1,959 research outputs found
Trend-based analysis of a population model of the AKAP scaffold protein
We formalise a continuous-time Markov chain with multi-dimensional discrete state space model of the AKAP scaffold protein as a crosstalk mediator between two biochemical signalling pathways. The analysis by temporal properties of the AKAP model requires reasoning about whether the counts of individuals of the same type (species) are increasing or decreasing. For this purpose we propose the concept of stochastic trends based on formulating the probabilities of transitions that increase (resp. decrease) the counts of individuals of the same type, and express these probabilities as formulae such that the state space of the model is not altered. We define a number of stochastic trend formulae (e.g. weakly increasing, strictly increasing, weakly decreasing, etc.) and use them to extend the set of state formulae of Continuous Stochastic Logic. We show how stochastic trends can be implemented in a guarded-command style specification language for transition systems. We illustrate the application of stochastic trends with numerous small examples and then we analyse the AKAP model in order to characterise and show causality and pulsating behaviours in this biochemical system
On Silicon Group Elements Ejected by Supernovae Type Ia
There is compelling evidence that the peak brightness of a Type Ia supernova
is affected by the electron fraction Ye at the time of the explosion. The
electron fraction is set by the aboriginal composition of the white dwarf and
the reactions that occur during the pre explosive convective burning. To date,
determining the makeup of the white dwarf progenitor has relied on indirect
proxies, such as the average metallicity of the host stellar population. In
this paper, we present analytical calculations supporting the idea that the
electron fraction of the progenitor systematically influences the
nucleosynthesis of silicon group ejecta in Type Ia supernovae. In particular,
we suggest the abundances generated in quasi nuclear statistical equilibrium
are preserved during the subsequent freezeout. This allows one to potential
recovery of Ye at explosion from the abundances recovered from an observed
spectra. We show that measurement of 28Si, 32S, 40Ca, and 54Fe abundances can
be used to construct Ye in the silicon rich regions of the supernovae. If these
four abundances are determined exactly, they are sufficient to recover Ye to 6
percent. This is because these isotopes dominate the composition of
silicon-rich material and iron rich material in quasi nuclear statistical
equilibrium. Analytical analysis shows that the 28Si abundance is insensitive
to Ye, the 32S abundance has a nearly linear trend with Ye, and the 40Ca
abundance has a nearly quadratic trend with Ye. We verify these trends with
post-processing of 1D models and show that these trends are reflected in model
synthetic spectra.Comment: Submitted to the Ap
Evaluating Systematic Dependencies of Type Ia Supernovae: The Influence of Deflagration to Detonation Density
We explore the effects of the deflagration to detonation transition (DDT)
density on the production of Ni-56 in thermonuclear supernova explosions (type
Ia supernovae). Within the DDT paradigm, the transition density sets the amount
of expansion during the deflagration phase of the explosion and therefore the
amount of nuclear statistical equilibrium (NSE) material produced. We employ a
theoretical framework for a well-controlled statistical study of
two-dimensional simulations of thermonuclear supernovae with randomized initial
conditions that can, with a particular choice of transition density, produce a
similar average and range of Ni-56 masses to those inferred from observations.
Within this framework, we utilize a more realistic "simmered" white dwarf
progenitor model with a flame model and energetics scheme to calculate the
amount of Ni-56 and NSE material synthesized for a suite of simulated
explosions in which the transition density is varied in the range 1-3x10^7
g/cc. We find a quadratic dependence of the NSE yield on the log of the
transition density, which is determined by the competition between plume rise
and stellar expansion. By considering the effect of metallicity on the
transition density, we find the NSE yield decreases by 0.055 +/- 0.004 solar
masses for a 1 solar metallicity increase evaluated about solar metallicity.
