1,504 research outputs found
Extending a Hybrid Godunov Method for Radiation Hydrodynamics to Multiple Dimensions
This paper presents a hybrid Godunov method for three-dimensional radiation
hydrodynamics. The multidimensional technique outlined in this paper is an
extension of the one-dimensional method that was developed by Sekora & Stone
2009, 2010. The earlier one-dimensional technique was shown to preserve certain
asymptotic limits and be uniformly well behaved from the photon free streaming
(hyperbolic) limit through the weak equilibrium diffusion (parabolic) limit and
to the strong equilibrium diffusion (hyperbolic) limit. This paper gives the
algorithmic details for constructing a multidimensional method. A future paper
will present numerical tests that demonstrate the robustness of the
computational technique across a wide-range of parameter space.Comment: 25 page
The scattering of LyA radiation in the intergalactic medium: numerical methods and solutions
Two methods are developed for solving the steady-state spherically symmetric
radiative transfer equation for resonance line radiation emitted by a point
source in the Intergalactic Medium. One method is based on solving the ray and
moment equations using finite differences. The second uses a Monte Carlo
approach incorporating methods that greatly improve the accuracy compared with
previous approaches in this context. Several applications are presented serving
as test problems for both a static medium and an expanding medium, including
inhomogeneities in the density and velocity fields. Solutions are obtained in
the coherent scattering limit and for Doppler RII redistribution with and
without recoils. We find generally that the radiation intensity is linear in
the cosine of the azimuthal angle with respect to radius to high accuracy over
a broad frequency region across the line centre for both linear and perturbed
velocity fields, yielding the Eddington factors f(nu) = 1/3 and g(nu) = 3/5. We
show the radiation field produced by a point source divides into three spatial
regimes for a uniformly expanding homogeneous medium: at radii r small compared
with a characteristic radius r*, the mean intensity near line centre varies as
1/ r^(7/3), while at r > r* it approaches 1/ r^2; for r << r* it is modified by
frequency redistribution. Before the reionization epoch, r* takes on the
universal value 1.1 Mpc, independent of redshift. The mean intensity and
scattering rate are found to be very sensitive to the gradient of the velocity
field, growing exponentially with the amplitude of the perturbation as the
limit of a vanishing velocity gradient is approached near the source. We expect
the 21cm signal from the Epoch of Reionization to thus be a sensitive probe of
both the density and the peculiar velocity fields.Comment: 27 pages, 26 figures, 10 supplementary tables; submitted to MNRA
Simple Waves in Ideal Radiation Hydrodynamics
In the dynamic diffusion limit of radiation hydrodynamics, advection
dominates diffusion; the latter primarily affects small scales and has
negligible impact on the large scale flow. The radiation can thus be accurately
regarded as an ideal fluid, i.e., radiative diffusion can be neglected along
with other forms of dissipation. This viewpoint is applied here to an analysis
of simple waves in an ideal radiating fluid. It is shown that much of the
hydrodynamic analysis carries over by simply replacing the material sound
speed, pressure and index with the values appropriate for a radiating fluid. A
complete analysis is performed for a centered rarefaction wave, and expressions
are provided for the Riemann invariants and characteristic curves of the
one-dimensional system of equations. The analytical solution is checked for
consistency against a finite difference numerical integration, and the validity
of neglecting the diffusion operator is demonstrated. An interesting physical
result is that for a material component with a large number of internal degrees
of freedom and an internal energy greater than that of the radiation, the sound
speed increases as the fluid is rarefied. These solutions are an excellent test
for radiation hydrodynamic codes operating in the dynamic diffusion regime. The
general approach may be useful in the development of Godunov numerical schemes
for radiation hydrodynamics.Comment: 16 pages, 10 figures, accepted for publication in The Astrophysical
Journa
Calcium Messenger Heterogeneity: A Possible Signal for Spike Timing-Dependent Plasticity
Calcium concentrations as well as time courses have been used to model the signaling cascades leading to changes in the strength of synaptic connections. Previous models consider the dendritic spines as uniform compartments regarding calcium signaling. However, calcium concentrations can vary drastically on distances much smaller than typical spine sizes, and downstream targets of calcium signals are often found exactly in these calcium nanodomains. Even though most downstream targets are activated by calcium via calmodulin, which is a diffusive molecule, the capacity of calmodulin to bind to its targets even when it is not fully loaded with calcium allows its downstream cascade to be highly local. In this study, a model is proposed which uses the heterogeneity of calcium concentrations as a signal for spike-timing-dependent plasticity (STDP). The model is minimalistic and includes three sources of calcium in spines: NMDA receptors (NMDARs), voltage gated calcium channels (VGCCs) and IP3 receptors (IP3Rs). It is based on the biochemical cascades and assumption of spatial locations of four calcium-dependent enzymes: calcium/calmodulin-dependent protein kinase II located near NMDARs, calcineurin located near VGCCs, cyclic nucleotide phosphodiesterase (PDE) located near IP3Rs or NMDARs and adenylyl cyclase, located between VDCCs and NMDARs. To quantify the changes in synaptic weights the model also includes a simple description of AMPA receptor insertion in the membrane and docking to the postsynaptic density. Two parameters of the model are tuned such that weight changes produced by either pre or postsynaptic firing alone are minimal. The model reproduces the typical shape of STDP for spike doublets. If PDE is located near IP3Rs, the behavior for spike triplets is consistent with that observed in hippocampal cell culture; if near NMDAR, the behavior is similar to that observed in cortical L2/3 slices
Radiative transfer in moving media II. Solution of the radiative transfer equation in axial symmetry
A new method for the formal solution of the 2D radiative transfer equation in
axial symmetry in the presence of arbitrary velocity fields is presented. The
combination of long and short characteristics methods is used to solve the
radiative transfer equation. We include the velocity field in detail using the
Local Lorentz Transformation. This allows us to obtain a significantly better
description of the photospheric region, where the gradient of the global
velocity is too small for the Sobolev approximation to be valid. Sample test
calculations for the case of a stellar wind and a rotating atmosphere are
presented.Comment: 11 pages, 19 figures. accepted by Astronomy and Astrophysic
- …