Constraints and Reality Conditions in the Ashtekar Formulation of General Relativity

We show how to treat the constraints and reality conditions in the $SO(3)$-ADM (Ashtekar) formulation of general relativity, for the case of a vacuum spacetime with a cosmological constant. We clarify the difference between the reality conditions on the metric and on the triad. Assuming the triad reality condition, we find a new variable, allowing us to solve the gauge constraint equations and the reality conditions simultaneously.Comment: LaTeX file, 12 pages, no figures; to appear in Classical and Quantum Gravit

Advantages of modified ADM formulation: constraint propagation analysis of Baumgarte-Shapiro-Shibata-Nakamura system

Several numerical relativity groups are using a modified ADM formulation for their simulations, which was developed by Nakamura et al (and widely cited as Baumgarte-Shapiro-Shibata-Nakamura system). This so-called BSSN formulation is shown to be more stable than the standard ADM formulation in many cases, and there have been many attempts to explain why this re-formulation has such an advantage. We try to explain the background mechanism of the BSSN equations by using eigenvalue analysis of constraint propagation equations. This analysis has been applied and has succeeded in explaining other systems in our series of works. We derive the full set of the constraint propagation equations, and study it in the flat background space-time. We carefully examine how the replacements and adjustments in the equations change the propagation structure of the constraints, i.e. whether violation of constraints (if it exists) will decay or propagate away. We conclude that the better stability of the BSSN system is obtained by their adjustments in the equations, and that the combination of the adjustments is in a good balance, i.e. a lack of their adjustments might fail to obtain the present stability. We further propose other adjustments to the equations, which may offer more stable features than the current BSSN equations.Comment: 10 pages, RevTeX4, added related discussion to gr-qc/0209106, the version to appear in Phys. Rev.

Novel Pressure Induced Structural Phase Transition in AgSbTe2_{2}

We report a novel high pressure structural sequence for the functionally graded thermoelectric, narrow band gap semiconductor AgSbTe$_{2}$, using angle dispersive x-ray diffraction in a diamond anvil cell with synchrotron radiation at room temperature. The compound undergoes a B1 to B2 transition; the transition proceeds through an intermediate amorphous phase found between 17-26 GPa that is quenchable down to ambient conditions. The pressure induced structural transition observed in this compound is the first of its type reported in this ternary cubic family, and it is new for the B1-B2 transition pathway reported to date. Density Functional Theory (DFT) calculations performed for the B1 and B2 phases are in good agreement with the experimental results.Comment: 4 pages, 3 figure

Reality conditions for Ashtekar variables as Dirac constraints

We show that the reality conditions to be imposed on Ashtekar variables to recover real gravity can be implemented as second class constraints a la Dirac. Thus, counting gravitational degrees of freedom follows accordingly. Some constraints of the real theory turn out to be non-polynomial, regardless of the form, polynomial or non-polynomial, taken for the reality conditions. We comment upon the compatibility of our approach with the recently proposed Wick transform point of view, as well as on some alternatives for dealing with such second class constraints.Comment: 16 pages, plain LaTeX, submitted to Class. Quant. Grav. E-mail: [email protected]

Neutron knockout of 12Be populating neutron-unbound states in 11Be

Neutron-unbound resonant states of 11Be were populated in neutron knock-out reactions from 12Be and identified by 10Be-n coincidence measurements. A resonance in the decay-energy spectrum at 80(2) keV was attributed to a highly excited unbound state in 11Be at 3.949(2) MeV decaying to the 2+ excited state in 10Be. A knockout cross section of 15(3) mb was inferred for this 3.949(2) MeV state suggesting a spectroscopic factor near unity for this 0p3/2- level, consistent with the detailed shell model calculations.Comment: 5 pages, 2 figures \pacs{29.38.Db, 29.30.Hs, 24.50.+g, 21.10.Pc, 21.10.Hw, 27.20.+n} \keywords{neutron decay spectroscopy, neutron-unbound states in 11Be

