696 research outputs found
Global Behavior of A System of Two Nonlinear Difference Equation
In this paper, we study the global behavior for a system of two nonlinear difference equations
We find thatnbsp the unique positive equilibrium is global asymptotically stable under certain conditions. Finally, some illustrative examples are given to show the effective of results obtained
Asymptotology of Chemical Reaction Networks
The concept of the limiting step is extended to the asymptotology of
multiscale reaction networks. Complete theory for linear networks with well
separated reaction rate constants is developed. We present algorithms for
explicit approximations of eigenvalues and eigenvectors of kinetic matrix.
Accuracy of estimates is proven. Performance of the algorithms is demonstrated
on simple examples. Application of algorithms to nonlinear systems is
discussed.Comment: 23 pages, 8 figures, 84 refs, Corrected Journal Versio
New parametrization for spherically symmetric black holes in metric theories of gravity
We propose a new parametric framework to describe in generic metric theories
of gravity the spacetime of spherically symmetric and slowly rotating black
holes. In contrast to similar approaches proposed so far, we do not use a
Taylor expansion in powers of M/r, where M and r are the mass of the black hole
and a generic radial coordinate, respectively. Rather, we use a
continued-fraction expansion in terms of a compactified radial coordinate. This
choice leads to superior convergence properties and allows us to approximate a
number of known metric theories with a much smaller set of coefficients. The
measure of these coefficients via observations of near-horizon processes can be
used to effectively constrain and compare arbitrary metric theories of gravity.
Although our attention is here focussed on spherically symmetric black holes,
we also discuss how our approach could be extended to rotating black holes.Comment: Appendix added for a more detailed comparison; matches version in PR
A Method for Calculating the Structure of (Singular) Spacetimes in the Large
A formalism and its numerical implementation is presented which allows to
calculate quantities determining the spacetime structure in the large directly.
This is achieved by conformal techniques by which future null infinity
(\Scri{}^+) and future timelike infinity () are mapped to grid points on
the numerical grid. The determination of the causal structure of singularities,
the localization of event horizons, the extraction of radiation, and the
avoidance of unphysical reflections at the outer boundary of the grid, are
demonstrated with calculations of spherically symmetric models with a scalar
field as matter and radiation model.Comment: 29 pages, AGG2
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