Related papers: Physical Basis for a Constant Lag Time
In a body periodically strained by tides, heating produced by viscous friction is far from homogeneous. I show here that the distribution of the dissipated power within a spherically stratified body is a linear combination of three angular…
We prove integrated local energy decay for solutions of the damped wave equation with time-dependent damping satisfying an appropriate generalization of the geometric control condition on asymptotically flat, stationary space-times. We…
Most aquatic vertebrates swim by lateral flapping of their bodies and caudal fins. While much effort has been devoted to understanding the flapping kinematics and its influence on the swimming efficiency, little is known about the stability…
In this article, we investigate the existence and properties of time-periodic solutions for damped evolutionary partial differential equations subject to periodic forcing. Particular emphasis is placed on configurations where the energy…
We derive the second-order dissipative relativistic hydrodynamic equations in a generic frame with a continuous parameter from the relativistic Boltzmann equation. We present explicitly the relaxation terms in the energy and particle…
We study tidal dissipation in stars with masses in the range $0.1-1.6 M_\odot$ throughout their evolution, including turbulent effective viscosity acting on equilibrium tides and inertial waves in convection zones, and internal gravity…
We consider the tidal interaction of a fully convective primary star and a point mass. Using a normal mode decomposition we calculate the evolution of the primary angular velocity and orbit for arbitrary eccentricity e. The dissipation…
We study the coupled small-amplitude motion of the mechanical system consisting of infinitely deep water and a structure immersed in it. The former is bounded above by a free surface, whereas the latter is formed by an arbitrary finite…
The dynamics of the fluid fields in a large class of causal dissipative fluid theories is studied. It is shown that the physical fluid states in these theories must relax (on a time scale that is characteristic of the microscopic particle…
We present an analogy between natural oscillations of the standing wave type on a pool of liquid with an interface and a mechanical oscillator model. It is shown that the equations of motion governing both systems have qualitatively similar…
The properties of a one space-dimension, one particle dynamical system under the influence of a purely dissipative force are investigated. Assuming this force depends only on the velocity, it is demonstrated, in contrast to the case of…
A new condition for the linear dissipative instability of the strong plane shock wave in an arbitrary medium is obtained. The instability of the shock is realized due to the flow instability behind its front, which is similar to the known…
A magnetically dominated plasma driven by motions on boundaries at which magnetic field lines are anchored is forced to dissipate the work being done upon it, no matter how small the electrical resistivity. Numerical experiments have…
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…
Tides are the main driving force behind the long-term evolution of planetary systems. The associated energy dissipation and momentum exchanges are commonly described by Love numbers, which relate the exciting potential to the tidally…
We consider a class of singular ordinary differential equations describing analytic systems of arbitrary finite dimension, subject to a quasi-periodic forcing term and in the presence of dissipation. We study the existence of response…
The notion of a physical collapse of the wave function is embodied in dynamical collapse models. These involve a modification of the unitary evolution of the wave function such as to give a dynamical account of collapse. The resulting…
By solving Laplace's tidal equations with friction terms we study the surface tide on a rapidly rotating body. When $\epsilon=\Omega^2 R/g$, the square of the ratio of dynamical timescale to rotational timescale, is very small for the Earth…
We study the motion of a rigid body within a compressible, isentropic, and viscous fluid contained in a fixed bounded domain $\Omega \subset \mathbb{R}^3$. The fluid's behavior is described by the Navier-Stokes equations, while the motion…
We discuss dynamical friction in an $N$-body system in the presence of tidal interactions caused by a distant external source. Using the distant tide approximation, we develop a perturbation scheme for the calculation of dynamical friction…