Chaos in the Hill system

We define the general Hill system and briefly analyze its dynamical behavior. A particular Hill system representing the interaction of a Keplerian binary system with a normally incident circularly polarized gravitational wave is discussed in detail. In this case, we compute the Poincar\'e-Melnikov function explicitly and determine its zeros. Moreover, we provide numerical evidence in favor of chaos in this system. The partially averaged equations for the Hill system are used to predict the regular behavior of the Keplerian orbit at resonance with the external radiation.Comment: 35 pages, 6 figure

Gravitational Ionization: Periodic Orbits of Binary Systems Perturbed by Gravitational Radiation

The long term perturbation of a Newtonian binary system by an incident gravitational wave is discussed in connection with the issue of gravitational ionization. The periodic orbits of the planar tidal equation are investigated and the conditions for their existence are presented. The possibility of ionization of a Keplerian orbit via gravitational radiation is discussed.Comment: ps file, 35 page

Sustained resonance: a binary system perturbed by gravitational radiation

The general phenomena associated with sustained resonance are studied in this paper in connection with relativistic binary pulsars. We represent such a system by two point masses in a Keplerian binary system that evolves via gravitational radiation damping as well as an external tidal perturbation. For further simplification, we assume that the external tidal perturbation is caused by a normally incident circularly polarized monochromatic gravitational wave. In this case, the second-order partially averaged equations are studied and a theorem of C. Robinson is employed to prove that for certain values of the physical parameters resonance capture followed by sustained resonance is possible in the averaged system. We conjecture that sustained resonance can occur in the physical system when the perturbing influences nearly balance each other.Comment: 21 pages, 5 figures. To appear in Journal of Physics

On the Ionization of a Keplerian Binary System by Periodic Gravitational Radiation

The gravitational ionization of a Keplerian binary system via normally incident periodic gravitational radiation of definite helicity is discussed. The periodic orbits of the planar tidal equation are investigated on the basis of degenerate continuation theory. The relevance of the Kolmogorov-Arnold-Moser theory to the question of gravitational ionization is elucidated, and it is conjectured that the process of ionization is closely related to the Arnold diffusion of the perturbed system.Comment: 19 pages, REVTEX Style, To appear in JM

Chaos in the Kepler System

The long-term dynamical evolution of a Keplerian binary orbit due to the emission and absorption of gravitational radiation is investigated. This work extends our previous results on transient chaos in the planar case to the three dimensional Kepler system. Specifically, we consider the nonlinear evolution of the relative orbit due to gravitational radiation damping as well as external gravitational radiation that is obliquely incident on the initial orbital plane. The variation of orbital inclination, especially during resonance capture, turns out to be very sensitive to the initial conditions. Moreover, we discuss the novel phenomenon of chaotic transition.Comment: RevTeX, 22 pages, 6 figure

Evolutionary Dynamics While Trapped in Resonance: A Keplerian Binary System Perturbed by Gravitational Radiation

The method of averaging is used to investigate the phenomenon of capture into resonance for a model that describes a Keplerian binary system influenced by radiation damping and external normally incident periodic gravitational radiation. The dynamical evolution of the binary orbit while trapped in resonance is elucidated using the second order partially averaged system. This method provides a theoretical framework that can be used to explain the main evolutionary dynamics of a physical system that has been trapped in resonance.Comment: REVTEX Style, Submitte

Gravitational Ionization: A Chaotic Net in the Kepler System

The long term nonlinear dynamics of a Keplerian binary system under the combined influences of gravitational radiation damping and external tidal perturbations is analyzed. Gravitational radiation reaction leads the binary system towards eventual collapse, while the external periodic perturbations could lead to the ionization of the system via Arnold diffusion. When these two opposing tendencies nearly balance each other, interesting chaotic behavior occurs that is briefly studied in this paper. It is possible to show that periodic orbits can exist in this system for sufficiently small damping. Moreover, we employ the method of averaging to investigate the phenomenon of capture into resonance.Comment: REVTEX Style, Submitte

Orbital effects of a monochromatic plane gravitational wave with ultra-low frequency incident on a gravitationally bound two-body system

We analytically compute the long-term orbital variations of a test particle orbiting a central body acted upon by an incident monochromatic plane gravitational wave. We assume that the characteristic size of the perturbed two-body system is much smaller than the wavelength of the wave. Moreover, we also suppose that the wave's frequency is much smaller than the particle's orbital one. We make neither a priori assumptions about the direction of the wavevector nor on the orbital geometry of the planet. We find that, while the semi-major axis is left unaffected, the eccentricity, the inclination, the longitude of the ascending node, the longitude of pericenter and the mean anomaly undergo non-vanishing long-term changes. They are not secular trends because of the slow modulation introduced by the tidal matrix coefficients and by the orbital elements themselves. They could be useful to indepenedently constrain the ultra-low frequency waves which may have been indirectly detected in the BICEP2 experiment. Our calculation holds, in general, for any gravitationally bound two-body system whose characteristic frequency is much larger than the frequency of the external wave. It is also valid for a generic perturbation of tidal type with constant coefficients over timescales of the order of the orbital period of the perturbed particle.Comment: LaTex2e, 24 pages, no figures, no tables. Changes suggested by the referees include

Radiolabelled peptides for oncological diagnosis

Radiolabelled receptor-binding peptides targeting receptors (over)expressed on tumour cells are widely under investigation for tumour diagnosis and therapy. The concept of using radiolabelled receptor-binding peptides to target receptor-expressing tissues in vivo has stimulated a large body of research in nuclear medicine. The 111In-labelled somatostatin analogue octreotide (OctreoScan™) is the most successful radiopeptide for tumour imaging, and was the first to be approved for diagnostic use. Based on the success of these studies, other receptor-targeting peptides such as cholecystokinin/gastrin analogues, glucagon-like peptide-1, bombesin (BN), chemokine receptor CXCR4 targeting peptides, and RGD peptides are currently under development or undergoing clinical trials. In this review, we discuss some of these peptides and their analogues, with regard to their potential for radionuclide imaging of tumours