Polynomial Similarity Transformation Theory: A smooth interpolation between coupled cluster doubles and projected BCS applied to the reduced BCS Hamiltonian

We present a similarity transformation theory based on a polynomial form of a particle-hole pair excitation operator. In the weakly correlated limit, this polynomial becomes an exponential, leading to coupled cluster doubles. In the opposite strongly correlated limit, the polynomial becomes an extended Bessel expansion and yields the projected BCS wavefunction. In between, we interpolate using a single parameter. The effective Hamiltonian is non-hermitian and this Polynomial Similarity Transformation Theory follows the philosophy of traditional coupled cluster, left projecting the transformed Hamiltonian onto subspaces of the Hilbert space in which the wave function variance is forced to be zero. Similarly, the interpolation parameter is obtained through minimizing the next residual in the projective hierarchy. We rationalize and demonstrate how and why coupled cluster doubles is ill suited to the strongly correlated limit whereas the Bessel expansion remains well behaved. The model provides accurate wave functions with energy errors that in its best variant are smaller than 1\% across all interaction stengths. The numerical cost is polynomial in system size and the theory can be straightforwardly applied to any realistic Hamiltonian

Extension of a fast method for 2D steady free surface flow to stretched surface grids

Steady free surface flow is often encountered in marine engineering, e.g. for calculating ship hull resistance. When these flows are solved with CFD, the water-air interface can be represented using a surface fitting approach. The resulting free boundary problem requires an iterative technique to solve the flow and at the same time determine the free surface position. Most such methods use a time-stepping scheme, which is inefficient for solving steady flows. There is one steady technique which uses a special boundary condition at the free surface, but that method needs a dedicated coupled flow solver. To overcome these disadvantages an efficient free surface method was developed recently, in which the flow solver can be a black-box. It is based on quasi-Newton iterations which use a surrogate model in combination with flow solver inputs and outputs from previous iterations to approximate the Jacobian. As the original method was limited to uniform free surface grids, it is extended in this paper to stretched free surface grids. For this purpose, a different surrogate model is constructed by transforming a relation between perturbations of the free surface height and pressure from the wavenumber domain to the spatial domain using the convolution theorem. The method is tested on the 2D flow over an object. The quasi-Newton iterations converge exponentially and in a low number of iterations

Combining a least-squares approximate jacobian with an analytical model to couple a flow solver with free surface position updates

This paper presents a new quasi-Newton method suitable for systems that can be solved with a black-box solver for which a cheap surrogate model is available. In order to have fast convergence, the approximate Jacobian consists of two different contribution: a full rank surrogate model of the system is combined with a low rank least-squares model based on known input-output pairs of the system. It is then shown how this method can be used to solve 2D steady free surface flows with a black-box flow solver. The inviscid flow over a ramp is calculated for supercritical and subcritical conditions. For both simulations the quasi-Newton iterations converge exponentially and the results match the analytical predictions accurately

The blue-edge problem of the V1093 Her instability strip revisited using evolutionary models with atomic diffusion

We have computed a new grid of evolutionary subdwarf B star (sdB) models from the start of central He burning, taking into account atomic diffusion due to radiative levitation, gravitational settling, concentration diffusion, and thermal diffusion. We have computed the non-adiabatic pulsation properties of the models and present the predicted p-mode and g-mode instability strips. In previous studies of the sdB instability strips, artificial abundance enhancements of Fe and Ni were introduced in the pulsation driving layers. In our models, the abundance enhancements of Fe and Ni occur naturally, eradicating the need to use artificial enhancements. We find that the abundance increases of Fe and Ni were previously underestimated and show that the instability strip predicted by our simulations solves the so-called blue edge problem of the subdwarf B star g-mode instability strip. The hottest known g-mode pulsator, KIC 10139564, now resides well within the instability strip {even when only modes with low spherical degrees (l<=2) are considered.Comment: 7 pages, 7 figures. Accepted for publication in Astronomy & Astrophysic

Physics Of Eclipsing Binaries. II. Towards the Increased Model Fidelity

The precision of photometric and spectroscopic observations has been systematically improved in the last decade, mostly thanks to space-borne photometric missions and ground-based spectrographs dedicated to finding exoplanets. The field of eclipsing binary stars strongly benefited from this development. Eclipsing binaries serve as critical tools for determining fundamental stellar properties (masses, radii, temperatures and luminosities), yet the models are not capable of reproducing observed data well either because of the missing physics or because of insufficient precision. This led to a predicament where radiative and dynamical effects, insofar buried in noise, started showing up routinely in the data, but were not accounted for in the models. PHOEBE (PHysics Of Eclipsing BinariEs; http://phoebe-project.org) is an open source modeling code for computing theoretical light and radial velocity curves that addresses both problems by incorporating missing physics and by increasing the computational fidelity. In particular, we discuss triangulation as a superior surface discretization algorithm, meshing of rotating single stars, light time travel effect, advanced phase computation, volume conservation in eccentric orbits, and improved computation of local intensity across the stellar surfaces that includes photon-weighted mode, enhanced limb darkening treatment, better reflection treatment and Doppler boosting. Here we present the concepts on which PHOEBE is built on and proofs of concept that demonstrate the increased model fidelity.Comment: 60 pages, 15 figures, published in ApJS; accompanied by the release of PHOEBE 2.0 on http://phoebe-project.or

New techniques for solving the steady free surface flow problem

Steady free surface (FS) flows can be solved numerically with capturing or fitting methods, the latter being the subject of this paper. Most fitting methods are (pseudo-)transient and thus quite slow for steady flows; the so-called steady iterative method is much faster, but requires a dedicated solver because of the complex FS boundary conditions. The goal is to develop a (currently 2D) fitting method which is fast and can be used with a black box flow solver. Results from a perturbation analysis are used in combination with the IQN-ILS algorithm to construct such a method, applicable to supercritical flows. To tackle this method's scaling problem when the mesh is refined, an extension is proposed which uses a multigrid technique for the surface update. The flow over an object is simulated with the original and multigrid enhanced methods for three meshes. The multigrid method clearly outperforms the original one and is even mesh independent during part of its convergence.</p