Functional Phonology: chapter 3

Chapter 3: Acoustical simulation

This chapter derives the aerodynamic equations needed in our articulation model, translates the myoelastic and aerodynamic equations into difference equations for numerical simulation, and presents the actual computer algorithm.


3.1   The equation of continuity of mass flow
   3.1.1   The integral equation of continuity
         Figure 3.1 (moving boundaries and walls)
   3.1.2   Pumping and sucking
   3.1.3   Others' choices for the continuity equation
3.2   The equation of motion
   3.2.1   Pressure gradient
         Figure 3.3 (moving particle)
   3.2.2   Bernoulli effect
   3.2.3   Friction
         Figure 3.4 (transverse velocity gradient)
         Figure 3.5 (velocity profile)
         Figure 3.6 (resistance)
   3.2.4   Complete equation of motion
   3.2.5   Others' choices for the equation of motion
3.3   The equation of state
3.4   Turbulence
   3.4.1   Energy loss
         Figure 3.7 (outlet)
   3.4.2   Turbulence noise
3.5   Boundary conditions
   3.5.1   At a closed boundary
         Figure 3.8 (closed boundary)
   3.5.2   At a boundary open to the atmosphere
         Figure 3.9 (open boundary)
   3.5.3   At a boundary between two tube sections
         Figure 3.10 (two-way boundary)
   3.5.4   At a three-way boundary
         Figure 3.11 (three-way boundary)
3.6   Simplifying the aerodynamic equations
   3.6.1   The aerodynamic equations in terms of continuous quantities
   3.6.2   Eliminating the equation of state
   3.6.3   A paradoxical factor of one half
3.7   Acoustic output
3.8   Digital simulation
3.9   The dissipative part of the equations
   3.9.1   The exponential method
   3.9.2   The first-order explicit method
   3.9.3   The first-order implicit method
   3.9.4   The second-order method
   3.9.5   Which method should we use?
         Figure 3.13 (four dampings)
3.10   The harmonic part of the myo-elastic equations
      Figure 3.14 (four frequency and amplitude warpings)
   3.10.1   The "explicit" method
   3.10.2   The "exact" method
   3.10.3   The "implicit" method
   3.10.4   The "second-order" method
   3.10.5   The amplitude of the periodic motion
   3.10.6   Which method should we use?
3.11   The hyperbolic part of the aerodynamic equations
   3.11.1   The Lax-Wendroff method
   3.11.2   Stability, numerical damping, and frequency warping
         Figure 3.15 (Lax-Wendroff warping)
         Figure 3.16 (formant and bandwidth warping)
   3.11.3   Four extensions to the Lax-Wendroff method
   3.11.4   Stability, frequency warping, and numerical damping
   3.11.5   Accuracy
3.12   The algorithm
3.13   Conclusion
Forward to chapter 4.
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