Nonlocal Mechanics in the Framework of the General Nonlocal Theory

Shaat, Mohamed; Ghavanloo, Esmaeal

doi:10.1007/978-3-030-63050-8_3

Cited by 1 publication

(2 citation statements)

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“…This classical rogue-wave soliton solution features a selffocussing wave that appears from low background oscillations for t < 0, suddenly reaches a peak at x = 0 and t = 0, and vanishes quickly into the background noise. The criticality condition for the Peregrine soliton requires the wavelength of the background perturbation to be very large, which has been used as an argument for forecasting Peregrine solitons simply by the absence or presence of such longwavelength perturbations in measurement of wave spectra (Shrira and Geogjaev, 2010). This criticality condition also shows that the Peregrine soliton achieves maximum spatial and temporal compression of wave energy by sampling energy from the far field.…”

Section: Three Different Fundamental Wave Solutions and The Long-wavelength Cross-diffusion Limitmentioning

confidence: 99%

“…Along the same vein, the paper also attempts to give a somewhat simpler description of the theory from a mesoscale perspective, putting Part 1 into the context of non-local processes summarized in recent developments on size-dependent continuum mechanics approaches (Shaar and Ghavanloo, 2021). We identify that these ideas can be amalgamated with new concepts in physics and mathematics on non-local reaction (Rubinstein and Sternberg, 1992) and diffusion (Amdreo-Valle et al, 2010) processes.…”

Section: Introductionmentioning

confidence: 99%

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Cross-diffusion waves resulting from multiscale, multiphysics instabilities: application to earthquakes

Regenauer-Lieb

Schrank

et al. 2021

Solid Earth

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Abstract. Theoretical approaches to earthquake instabilities propose shear-dominated source mechanisms. Here we take a fresh look at the role of possible volumetric instabilities preceding a shear instability. We investigate the phenomena that may prepare earthquake instabilities using the coupling of thermo-hydro-mechano-chemical reaction–diffusion equations in a THMC diffusion matrix. We show that the off-diagonal cross-diffusivities can give rise to a new class of waves known as cross-diffusion or quasi-soliton waves. Their unique property is that for critical conditions cross-diffusion waves can funnel wave energy into a stationary wave focus from large to small scale. We show that the rich solution space of the reaction–cross-diffusion approach to earthquake instabilities can recover classical Turing instabilities (periodic in space instabilities), Hopf bifurcations (spring-slider-like earthquake models), and a new class of quasi-soliton waves. Only the quasi-soliton waves can lead to extreme focussing of the wave energy into short-wavelength instabilities of short duration. The equivalent extreme event in ocean waves and optical fibres leads to the appearance of “rogue waves” and high energy pulses of light in photonics. In the context of hydromechanical coupling, a rogue wave would appear as a sudden fluid pressure spike. This spike is likely to cause unstable slip on a pre-existing (near-critically stressed) fault acting as a trigger for the ultimate (shear) seismic moment release.

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Section: Three Different Fundamental Wave Solutions and The Long-wavelength Cross-diffusion Limitmentioning

confidence: 99%