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A mirror in the vacuum is submitted to a radiation pressure exerted by scattered fields. It is known that the resulting mean force is zero for a motionless mirror, but not for a mirror moving with a non-uniform acceleration. We show here…

We study the long-term dynamics of a planetary system composed of a star and a planet. Both bodies are considered as extended, non-spherical, rotating objects. There are no assumptions made on the relative angles between the orbital angular…

Lepton number charges might be the source of long range forces. If one accepts that neutrinos produced in the Sun do indeed oscillate while crossing the interior of the Sun, then the shift in the phase of the neutrino wavefunction caused by…

Wave-packet scattering from a stationary potential is significantly modified when the wave-packet is subject to an external time-dependent force during the interaction. In the semiclassical limit, wave--packet motion is simply described by…

Using the Ricci and scalar curvatures of the configuration manifold of gravitational N-body systems, we study the exponential instability in their trajectories. It is found that the exponentiation time-scale for isotropic Plummer spheres…

The law of balance of angular momentum is shown to imply the existence of absolute time, a fundamental physical quantity that is independent of the motion or position of the observer. Absolute time implies the notion of absolute…

A fundamental question in the study of water waves is the existence and stability of solitary waves. Solitary waves have been proved to exist and have been studied in many interesting situations, and often arise from the balance of…

For more than 35 years theorists have studied quantum or Casimir friction, which occurs when two smooth bodies move transversely to each other, experiencing a frictional dissipative force due to quantum electromagnetic fluctuations, which…

As revealed by space-time probing, mechanics and field theory come out as complementary descriptions for motions in space-time. In particular, quantum fields exert a radiation pressure on scatterers which results in mechanical effects that…

In this paper the motion of two-phase, incompressible, viscous fluids with surface tension is investigated. Three cases are considered: (1) the case of heat-conducting fluids, (2) the case of isothermal fluids, and (3) the case of Stokes…

The gravitational collapse of cylindrically distributed perfect fluid is studied. We assume the collapsing speed of fluid is very large and investigate such a situation by recently proposed high-speed approximation scheme. We show that if…

We consider a semiconductor in a non-equilibrium steady state, with a dc current. On top of the stationary carrier motion there are fluctuations. It is shown that the stationary motion of the carriers (i.e., their drift) can have a profound…

We study a class of time dependent solutions of the vacuum Einstein equations which are plane waves with weak null singularities. This singularity is weak in the sense that though the tidal forces diverge at the singularity, the rate of…

A classical system, which is analogous to the quantum one with a backflow of probability, is proposed. The system consists of a chain of masses interconnected by springs, as well attached by other springs to fixed supports. Thanks to the…

The {\it two-fold singularity} has played a significant role in our understanding of uniqueness and stability in piecewise smooth dynamical systems. When a vector field is discontinuous at some hypersurface, it can become tangent to that…

Standard solar models predict a solar luminosity that gradually increased by about 30% over the past 4.5 billion years. Under the faint sun, Earth should have been frozen solid for most of its existence. Yet, running water is observed to…

This paper is a preliminary work to address the problem of dynamical systems with parameters varying in time. An idea to predict their behaviour is proposed. These systems are called \emph{transient systems}, and are distinguished from…

We investigate the relativistic effective field theory (EFT) describing a non-dissipative gravitating continuum. In addition to ordinary continua, namely solids and fluids, we find an extraordinary more symmetric continuum, aether. In…

The interaction of a fast magnetoacoustic wave with a magnetic null point is studied in the context of the sympathetic flare phenomenon. Attention is paid to steepening the wave caused by the finite-amplitude effects in a non-uniform plasma…

We combine theories of scattering for linearized water waves and flexural waves in thin plates to characterize and achieve control of water wave scattering using floating plates. This requires manipulating a sixth-order partial differential…