We present numerical solutions of the semi-empirical model of self-propagating
fluid pulses (auto-pulses) through the channel simulating an artificial artery. The key
mechanism behind the model is the active motion of the walls in line with the earlier
model of Roberts. Our model is autonomous, nonlinear and is based on the partial
differential equation describing the displacement of the wall in time and along the
channel. A theoretical plane configuration is adopted for the walls at rest. For solving
the equation we used the One-dimensional Integrated Radial Basis Function Network
(1D-IRBFN) method. We demonstrated that different initial conditions always lead to
the settling of pulse trains where an individual pulse has certain speed and amplitude
controlled by the governing equation. A variety of pulse solutions is obtained using
homogeneous and periodic boundary conditions. The dynamics of one, two and three
pulses per period are explored. The fluid mass flux due to the pulses is calculated.
Dmitry Strunin is an Associate Professor at the University of Southern Queensland, Australia, affiliated with the Computational Engineering and Science Research Centre and
the Faculty of Health, Engineering and Sciences. His research interests are in nonlinear dynamics, active dissipative systems and continuum mechanics.
He graduated from the Institute of Physics and Technology, Moscow, Russia, and received his PhD in 1989 from the Institute of Oceanology of the Russian Academy of Sciences, Moscow.
After taking a postdoc position at the University of Melbourne, Australia, he worked as a researcher at the University of Wollongong and University of Southern Queensland (USQ)
before becoming a lecturer at the USQ in 2002. Dmitry Strunin, jointly with Prof. Anthony Roberts, received two Discovery Project grants (three-year each) from the Australian
Research Council (analogy to NSF). He was an invited guest scientist at the Max Planck Institute for the Physics of Complex Systems, Dresden, Germany,
and Schmidt Institute of Physics of the Earth of the Russian Academy of Sciences, Moscow. He acted as Associate Editor for the Australian and New Zealand Industrial and Applied Mathematics Journal; is a member of Editorial Board for Multiphysics Modelling (CRC Press, Taylor and Francis group).