Constraints and evolution in cosmology

We review some old and new results about strict and non strict hyperbolic formulations of the Einstein equations.Comment: To appear in the proceedings of the first Aegean summer school in General Relativity, S. Cotsakis ed. Springer Lecture Notes in Physic

Understanding the α-crystallin cell membrane conjunction

PURPOSE. It is well established that levels of soluble α-crystallin in the lens cytoplasm fall steadily with age, accompanied by a corresponding increase in the amount of membrane-bound α-crystallin. Less well understood, is the mechanism driving this age-dependent membrane association. The aim of this study was to investigate the role of the membrane and its associated proteins and peptides in the binding of α-crystallin. METHODS. Fibre cell membranes from human and bovine lenses were separated from soluble proteins by centrifugation. Membranes were stripped of associated proteins with successive aqueous, urea and alkaline solutions. Protein constituents of the respective membrane isolates were examined by SDS-PAGE and Western immunoblotting. Recombinant αA- and αB-crystallins were fluorescently-labeled with Alexa350® dye and incubated with the membrane isolates and the binding capacity of membrane for α-crystallin was determined. RESULTS. The binding capacity of human membranes was consistently higher than that of bovine membranes. Urea- and alkali-treated membranes from the nucleus had similar binding capacities for αA-crystallin, which were significantly higher than both cortical membrane extracts. αB-Crystallin also had a higher affinity for nuclear membrane. However, urea-treated nuclear membrane had three times the binding capacity for αB-crystallin as compared to the alkali-treated nuclear membrane. Modulation of the membrane-crystallin interaction was achieved by the inclusion of an N-terminal peptide of αB-crystallin in the assays, which significantly increased the binding. Remarkably, following extraction with alkali, full length αA- and αB-crystallins were found to remain associated with both bovine and human lens membranes. CONCLUSIONS. Fiber cell membrane isolated from the lens has an inherent capacity to bind α-crystallin. For αB-crystallin, this binding was found to be proportional to the level of extrinsic membrane proteins in cells isolated from the lens nucleus, indicating these proteins may play a role in the recruitment of αB-crystallin. No such relationship was evident for αA-crystallin in the nucleus, or for cortical membrane binding. Intrinsic lens peptides, which increase in abundance with age, may also function to modulate the interaction between soluble α-crystallin and the membrane. In addition, the tight association between α-crystallin and the lens membrane suggests that the protein may be an intrinsic component of the membrane structure

Markov Properties of Electrical Discharge Current Fluctuations in Plasma

Using the Markovian method, we study the stochastic nature of electrical discharge current fluctuations in the Helium plasma. Sinusoidal trends are extracted from the data set by the Fourier-Detrended Fluctuation analysis and consequently cleaned data is retrieved. We determine the Markov time scale of the detrended data set by using likelihood analysis. We also estimate the Kramers-Moyal's coefficients of the discharge current fluctuations and derive the corresponding Fokker-Planck equation. In addition, the obtained Langevin equation enables us to reconstruct discharge time series with similar statistical properties compared with the observed in the experiment. We also provide an exact decomposition of temporal correlation function by using Kramers-Moyal's coefficients. We show that for the stationary time series, the two point temporal correlation function has an exponential decaying behavior with a characteristic correlation time scale. Our results confirm that, there is no definite relation between correlation and Markov time scales. However both of them behave as monotonic increasing function of discharge current intensity. Finally to complete our analysis, the multifractal behavior of reconstructed time series using its Keramers-Moyal's coefficients and original data set are investigated. Extended self similarity analysis demonstrates that fluctuations in our experimental setup deviates from Kolmogorov (K41) theory for fully developed turbulence regime.Comment: 25 pages, 9 figures and 4 tables. V3: Added comments, references, figures and major correction

Extending the lifetime of 3D black hole computations with a new hyperbolic system of evolution equations

We present a new many-parameter family of hyperbolic representations of Einstein's equations, which we obtain by a straightforward generalization of previously known systems. We solve the resulting evolution equations numerically for a Schwarzschild black hole in three spatial dimensions, and find that the stability of the simulation is strongly dependent on the form of the equations (i.e. the choice of parameters of the hyperbolic system), independent of the numerics. For an appropriate range of parameters we can evolve a single 3D black hole to $t \simeq 600 M$ -- $1300 M$, and are apparently limited by constraint-violating solutions of the evolution equations. We expect that our method should result in comparable times for evolutions of a binary black hole system.Comment: 11 pages, 2 figures, submitted to PR

Axially symmetric Hartree-Fock-Bogoliubov Calculations for Nuclei Near the Drip-Lines

Nuclei far from stability are studied by solving the Hartree-Fock-Bogoliubov (HFB) equations, which describe the self-consistent mean field theory with pairing interaction. Calculations for even-even nuclei are carried out on two-dimensional axially symmetric lattice, in coordinate space. The quasiparticle continuum wavefunctions are considered for energies up to 60 MeV. Nuclei near the drip lines have a strong coupling between weakly bound states and the particle continuum. This method gives a proper description of the ground state properties of such nuclei. High accuracy is achieved by representing the operators and wavefunctions using the technique of basis-splines. The detailed representation of the HFB equations in cylindrical coordinates is discussed. Calculations of observables for nuclei near the neutron drip line are presented to demonstrate the reliability of the method.Comment: 13 pages, 4 figures. Submitted to Physical Review C on 05/08/02. Revised on Dec/0

Spectrum of cardiac disease in maternity in a low-resource cohort in South Africa

