The effect of the cosmological constant on a quadrupole signal in the linearized approximation

In this study the effects of a nonzero cosmological constant [Formula: see text] on a quadrupole gravitational wave (GW) signal are analyzed. The linearized approximation of general relativity was used, so the perturbed metric can be written as the sum of [Formula: see text] GWs and [Formula: see text] background term, originated from [Formula: see text]. The [Formula: see text] term was also included in this study. To derive physically relevant consequences of [Formula: see text] comoving coordinates are used. In these coordinates, the equations of motion (EoMs) are not self-consistent so the result of the linearized theory has to be transformed to the FRW frame. The luminosity distance and the same order of the magnitude of frequency in accordance with the detected GWs were used to demonstrate the effects of the cosmological constant.

On the Theoretical Equivalence of Differently Proposed Ensemble–3DVAR Hybrid Analysis Schemes

Hybrid ensemble–three-dimensional variational analysis schemes incorporate flow-dependent, ensemble-estimated background-error covariances into the three-dimensional variational data assimilation (3DVAR) framework. Typically the 3DVAR background-error covariance estimate is assumed to be stationary, nearly homogeneous, and isotropic. A hybrid scheme can be achieved by 1) directly replacing the background-error covariance term in the cost function by a linear combination of the original background-error covariance with the ensemble covariance or 2) through augmenting the state vector with another set of control variables preconditioned upon the square root of the ensemble covariance. These differently proposed hybrid schemes are proven to be equivalent. The latter framework may be a simpler way to incorporate ensemble information into operational 3DVAR schemes, where the preconditioning is performed with respect to the background term.

Off-shell resonances in coupled channel problems

The coupled channel theory of nuclear reactions is extended off the energy shell so that the T-matrix can be constructed to include both the direct reaction contribution and the contribution from the off-shell background scattering. This has been shown to be important for (d,p) stripping reactions to unbound states. Three soluble two-channel models with square well, δ-function, and separable potentials, are presented and the resonance and bound state behaviour is discussed in some numerical detail. The importance of the off-shell background term is also studied.

Off-shell effects in (d,p) stripping reactions

The off-shell behavior of the differential cross section in (d,p) reactions is described within the R-matrix theory assuming a direct 'stripping into continuum' process. In particular, with the inclusion of the off-shell background term and its interference, some levels in the reaction 15N(d,p)16N (unbound) are interpreted. Other interesting consequences of this description are also discussed.