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The motion of a rigid, spinning disk on a flat surface ends with a dissipation-induced finite-time singularity. The problem of finding the dominant energy absorption mechanism during the last phase of the motion generated a lively debate…
We present an experimental study of the motion of a circular disk spun onto a table. With the help of a high speed video system, the temporal evolutions of (i) the inclination angle $\alpha$, (ii) the angular velocity $\omega$ and (iii) the…
Spatiotemporal spin dynamics under spin-orbit interaction is investigated in a (001) GaAs two-dimensional electron gas using magneto-optical Kerr rotation microscopy. Spin polarized electrons are diffused away from the excited position,…
Recent interest in the old problem of the motion of a coin spinning on a tabletop has focused on mechanisms of dissipation of energy as the angle alpha of the coin to the table decreases, while the angular velocity Omega of the point of…
We study the ascending motion of a disk rolling on an incline when its center of mass lies outside the disk axis. The problem is suitable as laboratory project for a first course in mechanics at the undergraduate level and goes beyond…
Accretion disc turbulence is investigated in the framework of the shearing box approximation. The turbulence is either driven by the magneto-rotational instability or, in the non-magnetic case, by an explicit and artificial forcing term in…
We consider the motion of a rigid body immersed in a two-dimensional viscous incompressible fluid with Navierslip-with-friction conditions at the solid boundary. The fluid-solid system occupies the whole plane. We provethe small-time exact…
When a gel absorbs solvent from surrounding, stress field is created in the gel, and this causes complex dynamics of the swelling behavior. Here we study this effect for disk-shaped gel by rigorously solving the diffusio-mechanical coupling…
Motivated by the normal form of a fast-slow ordinary differential equation exhibiting a pitchfork singularity we consider the discrete-time dynamical system that is obtained by an application of the explicit Euler method. Tracking…
This paper proposes a new general methodology for finite-time singularity formation for moving interface problems involving the incompressible Euler equations in the plane. The first problem considered is the two-phase Euler vortex sheets…
The article discusses the steady motion of a rigid disk of finite thickness rolling on its edge on a horizontal plane under the influence of gravity. The governing equations are presented and two cases allowing for a steady state solution…
We study the motion of a two-dimensional droplet on an inclined surface, under the action of gravity, using a diffuse interface model which allows for arbitrary equilibrium contact angles. The kinematics of motion is analysed by decomposing…
The motion of a rigid body is described in Classical Mechanics with the venerable Euler's equations which are based on the assumption that the relative distances among the constituent particles are fixed in time. Real bodies, however,…
We performed two-dimensional Molecular Dynamics simulations of cohesive disks under shear. The cohesion between the disks is added by the action of springs between very next neighbouring disks, modelling capillary forces. The geometry of…
The leaves of many plants are superhydrophobic, a property that may have evolved to clean the leaves by encouraging water droplets to bead up and roll off. Superhydrophobic surfaces can also exhibit reduced friction and liquids flowing over…
This research investigates the rotational dynamics of a charged axisymmetric spinning rigid body influenced by gyrostatic torque. The study also accounts for the effects of transverse and constant body-fixed torques and an electromagnetic…
The mechanical response of a circularly-driven disk in a dissipative medium is considered. We focus on the role played by viscous friction in the spinning motion of the disk, especially on the effect called reverse rotation, where the…
Accretion disks around stars, or other central massive bodies, can support long-lived, slowly precessing $m=1$ disturbances in which the fluid motion is nearly Keplerian with non-zero eccentricity. We study such `slow modes' in disks that…
We study the rolling and sliding motion of droplets on a corrugated substrate by Molecular Dynamics simulations. Droplets are driven by an external body force (gravity) and we investigate the velocity profile and dissipation mechanisms in…
We investigate the wrinkling dynamics of a thin elastic sheet that is indented or compressed while floating on a viscous liquid. We show that the deformation speed controls the dynamics, leading to a wrinkle wavelength significantly smaller…