Shell structure underlying the evolution of quadrupole collectivity in S-38 and S-40 probed by transient-field g-factor measurements on fast radioactive beams

The shell structure underlying shape changes in neutron-rich nuclei between N=20 and N=28 has been investigated by a novel application of the transient field technique to measure the first-excited state g factors in S-38 and S-40 produced as fast radioactive beams. Details of the new methodology are presented. In both S-38 and S-40 there is a fine balance between the proton and neutron contributions to the magnetic moments. Shell model calculations which describe the level schemes and quadrupole properties of these nuclei also give a satisfactory explanation of the g factors. In S-38 the g factor is extremely sensitive to the occupation of the neutron p3/2 orbit above the N=28 shell gap as occupation of this orbit strongly affects the proton configuration. The g factor of deformed S-40 does not resemble that of a conventional collective nucleus because spin contributions are more important than usual.Comment: 10 pages, 36 figures, accepted for publication in Physical Review

Algebraic stability analysis of constraint propagation

The divergence of the constraint quantities is a major problem in computational gravity today. Apparently, there are two sources for constraint violations. The use of boundary conditions which are not compatible with the constraint equations inadvertently leads to 'constraint violating modes' propagating into the computational domain from the boundary. The other source for constraint violation is intrinsic. It is already present in the initial value problem, i.e. even when no boundary conditions have to be specified. Its origin is due to the instability of the constraint surface in the phase space of initial conditions for the time evolution equations. In this paper, we present a technique to study in detail how this instability depends on gauge parameters. We demonstrate this for the influence of the choice of the time foliation in context of the Weyl system. This system is the essential hyperbolic part in various formulations of the Einstein equations.Comment: 25 pages, 5 figures; v2: small additions, new reference, publication number, classification and keywords added, address fixed; v3: update to match journal versio

Probing shell structure and shape changes in neutron-rich sulfur isotopes through transient-field g factor measurements on fast radioactive beams of 38S and 40S

The shell structure underlying shape changes in neutron-rich nuclei near N=28 has been investigated by a novel application of the transient field technique to measure the first-excited state g factors in 38S and 40S produced as fast radioactive beams. There is a fine balance between proton and neutron contributions to the magnetic moments in both nuclei. The g factor of deformed 40S does not resemble that of a conventional collective nucleus because spin contributions are more important than usual.Comment: 10 pages, 6 figures, accepted in PR

Availability of Cognitive Resources in Early Life Predicts Transitions Between Cognitive States in Middle and Older Adults From Europe

BACKGROUND AND OBJECTIVES: The existing literature highlights the importance of reading books in middle-to-older adulthood for cognitive functioning; very few studies, however, have examined the importance of childhood cognitive resources for cognitive outcomes later in life.RESEARCH DESIGN AND METHODS: Using data from 11 countries included in the Survey of Health, Ageing, and Retirement in Europe (SHARE) data set ( N  = 32,783), multistate survival models (MSMs) were fit to examine the importance of access to reading material in childhood on transitions through cognitive status categories (no cognitive impairment and impaired cognitive functioning) and death. Additionally, using the transition probabilities estimated by the MSMs, we estimated the remaining years of life without cognitive impairment and total longevity. All models were fit individually in each country, as well as within the pooled SHARE sample. RESULTS: Adjusting for age, sex, education, and childhood socioeconomic status, the overall pooled estimate indicated that access to more books at age 10 was associated with a decreased risk of developing cognitive impairment (adjusted hazard ratio = 0.79, confidence interval: 0.76-0.82). Access to childhood books was not associated with risk of transitioning from normal cognitive functioning to death, or from cognitive impairment to death. Total longevity was similar between participants reporting high (+1 standard deviation [ SD]) and low (-1 SD) number of books in the childhood home; however, individuals with more access to childhood books lived a greater proportion of this time without cognitive impairment. DISCUSSION AND IMPLICATIONS: Findings suggest that access to cognitive resources in childhood is protective for cognitive aging processes in older adulthood.</p