Intraglottal pressure profiles for a symmetric and oblique glottis with a divergence angle of 10 degrees

Human phonation does not always involve symmetric motions of the two vocal folds. Asymmetric motions can create slanted or oblique glottal angles. This study reports intraglottal pressure profiles for a Plexiglas model of the larynx with a glottis having a 10-degree divergence angle and either a symmetric orientation or an oblique angle of 15 degrees. For the oblique glottis, one side was divergent and the other convergent. The vocal fold surfaces had 14 pressure taps. The minimal glottal diameter was held constant at 0.04 cm. Results indicated that for either the symmetric or oblique case, the pressure profiles were different on the two sides of the glottis except for the symmetric geometry for a transglottal pressure of 3 cm H2O. For the symmetric case, flow separation created lower pressures on the side where the flow stayed attached to the wall, and the largest pressure differences between the two sides of the channel were 5%-6% of the transglottal pressure. For the oblique case, pressures were lower on the divergent glottal side near the glottal entry and exit, and the cross-channel pressures at the glottis entrance differed by 27% of the transglottal pressure. The empirical pressure distributions were supported by computational results. The observed aerodynamic asymmetries could be a factor contributing to normal jitter values and differences in vocal fold phasing.     

On the application of the lattice Boltzmann method to the investigation of glottal flow

The production of voice is directly related to the vibration of the vocal folds, which is generated by the interaction between the glottal flow and the tissue of the vocal folds. In the current study, the aerodynamics of the symmetric glottis is investigated numerically for a number of static configurations. The numerical investigation is based on the lattice Boltzmann method (LBM), which is an alternative approach within computational fluid dynamics. Compared to the traditional Navier-Stokes computational fluid dynamics methods, the LBM is relatively easy to implement and can deal with complex geometries without requiring a dedicated grid generator. The multiple relaxation time model was used to improve the numerical stability. The results obtained with LBM were compared to the results provided by a traditional Navier-Stokes solver and experimental data. It was shown that LBM results are satisfactory for all the investigated cases.     

Summation methods of Coulomb interactions in computer simulations of a system with one—dimensional periodic boundary conditions

The Ewald-type method, its modified version and the Lekner-type method for summing Coulomb interactions in a system periodic along one direction are presented and compared. Advantages and disadvantages of these methods are discussed, and the methods are tested in molecular dynamics simulations of acetone molecules confined to cylindrical silica pores.     

Electrostatic interactions in molecular dynamics simulation of a three-dimensional system with periodicity in one direction

The Mellin transform and Poisson summation formula are used to derive an expression for the Coulomb interaction energy of a three-dimensional system with periodicity in one direction. Initially, calculations are performed for interactions characterized by any inverse power and, using the analytical continuation of the energy function, one obtains the final expression for the interaction energy of charges. We consider also a special case when two different charges are located on a line parallel to the periodicity direction. The energy and force expressions are identical to those obtained from the Lekner summation which is simply a sum over reciprocal lattice terms. The convergence behaviour of the Lekner summation is compared with that based on the Ewald type approach.     

Coulomb interactions in a computer simulation of a system periodic in two directions

The integral representation of the gamma function and the Poisson summation formula are used to calculate the interaction energy of charged particles in a 3-dimensional system periodic in two directions. A parallelogram shape simulation box is considered. Calculations are carried out for interactions described by any inverse power, and analytical continuation of the energy function leads to the final expression for the Coulomb interaction energy. Summation over the simulation box replica along one or the other side of the box base is replaced by summation in reciprocal space. Therefore there are two equivalent formulas for the potential energy that offer the possibility of avoiding slowly convergent series. The energy expressions are identical to those obtained from the Lekner method. The special case is considered where the functions defining the energy are infinite, i.e. when two charges lie on a line parallel to the simulation box side that was chosen to convert real space summation into reciprocal space.