IRIS Pol. Torinohttps://iris.polito.itIl sistema di repository digitale IRIS acquisisce, archivia, indicizza, conserva e rende accessibili prodotti digitali della ricerca.Sat, 22 Jan 2022 03:03:30 GMT2022-01-22T03:03:30Z1041An Existence and Uniqueness Result for the Motion of Self-Propelled Microswimmershttp://hdl.handle.net/11583/2722521Titolo: An Existence and Uniqueness Result for the Motion of Self-Propelled Microswimmers
Abstract: We present an analytical framework to study the motion of microswimmers in a viscous fluid. Our main result is that, under very mild regularity assumptions, the change of body shape uniquely determines the motion of the swimmer. We assume that the Reynolds number is very small, so that the velocity field of the surrounding infinite fluid is governed by the Stokes system and all inertial effects can be neglected. Moreover, we enforce the self propulsion constraint (no external forces and torques). Therefore, Newton’s equations of motion reduce to the vanishing of the viscous force and torque acting on the body. By exploiting an integral representation of viscous force and torque, the equations of motion can be reduced to a system of six ordinary differential equations. Variational techniques are used to prove the boundedness and measurability of this system’s coefficients, so that classical results on ordinary differential equations can be invoked to prove existence and uniqueness of the solution.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/11583/27225212011-01-01T00:00:00ZTransmission conditions obtained by homogenisationhttp://hdl.handle.net/11583/2725880Titolo: Transmission conditions obtained by homogenisation
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/11583/27258802018-01-01T00:00:00ZOne-dimensional swimmers in viscous fluids: dynamics, controllability, and existence of optimal controlshttp://hdl.handle.net/11583/2722525Titolo: One-dimensional swimmers in viscous fluids: dynamics, controllability, and existence of optimal controls
Abstract: In this paper we study a mathematical model of one-dimensional swimmers performing a planar motion while fully immersed in a viscous fluid. The swimmers are assumed to be of small size, and all inertial effects are neglected. Hydrodynamic interactions are treated in a simplified way, using the local drag approximation of resistive force theory. We prove existence and uniqueness of the solution of the equations of motion driven by shape changes of the swimmer. Moreover, we prove a controllability result showing that given any pair of initial and final states, there exists a history of shape changes such that the resulting motion takes the swimmer from the initial to the final state. We give a constructive proof, based on the composition of elementary maneuvers (straightening and its inverse, rotation, translation), each of which represents the solution of an interesting motion planning problem. Finally, we prove the existence of solutions for the optimal control problem of finding, among the histories of shape changes taking the swimmer from an initial to a final state, the one of minimal energetic cost.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/11583/27225252015-01-01T00:00:00ZA model for the quasistatic growth of cracks with fractional dimensionhttp://hdl.handle.net/11583/2722530Titolo: A model for the quasistatic growth of cracks with fractional dimension
Abstract: We study a variational model for the quasistatic growth of cracks with fractional dimension in brittle materials. We give a minimal set of properties of the collection of admissible cracks which ensure the existence of a quasistatic evolution. Both the antiplane and the planar cases are treated.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/11583/27225302017-01-01T00:00:00Z