Anomalies of ac driven solitary waves with internal modes: Nonparametric resonances induced by parametric forces

We study the dynamics of kinks in the $\phi^4$ model subjected to a parametric ac force, both with and without damping, as a paradigm of solitary waves with internal modes. By using a collective coordinate approach, we find that the parametric force has a non-parametric effect on the kink motion. Specifically, we find that the internal mode leads to a resonance for frequencies of the parametric driving close to its own frequency, in which case the energy of the system grows as well as the width of the kink. These predictions of the collective coordinate theory are verified by numerical simulations of the full partial differential equation. We finally compare this kind of resonance with that obtained for non-parametric ac forces and conclude that the effect of ac drivings on solitary waves with internal modes is exactly the opposite of their character in the partial differential equation.Comment: To appear in Phys Rev

Symmetron Cosmology

The symmetron is a scalar field associated with the dark sector whose coupling to matter depends on the ambient matter density. The symmetron is decoupled and screened in regions of high density, thereby satisfying local constraints from tests of gravity, but couples with gravitational strength in regions of low density, such as the cosmos. In this paper we derive the cosmological expansion history in the presence of a symmetron field, tracking the evolution through the inflationary, radiation- and matter-dominated epochs, using a combination of analytical approximations and numerical integration. For a broad range of initial conditions at the onset of inflation, the scalar field reaches its symmetry-breaking vacuum by the present epoch, as assumed in the local analysis of spherically-symmetric solutions and tests of gravity. For the simplest form of the potential, the energy scale is too small for the symmetron to act as dark energy, hence we must add a cosmological constant to drive late-time cosmic acceleration. We briefly discuss a class of generalized, non-renormalizable potentials that can have a greater impact on the late-time cosmology, though cosmic acceleration requires a delicate tuning of parameters in this case.Comment: 42 page

The Driven Pendulum at Arbitrary Drive Angle

We discuss the equation of motion of the driven pendulum and generalize it to arbitrary driving angle. The pendulum will oscillate about a stable angle other than straight down if the drive amplitude and frequency are large enough for a given drive angle. The emphasis is on the parameters associated with a simply made demonstration apparatus.Comment: v1: 32 pages, 25 figures submitted to the American Journal of Physics. v2: 22 pages, 16 figures, after initial review. v3: 19 pages, 12 figures, accepted by the American Journal of Physics. After it is published it will be found at http://ojps.aip.org/aj

Tidal interaction of a rotating 1 Msun star with a binary companion

We calculate the tidal torque on a uniformly rotating 1 Msun star at various stages of core hydrogen burning by an orbiting companion. We apply the `traditional approximation' and solve the radial part of the tidal perturbations by matrix inversion of the set of finite difference equations on a very fine grid. We have identified resonances with gravity- and quasi-toroidal modes with up to 1000 radial nodes in the more evolved stellar models. For low forcing frequencies we find significant tidal response due to viscous damping of inertial modes in the convective envelope of the solar-type star. We conclude that effects due to stellar rotation (including resonance locking) may considerably enhance the speed of tidal evolution in solar-type stars.Comment: accepted for publ. in A&A, 11 pages, 6 figure