Vortex beam radiated by Gaussian vortex source: dimensionless code for Eq. (14) of
C. A. Gokani, M. R. Haberman, M. F. Hamilton. "Paraxial and ray approximations of acoustic vortex beams," J. Acoust. Soc. Am. 155, 2707-2723 (2024).The dimensionless form of Eq. (14) is in terms of the parameters \(Q = q/p_0\), \(R = r/a\), \(Z =z/z_R = 2z/ka^2\), and \(G = ka^2/2d\), where \(r\) and \(z\) are the cylindrical coordinates, \(a\) is the characteristic radius of the source, \(k\) is the wavenumber, and \(d\) is the focal length: \begin{align} {|Q|(R,Z)} &= \sqrt{2\pi} \frac{Z}{R^2} \big|\chi^{3/2} e^{-\chi} \big[I_{(\ell-1)/2}(\chi) - I_{(\ell+1)/2}(\chi)\big]\big|\,,\label{eq:gauss}\\ \chi(R,Z) &= \frac{iR^2/2Z}{1+ Z(i-G)} \,. \label{eq:chi} \end{align} Unfocused Gaussian vortex beams are obtained by setting \(G = 0\) in Eq. \eqref{eq:chi}. Both focused and unfocused cases are handled in the code.
Vortex beam radiated by circular vortex source: dimensionless code for magnitude of Eq. (6) of
C. A. Gokani, M. R. Haberman, M. F. Hamilton. "Analytical solutions for acoustic vortex beam radiation from planar and spherically focused circular pistons," JASA Express Lett. 4, 124001 (2024).The dimensionless form of Eq. (6) is in terms of the same parameters defined above. For an unfocused source, \begin{align}\label{eq:uni} |Q|(R,Z) = \frac{Z}{2R^2} F_\ell(2R/Z)\,, \end{align} where \(F_\ell(\xi)\) is provided by Eq. (8) of the paper referenced above and is encoded in the user-defined function closed_F.m for integers \(0 \leq \ell \leq 4\). (The closed_F.m function depends on the Struve functions encoded by Theo2—download that package and include it in the same directory as closed_F.m.) For all other values of \(\ell\), use the form in terms of the infinite sum given by Eq. (7), calculated by sum_F.m. For a focused source, \(Z\) in Eq. \eqref{eq:uni} is replaced by \(1/G\).
Exact integral solution of the Helmholtz equation for pistons: dimensionless code for magnitude of Eq. (21) of
C. A. Gokani, R. P. Williams, M. R. Haberman, M. F. Hamilton. "An alternative approach to modeling radiation from baffled circular pistons (L)," J. Acoust. Soc. Am., 158, 2642–2646 (2025).This code numerically evaluates \begin{align}\label{eq:int} P%(R,\theta,Z) &= e^{i\ell\theta} \int_0^\infty \frac{F_\ell(\zeta ) J_\ell(\zeta R)}{\zeta \sqrt{1-(\zeta/K)^2}} e^{iK^2Z\sqrt{1-(\zeta/K)^2}/2} \, d\zeta \,, \end{align} where \(F_\ell\) is defined above. It is more computationally efficient to use closed_F.m than it is to use sum_F.m.
Oscillator with damping: dimensionless code for motion of oscillator with damping.
fig_JASA: figure formatting file to match JASA numbering fonts (Times New Roman).
Laguerre polynomials demo in MATLAB: demo of MATLAB functions for Laguerre polynomials and generalized Laguerre polynomials in MATLAB.
Legendre Polynomials and Associated Legendre Functions in MATLAB: demo of MATLAB functions for Legendre polynomials and associated Legendre functions.
Spherical Bessel, Neumann, and Hankel functions in MATLAB: package that includes user-defined functions for the spherical Bessel, Neumann, and Hankel functions, along with a demo.
Introduction to LaTeX: a quick introduction presented to new graduate students in acoustics at UT Austin in 2024.
LaTeX continued: a continued introduction presented to graduate students in acoustics at UT Austin in 2025.