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Lagrangian formulation and symmetrical description of liquid dynamics
1School of Physics and Astronomy, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom.
Physical Review. E
|January 20, 2018
Summary
This study reveals a fundamental symmetry in liquid dynamics, showing that hydrodynamic and solid-like descriptions yield identical properties. It introduces a novel two-field Lagrangian predicting two unique gapped waves in liquids.
Area of Science:
- Physics
- Condensed Matter Physics
- Fluid Dynamics
Background:
- Theoretical descriptions of liquids traditionally rely on hydrodynamic approaches.
- Generalizations have extended these to solid-like regimes, but a unified framework is lacking.
Purpose of the Study:
- To demonstrate a fundamental symmetry between hydrodynamic and solid-like descriptions of liquid properties.
- To develop a unified theoretical framework for liquid dynamics.
Main Methods:
- Deriving liquid properties from solid-like equations by incorporating hydrodynamic flow.
- Constructing a two-field Lagrangian treating dissipative hydrodynamic and solid-like terms equally.
Main Results:
- Both hydrodynamic and solid-like approaches predict propagating shear waves with a k-space gap.
- The developed Lagrangian predicts two gapped waves propagating in opposite space-time directions.
- Dissipative and mass terms compete, influencing k-space gaps and energy.
Conclusions:
- A significant symmetry exists in the theoretical description of liquids.
- The unified Lagrangian offers new insights into liquid dynamics, wave propagation, and the interplay of dissipative and mass terms.
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