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

Seismic modelling of the β \beta\,Cep star HD\,180642 (V1449\,Aql)

We present modelling of the $\beta\,$Cep star HD\,180642 based on its observational properties deduced from CoRoT and ground-based photometry as well as from time-resolved spectroscopy. We investigate whether present-day state-of-the-art models are able to explain the full seismic behaviour of this star, which has extended observational constraints for this type of pulsator. We constructed a dedicated database of stellar models and their oscillation modes tuned to fit the dominant radial mode frequency of HD\,180642, by means of varying the hydrogen content, metallicity, mass, age, and core overshooting parameter. We compared the seismic properties of these models with those observed. We find models that are able to explain the numerous observed oscillation properties of the star, for a narrow range in mass of 11.4--11.8\,M$_\odot$ and no or very mild overshooting (with up to 0.05 local pressure scale heights), except for an excitation problem of the $\ell=3$, p$_1$ mode. We deduce a rotation period of about 13\,d, which is fully compatible with recent magnetic field measurements. The seismic models do not support the earlier claim of solar-like oscillations in the star. We instead ascribe the power excess at high frequency to non-linear resonant mode coupling between the high-amplitude radial fundamental mode and several of the low-order pressure modes. We report a discrepancy between the seismic and spectroscopic gravity at the $2.5\sigma$ level.Comment: 10 pages, 2 Tables, 6 Figures. Accepted for publication in Astronomy and Astrophysic

Transfer Matrices and Excitations with Matrix Product States

We investigate the relation between static correlation functions in the ground state of local quantum many-body Hamiltonians and the dispersion relations of the corresponding low energy excitations using the formalism of tensor network states. In particular, we show that the Matrix Product State Transfer Matrix (MPS-TM) - a central object in the computation of static correlation functions - provides important information about the location and magnitude of the minima of the low energy dispersion relation(s) and present supporting numerical data for one-dimensional lattice and continuum models as well as two-dimensional lattice models on a cylinder. We elaborate on the peculiar structure of the MPS-TM's eigenspectrum and give several arguments for the close relation between the structure of the low energy spectrum of the system and the form of static correlation functions. Finally, we discuss how the MPS-TM connects to the exact Quantum Transfer Matrix (QTM) of the model at zero temperature. We present a renormalization group argument for obtaining finite bond dimension approximations of MPS, which allows to reinterpret variational MPS techniques (such as the Density Matrix Renormalization Group) as an application of Wilson's Numerical Renormalization Group along the virtual (imaginary time) dimension of the system.Comment: 39 pages (+8 pages appendix), 14 figure

Patient-specific CFD simulation of intraventricular haemodynamics based on 3D ultrasound imaging

Background: The goal of this paper is to present a computational fluid dynamic (CFD) model with moving boundaries to study the intraventricular flows in a patient-specific framework. Starting from the segmentation of real-time transesophageal echocardiographic images, a CFD model including the complete left ventricle and the moving 3D mitral valve was realized. Their motion, known as a function of time from the segmented ultrasound images, was imposed as a boundary condition in an Arbitrary Lagrangian-Eulerian framework. Results: The model allowed for a realistic description of the displacement of the structures of interest and for an effective analysis of the intraventricular flows throughout the cardiac cycle. The model provides detailed intraventricular flow features, and highlights the importance of the 3D valve apparatus for the vortex dynamics and apical flow. Conclusions: The proposed method could describe the haemodynamics of the left ventricle during the cardiac cycle. The methodology might therefore be of particular importance in patient treatment planning to assess the impact of mitral valve treatment on intraventricular flow dynamics

Transfer matrices and excitations with matrix product states

We use the formalism of tensor network states to investigate the relation between static correlation functions in the ground state of local quantum many-body Hamiltonians and the dispersion relations of the corresponding low-energy excitations. In particular, we show that the matrix product state transfer matrix (MPS-TM)—a central object in the computation of static correlation functions—provides important information about the location and magnitude of the minima of the low-energy dispersion relation(s), and we present supporting numerical data for one-dimensional lattice and continuum models as well as two-dimensional lattice models on a cylinder. We elaborate on the peculiar structure of the MPS-TM's eigenspectrum and give several arguments for the close relation between the structure of the low-energy spectrum of the system and the form of the static correlation functions. Finally, we discuss how the MPS-TM connects to the exact quantum transfer matrix of the model at zero temperature. We present a renormalization group argument for obtaining finite bond dimension approximations of the MPS, which allows one to reinterpret variational MPS techniques (such as the density matrix renormalization group) as an application of Wilson's numerical renormalization group along the virtual (imaginary time) dimension of the system

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

Transient modelling of the rotor-tower interaction of wind turbines using fluid-structure interaction simulations

In this work, we focus on the effect of supporting structures on the loads acting on a large horizontal axis wind turbine. The transient fluid-structure interaction (FSI) is simulated by an in-house code which couples two solvers, one for the computational fluid dynamics (CFD) and one for the computational structure mechanics (CSM). Strong coupling is applied as the force and displacement equilibriums are always enforced on the fluid- structure interface. The flexibility of the three blades of the considered machine is taken into account. The accurate CSM model reproduces in details the composite layups, foam, adhesive and internal stiffeners of the blades. On the other hand, the supporting structures (tower and nacelle) are considered to be rigid. On the fluid side, a fully hexahedral mesh is generated by a multi-block strategy. The same mesh is continuously deformed and adapted according to the displacement of the fluid- structure interface. The atmospheric boundary layer (ABL) under neutral conditions is included and consistently preserved along the computational domain. Using the outlined model, the blade deflections with and without supporting structure are compared. The effects of this transient interaction are highlighted throughout the rotation of the rotor, in terms of both wind energy conversion performance of the machine and structural response of each component. The maximal stress in the blade material as a function of time is compared with and without the presence of the tower in the wake of the rotor. Only a few similar works are reported to appear in literature [1, 2], whereas none of them currently includes the ABL or show detailed information about the internal stresses in the composite blades

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