The R-matrix theory

The different facets of the $R$-matrix method are presented pedagogically in a general framework. Two variants have been developed over the years: $(i)$ The "calculable" $R$-matrix method is a calculational tool to derive scattering properties from the Schr\"odinger equation in a large variety of physical problems. It was developed rather independently in atomic and nuclear physics with too little mutual influence. $(ii)$ The "phenomenological" $R$-matrix method is a technique to parametrize various types of cross sections. It was mainly (or uniquely) used in nuclear physics. Both directions are explained by starting from the simple problem of scattering by a potential. They are illustrated by simple examples in nuclear and atomic physics. In addition to elastic scattering, the $R$-matrix formalism is applied to transfer and radiative-capture reactions. We also present more recent and more ambitious applications of the theory in nuclear physics.Comment: 93 pages, 26 figures. Rep. Prog. Phys., in pres

Numerical solution of gravitational dynamics in asymptotically anti-de Sitter spacetimes

A variety of gravitational dynamics problems in asymptotically anti-de Sitter (AdS) spacetime are amenable to efficient numerical solution using a common approach involving a null slicing of spacetime based on infalling geodesics, convenient exploitation of the residual diffeomorphism freedom, and use of spectral methods for discretizing and solving the resulting differential equations. Relevant issues and choices leading to this approach are discussed in detail. Three examples, motivated by applications to non-equilibrium dynamics in strongly coupled gauge theories, are discussed as instructive test cases. These are gravitational descriptions of homogeneous isotropization, collisions of planar shocks, and turbulent fluid flows in two spatial dimensions.Comment: 70 pages, 19 figures; v4: fixed minus sign typo in last term of eqn. (3.47

New method for extracting quasi-bound states from the continuum

A new parameter-free method is proposed for treatment of single-particle resonances in the real-energy continuum shell model. This method yields quasi-bound states embedded in the continuum which provide a natural generalization of weakly bound single-particle states.Comment: 22 pages, 10 figure

The origin of the negative torque density in disk-satellite interaction

Tidal interaction between a gaseous disk and a massive orbiting perturber is known to result in angular momentum exchange between them. Understanding astrophysical manifestations of this coupling such as gap opening by planets in protoplanetary disks or clearing of gas by binary supermassive black holes (SMBHs) embedded in accretion disks requires knowledge of the spatial distribution of the torque exerted on the disk by a perturber. Recent hydrodynamical simulations by Dong et al (2011) have shown evidence for the tidal torque density produced in a uniform disk to change sign at the radial separation of $\approx 3.2$ scale heights from the perturber's orbit, in clear conflict with the previous studies. To clarify this issue we carry out a linear calculation of the disk-satellite interaction putting special emphasis on understanding the behavior of the perturbed fluid variables in physical space. Using analytical as well as numerical methods we confirm the reality of the negative torque density phenomenon and trace its origin to the overlap of Lindblad resonances in the vicinity of the perturber's orbit - an effect not accounted for in previous studies. These results suggest that calculations of the gap and cavity opening in disks by planets and binary SMBHs should rely on more realistic torque density prescriptions than the ones used at present.Comment: 18 pages, 6 figures, accepted to Ap