Related papers: Stationary motion of a self gravitating toroidal i…
A stationary rotating surface is a compact surface in Euclidean space whose mean curvature $H$ at each point $x$ satisfies $2H(x)=a r^2+b$, where $r$ is the distance from $x$ to a fixed straight-line $L$, and $a$ and $b$ are constants.…
Manipulation ('shaking') of a rigid container filled with incompressible liquid starting from stationary generally results in some displacement, or mixing, of the liquid within it. If the liquid also has zero viscosity, a 'perfect', or…
This paper is devoted to the existence of a weak solution to a system describing a self-propelled motion of a rigid body in a viscous fluid in the whole $\mathbb{R}^3$. The fluid is modelled by the incompressible nonhomogeneous…
Typically the motion of self-propelled active particles is described in a quiescent environment establishing an inertial frame of reference. Here we assume that friction, self-propulsion and uctuations occur relative to a non-inertial frame…
An analysis of the toroidal modes of a rotating fluid, by means of the differential equations of motion is not readily tractable. A matrix representation of the equations in a suitable basis, however, simplifies the problem considerably and…
We consider the motion of the interface separating a vacuum from an inviscid, incompressible, and irrotational fluid, subject to the self-gravitational force and neglecting surface tension, in two space dimensions. The fluid motion is…
The hydrodynamic stationary states of a granular fluid are addressed theoretically when subject to energy injection and a time-independent, but otherwise arbitrary external potential force. When the latter is not too symmetrical in a well…
We consider a two-dimensional, incompressible fluid body, together with self-induced interactions. The body is perturbed by an external particle with small mass. The whole configuration rotates uniformly around the common center of mass. We…
Perfect fluid tori with uniform distribution of the specific angular momentum orbiting the Kerr-de Sitter black holes or naked singularities are studied. Closed equipotential surfaces corresponding to stationary toroidal discs are allowed…
The dynamics of a circular thin vortex ring and a sphere moving along the symmetry axis of the ring in an inviscid incompressible fluid is studied on the basis of Euler's equations of motion. The equations of motion for position and radius…
We study the motion of a single helical vortex in an unbounded, inviscid, incompressible fluid. The vortex is an infinite tube whose centerline is a helix and whose cross section is a circle of small radius (compared to the radius of…
We summarize the general formalism describing surface flows in three-dimensional space in a form which is suitable for various astrophysical applications. We then apply the formalism to the analysis of non-radial perturbations of…
Janus particles with the ability to move phoretically in self-generated chemical concentration gradients are model systems for active matter. Their motion typically consists of straight paths with rotational diffusion being the dominant…
We theoretically study the motion of a rigid dimer of self-propelling Janus particles. In a simple kinetic approach without hydrodynamic interactions, the dimer moves on a helical trajectory and, at the same time, it rotates about its…
For stationary, barotropic fluids in Newtonian gravity we give simple criteria on the equation of state and the "law of motion" which guarantee finite or infinite extent of the fluid region (providing a priori estimates for the…
We introduce a notion of stability for non-autonomous Hamiltonian flows on two-dimensional annular surfaces. This notion of stability is designed to capture the sustained twisting of particle trajectories. The main Theorem is applied to…
This paper examines the rigid body motion of a spheroid sedimenting in a Newtonian fluid with a spatially varying viscosity field. The fluid is at zero Reynolds number, and the viscosity varies linearly in space in an arbitrary direction…
We study the motion of an incompressible perfect liquid body in vacuum. This can be thought of as a model for the motion of the ocean or a star. The free surface moves with the velocity of the liquid and the pressure vanishes on the free…
The motion of a thin layer of granular material on a plate undergoing sinusoidal vibrations is considered. We develop equations of motion for the local thickness and the horizontal velocity of the layer. The driving comes from the violent…
We study stationary configurations of compressible barotropic fluids lying inside an incompressible fluid and acted upon by a constant gravitational field. Without gravity, it is a simple matter to construct solutions consisting of…