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- W2897576291 abstract "Equations for irrotational, linearized Euler fluid, where the mass continuity equation incorporates a linear equation of state, define linear acoustics that can be recast in terms of complexified quaternions, the biquaternions, which satisfy Cauchy-Fueter regularity equations. This gives first order partial differential equations from the four space-time dimensions to the four (complex) dimensional velocity-pressure space, with time and pressure in the biquaternionic scalar parts. The biquaternionic planar exponential provides the basis to elementary solutions as biquaternionic functions of a single biquaternionic variable. Analysis of this form shows significant geometrical algebraic properties including imaginary units for time distinct from those for space. The single biquaternion acoustic field at each point of space-time allows the propagation four complex coefficients in a single geometric algebraic structure, suitable for three or four dimensional Fourier analysis. (Work supported by the U.S. Office of Naval Research.)" @default.
- W2897576291 created "2018-10-26" @default.
- W2897576291 creator A5069423263 @default.
- W2897576291 date "2018-09-01" @default.
- W2897576291 modified "2023-09-24" @default.
- W2897576291 title "The Biquaternionic acoustic wave equation" @default.
- W2897576291 doi "https://doi.org/10.1121/1.5068240" @default.
- W2897576291 hasPublicationYear "2018" @default.
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