4,988 research outputs found
Relativistic central--field Green's functions for the RATIP package
From perturbation theory, Green's functions are known for providing a simple
and convenient access to the (complete) spectrum of atoms and ions. Having
these functions available, they may help carry out perturbation expansions to
any order beyond the first one. For most realistic potentials, however, the
Green's functions need to be calculated numerically since an analytic form is
known only for free electrons or for their motion in a pure Coulomb field.
Therefore, in order to facilitate the use of Green's functions also for atoms
and ions other than the hydrogen--like ions, here we provide an extension to
the Ratip program which supports the computation of relativistic
(one--electron) Green's functions in an -- arbitrarily given -- central--field
potential \rV(r). Different computational modes have been implemented to
define these effective potentials and to generate the radial Green's functions
for all bound--state energies . In addition, care has been taken to
provide a user--friendly component of the Ratip package by utilizing features
of the Fortran 90/95 standard such as data structures, allocatable arrays, or a
module--oriented design.Comment: 20 pages, 1 figur
Fractal fractal dimensions of deterministic transport coefficients
If a point particle moves chaotically through a periodic array of scatterers
the associated transport coefficients are typically irregular functions under
variation of control parameters. For a piecewise linear two-parameter map we
analyze the structure of the associated irregular diffusion coefficient and
current by numerically computing dimensions from box-counting and from the
autocorrelation function of these graphs. We find that both dimensions are
fractal for large parameter intervals and that both quantities are themselves
fractal functions if computed locally on a uniform grid of small but finite
subintervals. We furthermore show that there is a simple functional
relationship between the structure of fractal fractal dimensions and the
difference quotient defined on these subintervals.Comment: 16 pages (revtex) with 6 figures (postscript
AREPO-RT: Radiation hydrodynamics on a moving mesh
We introduce AREPO-RT, a novel radiation hydrodynamic (RHD) solver for the
unstructured moving-mesh code AREPO. Our method solves the moment-based
radiative transfer equations using the M1 closure relation. We achieve second
order convergence by using a slope limited linear spatial extrapolation and a
first order time prediction step to obtain the values of the primitive
variables on both sides of the cell interface. A Harten-Lax-Van Leer flux
function, suitably modified for moving meshes, is then used to solve the
Riemann problem at the interface. The implementation is fully conservative and
compatible with the individual timestepping scheme of AREPO. It incorporates
atomic Hydrogen (H) and Helium (He) thermochemistry, which is used to couple
the ultra-violet (UV) radiation field to the gas. Additionally, infrared
radiation is coupled to the gas under the assumption of local thermodynamic
equilibrium between the gas and the dust. We successfully apply our code to a
large number of test problems, including applications such as the expansion of
regions, radiation pressure driven outflows and the levitation
of optically thick layer of gas by trapped IR radiation. The new implementation
is suitable for studying various important astrophysical phenomena, such as the
effect of radiative feedback in driving galactic scale outflows, radiation
driven dusty winds in high redshift quasars, or simulating the reionisation
history of the Universe in a self consistent manner.Comment: v2, accepted for publication in MNRAS, changed to a Strang split
scheme to achieve second order convergenc
Non-Smooth Spatio-Temporal Coordinates in Nonlinear Dynamics
This paper presents an overview of physical ideas and mathematical methods
for implementing non-smooth and discontinuous substitutions in dynamical
systems. General purpose of such substitutions is to bring the differential
equations of motion to the form, which is convenient for further use of
analytical and numerical methods of analyses. Three different types of
nonsmooth transformations are discussed as follows: positional coordinate
transformation, state variables transformation, and temporal transformations.
Illustrating examples are provided.Comment: 15 figure
- …