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In this article we consider an optimization problem where the objective function is evaluated at the fixed-point of a contraction mapping parameterized by a control variable, and optimization takes place over this control variable. Since…
We consider the motion of a rigid body due to the pressure of a surrounded two-dimensional irrotational perfect incompressible fluid, the whole system being confined in a bounded domain with an impermeable condition on a part of the…
A fluid droplet in general deforms, if subject to active driving, such as a finite slip velocity or active tractions on its interface. We show that these deformations and their dynamics can be computed analytically in a perturbation theory…
The method of characteristics is a classical method for gaining understanding in the solution of a partial differential equation. It has recently been applied to the adjoint equations of the 2D Euler equations and the first goal of this…
An adjoint-based shape optimization method for solid bodies subjected to both rarefied and continuum gas flows is proposed. The gas-kinetic BGK equation with the diffuse-reflection boundary condition is used to describe the multiscale gas…
A finite-element algorithm for computing free-surface flows driven by arbitrary body forces is presented. The algorithm is primarily designed for the microfluidic parameter range where (i) the Reynolds number is small and (ii) force-driven…
Drawing inspiration from the lateral lines of fish, the inference of flow characteristics via surface-based data has drawn considerable attention. The current approaches often rely on analytical methods tailored exclusively for potential…
The problem of describing isolated rotating bodies in equilibrium in General Relativity has so far been treated under the assumption of the circularity condition in the interior of the body. For a fluid without energy flux, this condition…
Models for fluid deformable surfaces provide valid theories to describe the dynamics of thin fluidic sheets of soft materials. To use such models in morphogenesis and development requires to incorporate active forces. We consider active…
We develop a geometric formulation of fluid dynamics, valid on arbitrary Riemannian manifolds, that regards the momentum-flux and stress tensors as 1-form valued 2-forms, and their divergence as a covariant exterior derivative. We review…
It is shown how a complete set of hydrodynamic equations describing an unsteady three-dimensional viscous flow nearby a solid body, can be reduced to a closed system of surface equations using the method of dimension reduction of…
We present a new general method to construct an action functional for a non-potential field theory. The key idea relies on representing the governing equations of the theory relative to a diffeomorphic flow of curvilinear coordinates which…
Use of curvilinear coordinates is sometimes indicated by the inherent geometry of a fluid dynamics problem, but this introduces fictitious forces into the momentum equations that spoil strict conservative form. If one is willing to work in…
In most practical situations, active particles are affected by their environment, for example, by a chemical concentration gradient, light intensity, gravity, or confinement. In particular, the effect of an external flow field is important…
We present ShapeFlow, a flow-based model for learning a deformation space for entire classes of 3D shapes with large intra-class variations. ShapeFlow allows learning a multi-template deformation space that is agnostic to shape topology,…
We study a 2D potential flow of an ideal fluid with a free surface with decaying conditions at infinity. By using the conformal variables approach, we study a particular solution of Euler equations having a pair of square-root branch points…
An algorithm is proposed for generalized mean curvature flow of closed two-dimensional surfaces, which include inverse mean curvature flow, powers of mean and inverse mean curvature flow, etc. Error estimates are proven for semi- and full…
In contrast to the commonly used lattice Boltzmann method, off-lattice Boltzmann methods decouple the velocity discretization from the underlying spatial grid, thus allowing for more efficient geometric representations of complex…
Controlling the shapes of surfaces provides a novel way to direct self-assembly of colloidal particles on those surfaces and may be useful for material design. This motivates the investigation of an optimal control problem for surface shape…
The separated flow downstream a backward-facing step is controlled using visual information for feedback. This is done when looking at the flow from two vantage points. Flow velocity fields are computed in real-time and used to yield inputs…