Global dynamics of a novel delayed logistic equation arising from cell biology

The delayed logistic equation (also known as Hutchinson's equation or Wright's equation) was originally introduced to explain oscillatory phenomena in ecological dynamics. While it motivated the development of a large number of mathematical tools in the study of nonlinear delay differential equations, it also received criticism from modellers because of the lack of a mechanistic biological derivation and interpretation. Here we propose a new delayed logistic equation, which has clear biological underpinning coming from cell population modelling. This nonlinear differential equation includes terms with discrete and distributed delays. The global dynamics is completely described, and it is proven that all feasible nontrivial solutions converge to the positive equilibrium. The main tools of the proof rely on persistence theory, comparison principles and an $L^2$-perturbation technique. Using local invariant manifolds, a unique heteroclinic orbit is constructed that connects the unstable zero and the stable positive equilibrium, and we show that these three complete orbits constitute the global attractor of the system. Despite global attractivity, the dynamics is not trivial as we can observe long-lasting transient oscillatory patterns of various shapes. We also discuss the biological implications of these findings and their relations to other logistic type models of growth with delays

Bose-Einstein Condensate Dark Matter Halos confronted with galactic rotation curves

We present a comparative confrontation of both the Bose-Einstein Condensate (BEC) and the Navarro-Frenk-White (NFW) dark halo models with galactic rotation curves. We employ 6 High Surface Brightness (HSB), 6 Low Surface Brightness (LSB), and 7 dwarf galaxies with rotation curves falling into two classes. In the first class rotational velocities increase with radius over the observed range.The BEC and NFW models give comparable fits for HSB and LSB galaxies of this type, while for dwarf galaxies the fit is significantly better with the BEC model. In the second class the rotational velocity of HSB and LSB galaxies exhibits long flat plateaus, resulting in better fit with the NFW model for HSB galaxies and comparable fits for LSB galaxies. We conclude that due to its central density cusp avoidance the BEC model fits better dwarf galaxy dark matter distribution. Nevertheless it suffers from sharp cutoff in larger galaxies, where the NFW model performs better. The investigated galaxy sample obeys the Tully-Fisher relation, including the particular characteristics exhibited by dwarf galaxies. In both models the fitting enforces a relation between dark matter parameters: the characteristic density and the corresponding characteristic distance scale with an inverse power.Comment: published versio

Gravitational radiation reaction in compact binary systems: Contribution of the quadrupole-monopole interaction

The radiation reaction in compact spinning binaries on eccentric orbits due to the quadrupole-monopole interaction is studied. This contribution is of second post-Newtonian order. As result of the precession of spins the magnitude $L$ of the orbital angular momentum is not conserved. Therefore a proper characterization of the perturbed radial motion is provided by the energy $E$ and angular average $\bar{L}$. As powerful computing tools, the generalized true and eccentric anomaly parametrizations are introduced. Then the secular losses in energy and magnitude of orbital angular momentum together with the secular evolution of the relative orientations of the orbital angular momentum and spins are found for eccentric orbits by use of the residue theorem. The circular orbit limit of the energy loss agrees with Poisson's earlier result.Comment: accepted for publication in Phys. Rev.

Non-uniform Braneworld Stars: an Exact Solution

The first exact interior solution to Einstein's field equations for a static and non-uniform braneworld star with local and non-local bulk terms is presented. It is shown that the bulk Weyl scalar ${\cal U}(r)$ is always negative inside the stellar distribution, in consequence it reduces both the effective density and the effective pressure. It is found that the anisotropy generated by bulk gravity effect has an acceptable physical behaviour inside the distribution. Using a Reissner-N\"{o}rdstrom-like exterior solution, the effects of bulk gravity on pressure and density are found through matching conditions.Comment: 22 pages, 3 figures, version to be published in International Journal of Modern Physics D (IJMPD

Gravitational radiation reaction in compact binary systems: Contribution of the magnetic dipole-magnetic dipole interaction

We study the gravitational radiation reaction in compact binary systems composed of neutron stars with spin and huge magnetic dipole moments (magnetars). The magnetic dipole moments undergo a precessional motion about the respective spins. At sufficiently high values of the magnetic dipole moments, their interaction generates second post-Newtonian order contributions both to the equations of motion and to the gravitational radiation escaping the system. We parametrize the radial motion and average over a radial period in order to find the secular contributions to the energy and magnitude of the orbital angular momentum losses, in the generic case of \textit{eccentric} orbits. Similarly as for the spin-orbit, spin-spin, quadrupole-monopole interactions, here too we deduce the secular evolution of the relative orientations of the orbital angular momentum and spins. These equations, supplemented by the evolution equations for the angles characterizing the orientation of the dipole moments form a first order differential system, which is closed. The circular orbit limit of the energy loss agrees with Ioka and Taniguchi's earlier result

Constraining the parameters of the putative supermassive binary black hole in PG 1302-102 from its radio structure

We investigate the pc-scale kinematics and kpc-scale radio morphology of the quasar PG 1302-102, which may harbour a sub-pc separation supermassive binary black hole system at its centre as inferred from optical variability. High-resolution radio interferometric measurements obtained with the Very Long Baseline Array (VLBA) in the Monitoring Of Jets in Active galactic nuclei with VLBA Experiments (MOJAVE) programme at 15 GHz at 20 epochs spanning 17 years were analysed to investigate the pc-scale radio structure. Archival observations with the Very Large Array (VLA) at 1.4 GHz and 5 GHz were obtained to study the kpc-scale morphology. We find that the pc-scale jet is inclined within ~2.2 deg to the line of sight and has a half-opening angle of about 0.2 deg. The parameters derived from the pc-scale radio jet are qualitatively consistent with those obtained from the analysis of the optical light curve of PG 1302-102. We obtain at least 0.08 for the mass ratio of the two black holes in the system. We find some indication for a helical jet structure on kpc-scale, but the directions of the inner and the extended radio jets are significantly different, obstructing a straightforward connection of the pc- and kpc-scale jets within the binary scenario.Comment: 9 pages, 4 figures, 1 table, accepted to MNRA

The geometry of the Barbour-Bertotti theories II. The three body problem

We present a geometric approach to the three-body problem in the non-relativistic context of the Barbour-Bertotti theories. The Riemannian metric characterizing the dynamics is analyzed in detail in terms of the relative separations. Consequences of a conformal symmetry are exploited and the sectional curvatures of geometrically preferred surfaces are computed. The geodesic motions are integrated. Line configurations, which lead to curvature singularities for $N\neq 3$, are investigated. None of the independent scalars formed from the metric and curvature tensor diverges there.Comment: 16 pages, 2 eps figures, to appear in Classical and Quantum Gravit