Many biological organisms are comprised of deformable porous media, with additional complexity of an embedded muscle. Using geometric variational methods, we derive the equations of motion for the dynamics of such active porous media. The use of variational methods allows to incorporate both the muscle action and incompressibility of the fluid and the elastic matrix in a consistent, rigorous framework, with no need to guess the balance of forces and torques. We then derive conservation laws for the motion, perform numerical simulations and show the possibility of self-propulsion of a biological organism due to particular running wave-like application of the muscle stress.

Vakhtang Putkaradze is the Vice President for Transformation, Science, and Technology at ATCO Ltd. He holds a PhD in theoretical physics from the Niels Bohr Institute (Copenhagen, Denmark). He draws on more than 20 years of experience in research and academia prior to starting at ATCO in 2019. He has held the position of L.E. Dickson Instructor at the University of Chicago, faculty positions at the New Mexico and Colorado State Universities, and most recently the title of Centennial Professor of Mathematics and Chemical Engineering at the University of Alberta. He has received numerous prizes at the university, national, and international levels, including the CAIMS–Fields Prize for Industrial Mathematics, University of Alberta Commercialization Award, Japanese Society for Promotion of Sciences Senior Award, Flaherty Visiting Professorship, and Humboldt Fellowship. His research work has been supported by the U.S. Departments of Energy and Defense, Petroleum Research Fund, Sandia National Laboratory, U.S. National Science Foundation and NSERC Canada.

Organizer: D. Zenkov