Home-grown CASE tools with XML and XSLT

This paper demonstrates an approach to software generation where xml representations of models are transformed to implementations by XSLT style sheets. Although XSLT was not primarily intended for this use, it serves quite well. There are only few problems in this approach, and we identify these based on our examples

Global existence and asymptotic behaviour in the future for the Einstein-Vlasov system with positive cosmological constant

The behaviour of expanding cosmological models with collisionless matter and a positive cosmological constant is analysed. It is shown that under the assumption of plane or hyperbolic symmetry the area radius goes to infinity, the spacetimes are future geodesically complete, and the expansion becomes isotropic and exponential at late times. This proves a form of the cosmic no hair theorem in this class of spacetimes

The Einstein-Vlasov sytem/Kinetic theory

The main purpose of this article is to guide the reader to theorems on global properties of solutions to the Einstein-Vlasov system. This system couples Einstein's equations to a kinetic matter model. Kinetic theory has been an important field of research during several decades where the main focus has been on nonrelativistic- and special relativistic physics, e.g. to model the dynamics of neutral gases, plasmas and Newtonian self-gravitating systems. In 1990 Rendall and Rein initiated a mathematical study of the Einstein-Vlasov system. Since then many theorems on global properties of solutions to this system have been established. The Vlasov equation describes matter phenomenologically and it should be stressed that most of the theorems presented in this article are not presently known for other such matter models (e.g. fluid models). The first part of this paper gives an introduction to kinetic theory in non-curved spacetimes and then the Einstein-Vlasov system is introduced. We believe that a good understanding of kinetic theory in non-curved spacetimes is fundamental in order to get a good comprehension of kinetic theory in general relativity.Comment: 31 pages. This article has been submitted to Living Rev. Relativity (http://www.livingreviews.org

A numerical investigation of the stability of steady states and critical phenomena for the spherically symmetric Einstein-Vlasov system

The stability features of steady states of the spherically symmetric Einstein-Vlasov system are investigated numerically. We find support for the conjecture by Zeldovich and Novikov that the binding energy maximum along a steady state sequence signals the onset of instability, a conjecture which we extend to and confirm for non-isotropic states. The sign of the binding energy of a solution turns out to be relevant for its time evolution in general. We relate the stability properties to the question of universality in critical collapse and find that for Vlasov matter universality does not seem to hold.Comment: 29 pages, 10 figure

The formation of black holes in spherically symmetric gravitational collapse

We consider the spherically symmetric, asymptotically flat Einstein-Vlasov system. We find explicit conditions on the initial data, with ADM mass M, such that the resulting spacetime has the following properties: there is a family of radially outgoing null geodesics where the area radius r along each geodesic is bounded by 2M, the timelike lines $r=c\in [0,2M]$ are incomplete, and for r>2M the metric converges asymptotically to the Schwarzschild metric with mass M. The initial data that we construct guarantee the formation of a black hole in the evolution. We also give examples of such initial data with the additional property that the solutions exist for all $r\geq 0$ and all Schwarzschild time, i.e., we obtain global existence in Schwarzschild coordinates in situations where the initial data are not small. Some of our results are also established for the Einstein equations coupled to a general matter model characterized by conditions on the matter quantities.Comment: 36 pages. A corollary on global existence in Schwarzschild coordinates for data which are not small is added together with minor modification

Reaction Brownian Dynamics and the effect of spatial fluctuations on the gain of a push-pull network

Brownian Dynamics algorithms are widely used for simulating soft-matter and biochemical systems. In recent times, their application has been extended to the simulation of coarse-grained models of cellular networks in simple organisms. In these models, components move by diffusion, and can react with one another upon contact. However, when reactions are incorporated into a Brownian Dynamics algorithm, attention must be paid to avoid violations of the detailed-balance rule, and therefore introducing systematic errors in the simulation. We present a Brownian Dynamics algorithm for reaction-diffusion systems that rigorously obeys detailed balance for equilibrium reactions. By comparing the simulation results to exact analytical results for a bimolecular reaction, we show that the algorithm correctly reproduces both equilibrium and dynamical quantities. We apply our scheme to a ``push-pull'' network in which two antagonistic enzymes covalently modify a substrate. Our results highlight that the diffusive behaviour of the reacting species can reduce the gain of the response curve of this network.Comment: 25 pages, 7 figures, submitted to Journal of Chemical Physic

Circular Dichroism of Partially Purified Cytochrome P450 from Rabbit Liver Microsomes

The heme-related circular dichroic bands of solubilized cytochrome P450 from rabbit liver microsomes and some of its liganded derivatives were measured in the Soret region. All P450 derivatives exhibit negative circular dichroic bands in the region of the Soret absorption. The wavelengths of the dichroic bands and their ellipticities vary with ligand substitution and the oxidation state of the iron. The results are compared with CD-data from other hemoproteins and discussed with respect to stereochemical conclusions concerning the geometry and the physicochemical character of the vicinity of the heme group with regard to results obtained from other studies

Evidence of the Existence of a High Spin Low Spin Equilibrium in Liver Microsomal Cytochrome P450, and its Role in the Enzymatic Mechanism

In rabbit liver microsomal cytochrome P450 a high spin (S = = 5/2) low spin (S = 1/2) equilibrium has been proved to exist by recording temperature difference spectra in the Soret and in the visible region of the absorption spectrum of solubilized cytochrome P450. In the presence of type II substrates the predominantly low spin state of cytochrome P450 is maintained, only a very small shift to lower spin is observed. Ligands of the heme iron, such as cyanide and imidazole, pr9duce a pure low spin state and therefore in the presence of these ligands no temperature difference spectra can be obtained. In the presence of type I substrate, however, the spin equilibrium is shifted to the high spin state. The extent of this shift (1) depends on specific properties of the substrate and (2) it is generally relatively small, up to about 80/o in the case of substrates investigated so far