6,517 research outputs found
Vertical shear instability in accretion disc models with radiation transport
The origin of turbulence in accretion discs is still not fully understood.
While the magneto-rotational instability is considered to operate in
sufficiently ionized discs, its role in the poorly ionized protoplanetary disc
is questionable. Recently, the vertical shear instability (VSI) has been
suggested as a possible alternative. Our goal is to study the characteristics
of this instability and the efficiency of angular momentum transport, in
extended discs, under the influence of radiative transport and irradiation from
the central star. We use multi-dimensional hydrodynamic simulations to model a
larger section of an accretion disc. First we study inviscid and weakly viscous
discs using a fixed radial temperature profile in two and three spatial
dimensions. The simulations are then extended to include radiative transport
and irradiation from the central star. In agreement with previous studies we
find for the isothermal disc a sustained unstable state with a weak positive
angular momentum transport of the order of . Under the
inclusion of radiative transport the disc cools off and the turbulence
terminates. For discs irradiated from the central star we find again a
persistent instability with a similar value as for the isothermal
case. We find that the VSI can indeed generate sustained turbulence in discs
albeit at a relatively low level with about few times Comment: 12 pages, 24 figures, accepted for publication in Astronomy &
Astrophysic
On the ground state of solids with strong electron correlations
We formulate the calculation of the ground-state wavefunction and energy of a
system of strongly correlated electrons in terms of scattering matrices. A
hierarchy of approximations is introduced which results in an incremental
expansion of the energy. The present approach generalizes previous work
designed for weakly correlated electronic systems.Comment: 17 pages, Latex(revtex
Approximation of the scattering amplitude
The simultaneous solution of Ax=b and ATy=g is required in a number of situations. Darmofal and Lu have proposed a method based on the Quasi-Minimal residual algorithm (QMR). We will introduce a technique for the same purpose based on the LSQR method and show how its performance can be improved when using the Generalized LSQR method. We further show how preconditioners can be introduced to enhance the speed of convergence and discuss different preconditioners that can be used. The scattering amplitude gTx, a widely used quantity in signal processing for example, has a close connection to the above problem since x represents the solution of the forward problem and g is the right hand side of the adjoint system. We show how this quantity can be efficiently approximated using Gauss quadrature and introduce a Block-Lanczos process that approximates the scattering amplitude and which can also be used with preconditioners
Correlation-induced corrections to the band structure of boron nitride: a wave-function-based approach
We present a systematic study of the correlation-induced corrections to the
electronic band structure of zinc-blende BN. Our investigation employs an ab
initio wave-function-based local Hamiltonian formalism which offers a rigorous
approach to the calculation of the polarization and local charge redistribution
effects around an extra electron or hole placed into the conduction or valence
bands of semiconducting and insulating materials. Moreover, electron
correlations beyond relaxation and polarization can be readily incorporated.
The electron correlation treatment is performed on finite clusters. In
conducting our study, we make use of localized Wannier functions and embedding
potentials derived explicitly from prior periodic Hartree-Fock calculations.
The on-site and nearest-neighbor charge relaxation bring corrections of several
eV to the Hartree-Fock band gap. Additional corrections are caused by
long-range polarization effects. In contrast, the dispersion of the
Hartree-Fock bands is marginally affected by electron correlations. Our final
result for the fundamental gap of zinc-blende BN compares well with that
derived from soft x-ray experiments at the B and N K-edges.Comment: 18 pages, 8 figures; the following article has been submitted to J.
Chem. Phy
Ground state properties of heavy alkali halides
We extend previous work on alkali halides by calculations for the heavy-atom
species RbF, RbCl, LiBr, NaBr, KBr, RbBr, LiI, NaI, KI, and RbI. Relativistic
effects are included by means of energy-consistent pseudopotentials,
correlations are treated at the coupled-cluster level. A striking deficiency of
the Hartree-Fock approach are lattice constants deviating by up to 7.5 % from
experimental values which is reduced to a maximum error of 2.4 % by taking into
account electron correlation. Besides, we provide ab-initio data for in-crystal
polarizabilities and van der Waals coefficients.Comment: accepted by Phys. Rev.
A Bramble-Pasciak-like method with applications in optimization
Saddle-point systems arise in many applications areas, in fact in any situation where an extremum principle arises with constraints. The Stokes problem describing slow viscous flow of an incompressible fluid is a classic example coming from partial differential equations and in the area of Optimization such problems are ubiquitous.\ud
In this manuscript we show how new approaches for the solution of saddle-point systems arising in Optimization can be derived from the Bramble-Pasciak Conjugate Gradient approach widely used in PDEs and more recent generalizations thereof. In particular we derive a class of new solution methods based on the use of Preconditioned Conjugate Gradients in non-standard inner products and demonstrate how these can be understood through more standard machinery. We show connections to Constraint Preconditioning and give the results of numerical computations on a number of standard Optimization test examples
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