For the same change in metallicity, this result translates to a 0.067 +/- 0.004
solar mass decrease in the Ni-56 yield, slightly stronger than that due to the
variation in electron fraction from the initial composition. Observations
testing the dependence of the yield on metallicity remain somewhat ambiguous,
but the dependence we find is comparable to that inferred from some studies.Comment: 15 pages, 13 figures, accepted to ApJ on July 6, 201
Numerical Models of Binary Neutron Star System Mergers. I.: Numerical Methods and Equilibrium Data for Newtonian Models
The numerical modeling of binary neutron star mergers has become a subject of
much interest in recent years. While a full and accurate model of this
phenomenon would require the evolution of the equations of relativistic
hydrodynamics along with the Einstein field equations, a qualitative study of
the early stages on inspiral can be accomplished by either Newtonian or
post-Newtonian models, which are more tractable. In this paper we offer a
comparison of results from both rotating and non-rotating (inertial) frame
Newtonian calculations. We find that the rotating frame calculations offer
significantly improved accuracy as compared with the inertial frame models.
Furthermore, we show that inertial frame models exhibit significant and
erroneous angular momentum loss during the simulations that leads to an
unphysical inspiral of the two neutron stars. We also examine the dependence of
the models on initial conditions by considering initial configurations that
consist of spherical neutron stars as well as stars that are in equilibrium and
which are tidally distorted. We compare our models those of Rasio & Shapiro
(1992,1994a) and New & Tohline (1997). Finally, we investigate the use of the
isolated star approximation for the construction of initial data.Comment: 32 pages, 19 gif figures, manuscript with postscript figures
available at http://www.astro.sunysb.edu/dswesty/docs/nspap1.p
Flame Evolution During Type Ia Supernovae and the Deflagration Phase in the Gravitationally Confined Detonation Scenario
We develop an improved method for tracking the nuclear flame during the
deflagration phase of a Type Ia supernova, and apply it to study the variation
in outcomes expected from the gravitationally confined detonation (GCD)
paradigm. A simplified 3-stage burning model and a non-static ash state are
integrated with an artificially thickened advection-diffusion-reaction (ADR)
flame front in order to provide an accurate but highly efficient representation
of the energy release and electron capture in and after the unresolvable flame.
We demonstrate that both our ADR and energy release methods do not generate
significant acoustic noise, as has been a problem with previous ADR-based
schemes. We proceed to model aspects of the deflagration, particularly the role
of buoyancy of the hot ash, and find that our methods are reasonably
well-behaved with respect to numerical resolution. We show that if a detonation
occurs in material swept up by the material ejected by the first rising bubble
but gravitationally confined to the white dwarf (WD) surface (the GCD
paradigm), the density structure of the WD at detonation is systematically
correlated with the distance of the deflagration ignition point from the center
of the star. Coupled to a suitably stochastic ignition process, this
correlation may provide a plausible explanation for the variety of nickel
masses seen in Type Ia Supernovae.Comment: 14 pages, 10 figures, accepted to the Astrophysical Journa
Process algebra modelling styles for biomolecular processes
We investigate how biomolecular processes are modelled in process algebras, focussing on chemical reactions. We consider various modelling styles and how design decisions made in the definition of the process algebra have an impact on how a modelling style can be applied. Our goal is to highlight the often implicit choices that modellers make in choosing a formalism, and illustrate, through the use of examples, how this can affect expressability as well as the type and complexity of the analysis that can be performed
Simulations of Astrophysical Fluid Instabilities
We present direct numerical simulations of mixing at Rayleigh-Taylor unstable
interfaces performed with the FLASH code, developed at the ASCI/Alliances
Center for Astrophysical Thermonuclear Flashes at the University of Chicago. We
present initial results of single-mode studies in two and three dimensions. Our
results indicate that three-dimensional instabilities grow significantly faster
than two-dimensional instabilities and that grid resolution can have a
significant effect on instability growth rates. We also find that unphysical
diffusive mixing occurs at the fluid interface, particularly in poorly resolved
simulations.Comment: 3 pages, 1 figure. To appear in the proceedings of the 20th Texas
Symposium on Relativistic Astrophysic
- …