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 Einstein-Vlasov System/Kinetic Theory

The main purpose of this article is to provide a guide 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 in which the main focus has been on non-relativistic and special relativistic physics, i.e., 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.Comment: Published version http://www.livingreviews.org/lrr-2011-

Existence of axially symmetric static solutions of the Einstein-Vlasov system

We prove the existence of static, asymptotically flat non-vacuum spacetimes with axial symmetry where the matter is modeled as a collisionless gas. The axially symmetric solutions of the resulting Einstein-Vlasov system are obtained via the implicit function theorem by perturbing off a suitable spherically symmetric steady state of the Vlasov-Poisson system.Comment: 32 page

Estimating the public health impact of disbanding a government alcohol monopoly: Application of new methods to the case of Sweden

Background: Government alcohol monopolies were created in North America and Scandinavia to limit health and social problems. The Swedish monopoly, Systembolaget, reports to a health ministry and controls the sale of all alcoholic beverages with > 3.5% alcohol/volume for off-premise consumption, within a public health mandate. Elsewhere, alcohol monopolies are being dismantled with evidence of increased consumption and harms. We describe innovative modelling techniques to estimate health outcomes in scenarios involving Systembolaget being replaced by 1) privately owned liquor stores, or 2) alcohol sales in grocery stores. The methods employed can be applied in other jurisdictions and for other policy changes. Methods: Impacts of the privatisation scenarios on pricing, outlet density, trading hours, advertising and marketing were estimated based on Swedish expert opinion and published evidence. Systematic reviews were conducted to estimate impacts on alcohol consumption in each scenario. Two methods were applied to estimate harm impacts: (i) alcohol attributable morbidity and mortality were estimated utilising the International Model of Alcohol Harms and Policies (InterMAHP); (ii) ARIMA methods to estimate the relationship between per capita alcohol consumption and specific types of alcohol-related mortality and crime. Results: Replacing government stores with private liquor stores (Scenario 1) led to a 20.0% (95% CI, 15.3-24.7) increase in per capita consumption. Replacement with grocery stores (Scenario 2) led to a 31.2% (25.1-37.3%) increase. With InterMAHP there were 763 or + 47% (35-59%) and 1234 or + 76% (60-92%) more deaths per year, for Scenarios 1 and 2 respectively. With ARIMA, there were 850 (334-1444) more deaths per year in Scenario 1 and 1418 more in Scenario 2 (543-2505). InterMAHP also estimated 10,859 or + 29% (22-34%) and 16,118 or + 42% (35-49%) additional hospital stays per year respectively. Conclusions: There would be substantial adverse consequences for public health and safety were Systembolaget to be privatised. We demonstrate a new combined approach for estimating the impact of alcohol policies on consumption and, using two alternative methods, alcohol-attributable harm. This approach could be readily adapted to other policies and settings. We note the limitation that some significant sources of uncertainty in the estimates of harm impacts were not modelled

Asymptotic Stability of the Relativistic Boltzmann Equation for the Soft Potentials

In this paper it is shown that unique solutions to the relativistic Boltzmann equation exist for all time and decay with any polynomial rate towards their steady state relativistic Maxwellian provided that the initial data starts out sufficiently close in $L^\infty_\ell$. If the initial data are continuous then so is the corresponding solution. We work in the case of a spatially periodic box. Conditions on the collision kernel are generic in the sense of (Dudy{\'n}ski and Ekiel-Je{\.z}ewska, Comm. Math. Phys., 1988); this resolves the open question of global existence for the soft potentials.Comment: 64 page

Strange stars in Krori-Barua space-time

The singularity space-time metric obtained by Krori and Barua\cite{Krori1975} satisfies the physical requirements of a realistic star. Consequently, we explore the possibility of applying the Krori and Barua model to describe ultra-compact objects like strange stars. For it to become a viable model for strange stars, bounds on the model parameters have been obtained. Consequences of a mathematical description to model strange stars have been analyzed.Comment: 9 pages (two column), 12 figures. Some changes have been made. " To appear in European Physical Journal C

Mutations in CEP78 Cause Cone-Rod Dystrophy and Hearing Loss Associated with Primary-Cilia Defects.

Cone-rod degeneration (CRD) belongs to the disease spectrum of retinal degenerations, a group of hereditary disorders characterized by an extreme clinical and genetic heterogeneity. It mainly differentiates from other retinal dystrophies, and in particular from the more frequent disease retinitis pigmentosa, because cone photoreceptors degenerate at a higher rate than rod photoreceptors, causing severe deficiency of central vision. After exome analysis of a cohort of individuals with CRD, we identified biallelic mutations in the orphan gene CEP78 in three subjects from two families: one from Greece and another from Sweden. The Greek subject, from the island of Crete, was homozygous for the c.499+1G>T (IVS3+1G>T) mutation in intron 3. The Swedish subjects, two siblings, were compound heterozygotes for the nearby mutation c.499+5G>A (IVS3+5G>A) and for the frameshift-causing variant c.633delC (p.Trp212Glyfs(∗)18). In addition to CRD, these three individuals had hearing loss or hearing deficit. Immunostaining highlighted the presence of CEP78 in the inner segments of retinal photoreceptors, predominantly of cones, and at the base of the primary cilium of fibroblasts. Interaction studies also showed that CEP78 binds to FAM161A, another ciliary protein associated with retinal degeneration. Finally, analysis of skin fibroblasts derived from affected individuals revealed abnormal ciliary morphology, as compared to that of control cells. Altogether, our data strongly suggest that mutations in CEP78 cause a previously undescribed clinical entity of a ciliary nature characterized by blindness and deafness but clearly distinct from Usher syndrome, a condition for which visual impairment is due to retinitis pigmentosa

Theorems on existence and global dynamics for the Einstein equations

This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations. It draws attention to open questions in the field. The local-in-time Cauchy problem, which is relatively well understood, is surveyed. Global results for solutions with various types of symmetry are discussed. A selection of results from Newtonian theory and special relativity that offer useful comparisons is presented. Treatments of global results in the case of small data and results on constructing spacetimes with prescribed singularity structure or late-time asymptotics are given. A conjectural picture of the asymptotic behaviour of general cosmological solutions of the Einstein equations is built up. Some miscellaneous topics connected with the main theme are collected in a separate section.Comment: Submitted to Living Reviews in Relativity, major update of Living Rev. Rel. 5 (2002)

Characterization of the thermal and photoinduced reactions of photochromic spiropyrans in aqueous solution

Six water-soluble spiropyran derivatives have been characterized with respect to the thermal and photoinduced reactions over a broad pH-interval. A comprehensive kinetic model was formulated including the spiro- and the merocyanine isomers, the respective protonated forms, and the hydrolysis products. The experimental studies on the hydrolysis reaction mechanism were supplemented by calculations using quantum mechanical (QM) models employing density functional theory. The results show that (1) the substitution pattern dramatically influences the pKa-values of the protonated forms as well as the rates of the thermal isomerization reactions, (2) water is the nucleophile in the hydrolysis reaction around neutral pH, (3) the phenolate oxygen of the merocyanine form plays a key role in the hydrolysis reaction. Hence, the nonprotonated merocyanine isomer is susceptible to hydrolysis, whereas the corresponding protonated form is stable toward hydrolytic degradation