Evolution equations for nonlinear Lucassen waves

Simon, Blake E.; Cormack, John M.; Hamilton, Mark F.

doi:10.1121/2.0001028

Cited by 3 publications

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“…Lipid monolayers at the air/water interface provide a robust platform for investigating interfacial compression waves, also known as Lucassen waves (Kappler et al, 2017;Lucassen, 1968;Simon et al, 2019). The propagation of these waves is characterized by the interfacial or lateral compressibility of the interface, in analogy with sound waves, hence they are also referred to as two-dimensional sound waves.…”

Section: Introductionmentioning

confidence: 99%

Shock and detonation waves at an interface and the collision of action potentials

Shrivastava

2021

Progress in Biophysics and Molecular Biology

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This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Section: Introductionmentioning

confidence: 99%

Shock and detonation waves at an interface and the collision of action potentials

Shrivastava

2021

Progress in Biophysics and Molecular Biology

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“…Lipid monolayers at the air/water interface provide a robust platform for investigating interfacial compression waves, also known as Lucassen waves (11)(12)(13). The propagation of these waves is characterized by the interfacial or lateral compressibility of the interface, in analogy with sound waves, hence they are also referred to as two-dimensional sound waves.…”

Section: Introductionmentioning

confidence: 99%

Shock and Detonation Waves at an Interface and the Collision of Action Potentials

Shrivastava

2020

Preprint

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Action potentials in neurons are known to annihilate each other upon collision, while there are cases where they might penetrate each other. Compression waves that travel within the plasma membrane of a neuron have previously been proposed as a thermodynamic basis for the propagation of action potentials. In this context, it was recently shown that two dimensional compressive shock waves in the model system of lipid monolayers can nearly annihilate each other upon head on collision when excited close to a phase transition. However, weaker shock waves showed penetration. In general, once the approximation of small perturbation is not valid, compression waves do not interact linearly anymore. While experiments in lipid monolayers demonstrated this principle, a mechanism remained unclear. In this article, we summarise the fundamentals of shock physics as applied to an interface and how it previously explained the observation of threshold and saturation of shockwaves in the lipid monolayer (all or none). While the theory has the same fundamental premise as the soliton model, i.e. the conservation laws and thermodynamics, we elaborate on how the two approaches make different predictions with regards to collisions and the detailed structure of the wave-front. As a case study and a new result, we show that previously unexplained annihilation of shock waves in the lipid monolayer is a direct consequence of the nature of state changes, i.e. jump conditions, within these shockwaves, and elaborate on the consequence of these results for the general understanding of the excitation waves in a thermo-fluids framework.

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Evolution equation for nonlinear Lucassen waves, with application to a threshold phenomenon

Simon

Cormack

Hamilton

2021

The Journal of the Acoustical Society of America

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A nonlinear, fractional, surface wave equation with a spatial derivative of second order was developed by Kappler, Shrivastava, Schneider, and Netz [Phys. Rev. Fluids 2, 114804 (2017)] for propagation along an elastic interface coupled to a viscous incompressible liquid. Linear theory for the attenuation and dispersion was developed originally by Lucassen [Trans. Faraday Soc. 64, 2221 (1968)]. Kappler et al. introduced a fractional time derivative to account for the Lucassen wave attenuation and dispersion, and they included quadratic and cubic nonlinearity associated with compression of the elastic interface. Presented here is an integrated form of their time domain equation for progressive waves that is first order in the spatial derivative. Solutions of this evolution equation capture the main features of waveforms predicted by the full model equation of Kappler et al., especially the formation and propagation of shocks, while the evolution equation can be solved numerically with substantially less computational cost. Approximate analytical expressions obtained from the evolution equation for the nonlinear propagation speed and attenuation of a compression pulse reveal that a threshold phenomenon discussed by Kappler et al. is due to competition between quadratic and cubic nonlinearity associated with a lipid monolayer interface.

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Evolution equations for nonlinear Lucassen waves

Cited by 3 publications

References 0 publications

Shock and detonation waves at an interface and the collision of action potentials

Shock and detonation waves at an interface and the collision of action potentials

Shock and Detonation Waves at an Interface and the Collision of Action Potentials

Evolution equation for nonlinear Lucassen waves, with application to a threshold phenomenon

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