Nonlinear fractional waves at elastic interfaces

Abstract

We derive the nonlinear fractional surface wave equation that governs compression waves at an interface that is coupled to a viscous bulk medium. The fractional character of the differential equation comes from the fact that the effective thickness of the bulk layer that is coupled to the interface is frequency dependent. The nonlinearity arises from the nonlinear dependence of the interface compressibility on the local compression, which is obtained from experimental measurements and reflects a phase transition at the interface. Numerical solutions of our nonlinear fractional theory reproduce several experimental key features of surface waves in phospholipid monolayers at the air-water interface without freely adjustable fitting parameters. In particular, the propagation length of the surface wave abruptly increases at a threshold excitation amplitude. The wave velocity is found to be of the order of 40 cm/s both in experiments and theory and slightly increases as a function of the excitation amplitude. Nonlinear acoustic switching effects in membranes are thus shown to arise purely based on intrinsic membrane properties, namely the presence of compressibility nonlinearities that accompany phase transitions at the interface.

arXiv comment12 pages, 7 figures; supplemental information provided as ancillary file

References in corpus (7)

• Mechanical Surface Waves Accompany Action Potential Propagation
• Ship wakes: Kelvin or Mach angle?
• Evidence for 2D Solitary Sound Waves in a Lipid Controlled Interface and its Biological Implications
• Comparison of fractional wave equations for power law attenuation in ultrasound and elastography
• Periodic solutions and refractory periods in the soliton theory for nerves and the locust femoral nerve
• On axoplasmic pressure waves and their possible role in nerve impulse propagation
• Solitary Shock Waves and Adiabatic Phase Transition in Lipid Interfaces and Nerves

Cited by in corpus (5)

• The excitable fluid mosaic
• The effect of stretching on nerve excitability
• The mechanical properties of nerves, the size of the action potential, and consequences for the brain
• Surface response of a polymer network: Semi-infinite network
• Generation of two-dimensional pulses in lipid monolayers by rapid photoswitching