Related papers: Solution of the Kirchhoff-Plateau problem
We consider a fluid model including viscoelastic and viscoplastic effects. The state is given by the fluid velocity and an internal stress tensor that is transported along the flow with the Zaremba-Jaumann derivative. Moreover, the stress…
A mechanical system consisting of a rigid body and attached Kirchhoff plates under the action of three independent controls torques is considered. The equations of motion of such model are derived in the form of a system of coupled…
We study numerically and theoretically the gravity-driven flow of a viscous liquid film coating the inner side of a horizontal cylindrical tube and surrounding a shear-free dynamically inert gaseous core. The liquid-gas interface is prone…
We propose a method to stabilise a solution to equations describing the interface of thin liquid films falling under gravity with a finite number of actuators and restricted observations. As for many complex systems, full observation of the…
A suspended fluid film with two free surfaces convects when a sufficiently large voltage is applied across it. We present a linear stability analysis for this system. The forces driving convection are due to the interaction of the applied…
Minimal surface problems arise naturally in many soft matter systems whose free energies are dominated by surface or interface energies. Of particular interest are the shapes, stability and mechanical stresses of minimal surfaces spanning…
Hydrodynamic instability of a gravity-driven flow down an inclined plane is investigated in the presence of a floating elastic plate which rests on the top surface of the flow. Linear instability of the system with respect to infinitesimal…
We present a novel computational modeling framework to numerically investigate fluid-structure interaction in viscous fluids using the phase field embedding method. Each rigid body or elastic structure immersed in the incompressible viscous…
A finite element approach for approximating the solution of a mathematical model for the response of a penetrable, bounded object (obstacle) to the excitation by an external electromagnetic field is presented and investigated. The model…
The problem of determining the manner in which an incoming acoustic wave is scattered by an elastic body immersed in a fluid is one of central importance in detecting and identifying submerged objects. The problem is generally referred to…
Inspired by recent results on self-avoiding inextensible curves, we propose and experimentally investigate a numerical method for simulating isometric plate bending without self-intersections. We consider a nonlinear two-dimensional…
We study a novel approach for the existence of solutions to an incompressible fluid-rigid body interaction problem in three dimensions. Our approach introduces an iteration based on a sequence of related problems posed on domains with…
We study a Cahn--Hilliard two-phase model describing the flow of two viscoelastoplastic fluids, which arises in geodynamics. A phase-field variable indicates the proportional distribution of the two fluids in the mixture. The motion of the…
We consider the control of a three-dimensional thin liquid film on a flat substrate, inclined at a non-zero angle to the horizontal. Controls are applied via same-fluid blowing and suction through the substrate surface. We consider both…
We show short-time well-posedness of a diffuse interface model describing the flow of a fluid through a deformable porous medium consisting of two phases. The system non-linearly couples Biot's equations for poroelasticity, including…
Kirchhoff's kinetic analogy relates the equilibrium solutions of an elastic rod or strip to the motion of a spinning top. In this analogy, time is replaced by the arc length parameter in the phase portrait to determine the equilibrium…
The duality between deformations of elastic bodies and non-inertial flows in viscous liquids has been a guiding principle in decades of research. However, this duality is broken when a spheroidal or other doubly-curved liquid film is…
In this paper, we investigate the dynamics of an incompressible viscous Navier-Stokes fluid evolving above a one-dimensional flat surface. The fluid is subject to a uniform gravitational field and capillary forces acting along the free…
The mechanism by which a patterned state accommodates the breaking of translational symmetry by a phase boundary or a sample wall has been addressed in the context of Landau branching in type-I superconductors, refinement of magnetic…
We present a loosely coupled approach for the solution of fluid-structure interaction problems between a compressible flow and a deformable structure. The method is based on staggered Dirichlet-Neumann partitioning. The interface motion in…