Hints for a Gravitational Transition in Tully–Fisher Data

We use an up-to-date compilation of Tully–Fisher data to search for transitions in the evolution of the Tully–Fisher relation. Using an up-to-date data compilation, we find hints at ≈3σ level for a transition at critical distances Dc≃9 Mpc and Dc≃17 Mpc. We split the full sample in two subsamples, according to the measured galaxy distance with respect to splitting distance Dc, and identify the likelihood of the best-fit slope and intercept of one sample with respect to the best-fit corresponding values of the other sample. For Dc≃9 Mpc and Dc≃17 Mpc, we find a tension between the two subsamples at a level of Δχ2>17(3.5σ). Using Monte Carlo simulations, we demonstrate that this result is robust with respect to random statistical and systematic variations of the galactic distances and is unlikely in the context of a homogeneous dataset constructed using the Tully–Fisher relation. If the tension is interpreted as being due to a gravitational strength transition, it would imply a shift in the effective gravitational constant to lower values for distances larger than Dc by ΔGG≃−0.1. Such a shift is of the anticipated sign and magnitude but at a somewhat lower distance (redshift) than the gravitational transition recently proposed to address the Hubble and growth tensions (ΔGG≃−0.1 at the transition redshift of zt≲0.01 (Dc≲40 Mpc)).

Splitting of Separatrices in the Rapidly Forced Duffing Oscillator

The splitting of the stable and unstable manifolds of the rapidly forced Duffing oscillator with negative stiffness is investigated. The method used relies on the computation of analytic approximations for the orbits on the perturbed manifolds, and the asymptotic approximation of these orbits by successive integrations by parts. It is shown, that the splitting of the manifolds becomes exponentially small as the perturbation parameter tends to zero, and that the estimate for the splitting distance given by the Melnikov Integral dominates over high order corrections.

Modulated structure of Laves phase in a cast Mg-Zn-RE alloy

Comparison of the two SAED patterns (Fig.l) obtained from Laves phase in Mg-9Zn and Mg- 8Zn-1.5RE (RE: rare earth additions made by adding misch metal), shows that the small amount of rare earth additions has a considerble influence on the crystal structure of this phase. The diffraction features suggest that the crystal structure of the Laves phase in the Mg-Zn-RE alloy is modulated by planar translation interfaces which are equivalent to a uniform sequence of antiphase boundaries (APBs) in a long period superstructure. From the splitting distance of the superlattice spots as illustrated in the schematic diagram in Fig. 1(c), the mean half period, which is measured in units of (100) interplanar spacings, is M ≈ 4.86. As shown by Van Dyck et al. the superstructure reflections (or the satellites of the basic spots) of a periodic APB structure are peaked at positions given by: g' = g - (1/d)(m - g.R),