Background: Lack of evidence-based data on the spectrum of cardiovascular disease (CVD) in pregnancy or in the postpartum period, as well as on maternal and fetal outcome, provides challenges for treating physicians, particularly in areas of low resources. The objectives of this study were to investigate the spectrum of disease, mode of presentation and maternal and fetal outcome of patients referred to a dedicated Cardiac Disease and Maternity Clinic (CDM). Methods: The prospective cohort study was conducted at a single tertiary care centre in South Africa. Two hundred and twenty-five women presenting with CVD in pregnancy, or within 6 months postpartum, were studied over a period of 2 years. Clinical assessment, echocardiography and laboratory tests were performed at baseline and follow-up visits. Prepartum, peripartum and postpartum complications were grouped into cardiac, neonatal and obstetric events. Results: Ethnicity was black African (45%), mixed ethnicity (32%), white (15%), Indian/others (8%) and 12% were HIV positive. Of the 225 consecutive women (mean age 28.8±6.4), 196 (86.7%) presented prepartum and 73 in modified WHO class I. The 152 women presenting in a higher risk group (modified WHO class II-IV) were offered close follow-up at the CDM clinic and were diagnosed with congenital heart disease (32%, 15 operated previously), valvular heart disease (26%, 15 operated previously), cardiomyopathy (27%) and other (15%). Women presenting with symptoms of CVD or heart failure postpartum (n=30) presented in a higher New York Heart Association, had higher heart rates (p42 days postpartum. Perinatal death occurred in 1/152 (0.7%) - translating to a perinatal mortality rate of 7/1000 live births. Conclusions: Disease patterns were markedly different to that seen in the developed world. However, joint obstetric-cardiac care in the low-resource cohort was associated with excellent survival outcome rates of pregnant mothers (even with complex diseases) and their offspring and was similar to that seen in the western world. Mortality typically occurred in the postpartum period, beyond the standard date of recording maternal death

On the geometrization of matter by exotic smoothness

In this paper we discuss the question how matter may emerge from space. For that purpose we consider the smoothness structure of spacetime as underlying structure for a geometrical model of matter. For a large class of compact 4-manifolds, the elliptic surfaces, one is able to apply the knot surgery of Fintushel and Stern to change the smoothness structure. The influence of this surgery to the Einstein-Hilbert action is discussed. Using the Weierstrass representation, we are able to show that the knotted torus used in knot surgery is represented by a spinor fulfilling the Dirac equation and leading to a mass-less Dirac term in the Einstein-Hilbert action. For sufficient complicated links and knots, there are "connecting tubes" (graph manifolds, torus bundles) which introduce an action term of a gauge field. Both terms are genuinely geometrical and characterized by the mean curvature of the components. We also discuss the gauge group of the theory to be U(1)xSU(2)xSU(3).Comment: 30 pages, 3 figures, svjour style, complete reworking now using Fintushel-Stern knot surgery of elliptic surfaces, discussion of Lorentz metric and global hyperbolicity for exotic 4-manifolds added, final version for publication in Gen. Rel. Grav, small typos errors fixe

Cartan's spiral staircase in physics and, in particular, in the gauge theory of dislocations

In 1922, Cartan introduced in differential geometry, besides the Riemannian curvature, the new concept of torsion. He visualized a homogeneous and isotropic distribution of torsion in three dimensions (3d) by the "helical staircase", which he constructed by starting from a 3d Euclidean space and by defining a new connection via helical motions. We describe this geometric procedure in detail and define the corresponding connection and the torsion. The interdisciplinary nature of this subject is already evident from Cartan's discussion, since he argued - but never proved - that the helical staircase should correspond to a continuum with constant pressure and constant internal torque. We discuss where in physics the helical staircase is realized: (i) In the continuum mechanics of Cosserat media, (ii) in (fairly speculative) 3d theories of gravity, namely a) in 3d Einstein-Cartan gravity - this is Cartan's case of constant pressure and constant intrinsic torque - and b) in 3d Poincare gauge theory with the Mielke-Baekler Lagrangian, and, eventually, (iii) in the gauge field theory of dislocations of Lazar et al., as we prove for the first time by arranging a suitable distribution of screw dislocations. Our main emphasis is on the discussion of dislocation field theory.Comment: 31 pages, 8 figure

Approach to ergodicity in quantum wave functions

According to theorems of Shnirelman and followers, in the semiclassical limit the quantum wavefunctions of classically ergodic systems tend to the microcanonical density on the energy shell. We here develop a semiclassical theory that relates the rate of approach to the decay of certain classical fluctuations. For uniformly hyperbolic systems we find that the variance of the quantum matrix elements is proportional to the variance of the integral of the associated classical operator over trajectory segments of length $T_H$, and inversely proportional to $T_H^2$, where $T_H=h\bar\rho$ is the Heisenberg time, $\bar\rho$ being the mean density of states. Since for these systems the classical variance increases linearly with $T_H$, the variance of the matrix elements decays like $1/T_H$. For non-hyperbolic systems, like Hamiltonians with a mixed phase space and the stadium billiard, our results predict a slower decay due to sticking in marginally unstable regions. Numerical computations supporting these conclusions are presented for the bakers map and the hydrogen atom in a magnetic field.Comment: 11 pages postscript and 4 figures in two files, tar-compressed and uuencoded using uufiles, to appear in Phys Rev E. For related papers, see http://www.icbm.uni-oldenburg.de/icbm/kosy/ag.htm