Related papers: On the Stopping Time of a Bouncing Ball
The steady state motion of cylindrical droplets under the action of external body force is investigated both theoretically and via lattice Boltzmann simulation. As long as the shape-invariance of droplet is maintained, the droplet's…
We aim at the stability of time-dependent motions, such as time-periodic ones, of a rigid body in a viscous fluid filling the exterior to it in 3D. The fluid motion obeys the incompressible Navier-Stokes system, whereas the motion of the…
Firstly, we get the completely bouncing criteria Cr for droplet on moving substrate. The bouncing without splashing condition is $\mathrm{Cr}>1$. Then, we mainly research the effect of wind field for droplet, and get the completely bouncing…
Nonlinear elastic theory studies the elastic constants of a material (such as Young's modulus or bulk modulus) as a power series in the applied load. The inverse bulk modulus K, for example depends on the compression P: $ {1/ K(P)} = c_0 +…
We present a numerical model of a collapsing radiating sphere, whose boundary surface undergoes bouncing due to a decreasing of its inertial mass density (and, as expected from the equivalence principle, also of the ``gravitational'' force…
We investigate the interactions between two drops in a heated environment and analyze the effect of evaporation on bouncing, coalescence and reflexive separation phenomena. A reliable mass transfer model is incorporated in a coupled…
The problem of the mechanical evolution of a shock between a cylindrically symmetric bat and a spherical ball is solved in the strict rigid approximation for arbitrary values of the initial conditions. The friction during the impact is…
The purpose of the present study is to extend the simple concept of apparent coefficient of restitution, widely approached in the literature for the case of a single-contact-point between a sphere and a wall, to the case of bouncing whose…
This paper is concerned with the mathematical analysis of time-dependent fluid-solid interaction problem associated with a bounded elastic body immersed in a homogeneous air or fluid above a local rough surface. We reformulate the unbounded…
Ball and hoop system is a well-known model for the education of linear control systems. In this paper, we have a look at this system from another perspective and show that it is also suitable for demonstration of more advanced control…
We introduce a model of friction between two contacting (stationary or co-sliding) rough surfaces, each comprising a random ensemble of polydisperse hemispherical bumps. In the simplest version of the model, the bumps experience on contact…
The problem of a general, symmetric contact, between elastically similar bodies, and capable of idealisation using half-plane theory, is studied in the presence of interfacial friction. It is subject to a constant set of loads - normal…
We study the dynamics of a bouncing coin whose motion is restricted to the two-dimensional plane. Such coin model is equivalent to the system of two equal masses connected by a rigid rod, making elastic collisions with a flat boundary. We…
Picking up, laying down, colliding, rolling, and peeling are partial-contact interactions involving moving discontinuities. We examine the balances of momentum and energy across a moving discontinuity in a string, with allowance for…
We consider a mechanical system consisting of an infinite rod (a straight line) and a ball (a massless point) on the plane. The rod rotates uniformly around one of its points. The ball is reflected elastically when colliding with the rod…
When a liquid drop falls on a solid substrate, the air layer in between them delays the occurrence of liquid--solid contact. For impacts on smooth substrates, the air film can even prevent wetting, allowing the drop to bounce off with…
We consider a non-linear system modelling the dynamics of a linearly elastic body immersed in an incompressible viscous fluid, without damping on the elastic part. We prove local existence of strong solutions and global existence and…
We formulate the quasi-static elastic contact problem with Coulomb friction in a very general setting, with possible jumps in time for both the load and the solution. Exploiting ideas originating in our recent paper [4], we exhibit an…
We consider the dynamics of an electrostatically actuated thin elastic plate being clamped at its boundary above a rigid plate. The model includes the harmonic electrostatic potential in the three-dimensional time-varying region between the…
A finite element approach to the elastic flow of a curve coupled with a diffusion equation on the curve is analysed. Considering the graph case, the problem is weakly formulated and approximated with continuous linear finite elements, which…