1,[22][23][24][25], and the solutions produce the angle profiles, θ n .…”

Section: Differential Equationmentioning

confidence: 99%

“…In earlier papers [1,2,[22][23][24][25], we engaged in a numerical search for solutions, which were gathered up in detailed bifurcation diagrams ( plots of energy, or another property, as a function of a control parameter, usually compression). This was done for up to N = 20 spheres [22].…”

Section: Introductionmentioning

confidence: 99%