Well-Posed Initial-Boundary Evolution in General Relativity

Maximally dissipative boundary conditions are applied to the initial-boundary value problem for Einstein's equations in harmonic coordinates to show that it is well-posed for homogeneous boundary data and for boundary data that is small in a linearized sense. The method is implemented as a nonlinear evolution code which satisfies convergence tests in the nonlinear regime and is robustly stable in the weak field regime. A linearized version has been stably matched to a characteristic code to compute the gravitational waveform radiated to infinity.Comment: 5 pages, 6 figures; added another convergence plot to Fig. 2 + minor change

Symmetric hyperbolic systems for a large class of fields in arbitrary dimension

Symmetric hyperbolic systems of equations are explicitly constructed for a general class of tensor fields by considering their structure as r-fold forms. The hyperbolizations depend on 2r-1 arbitrary timelike vectors. The importance of the so-called "superenergy" tensors, which provide the necessary symmetric positive matrices, is emphasized and made explicit. Thereby, a unified treatment of many physical systems is achieved, as well as of the sometimes called "higher order" systems. The characteristics of these symmetric hyperbolic systems are always physical, and directly related to the null directions of the superenergy tensor, which are in particular principal null directions of the tensor field solutions. Generic energy estimates and inequalities are presented too.Comment: 24 pages, no figure

The Nonlinear Future-Stability of the FLRW Family of Solutions to the Euler-Einstein System with a Positive Cosmological Constant

In this article, we study small perturbations of the family of Friedmann-Lema\^itre-Robertson-Walker cosmological background solutions to the 1 + 3 dimensional Euler-Einstein system with a positive cosmological constant. These background solutions describe an initially uniform quiet fluid of positive energy density evolving in a spacetime undergoing accelerated expansion. Our nonlinear analysis shows that under the equation of state pressure = c_s^2 * energy density, with 0 < c_s^2 < 1/3, the background solutions are globally future-stable. In particular, we prove that the perturbed spacetime solutions, which have the topological structure [0,infty) x T^3, are future causally geodesically complete. These results are extensions of previous results derived by the author in a collaboration with I. Rodnianski, in which the fluid was assumed to be irrotational. Our novel analysis of a fluid with non-zero vorticity is based on the use of suitably-defined energy currents.Comment: Accepted for publication in Selecta Mathematica, 78 pages. arXiv admin note: significant text overlap with arXiv:0911.550

Study of the doubly charmed tetraquark T+cc

Quantum chromodynamics, the theory of the strong force, describes interactions of coloured quarks and gluons and the formation of hadronic matter. Conventional hadronic matter consists of baryons and mesons made of three quarks and quark-antiquark pairs, respectively. Particles with an alternative quark content are known as exotic states. Here a study is reported of an exotic narrow state in the D0D0π+ mass spectrum just below the D*+D0 mass threshold produced in proton-proton collisions collected with the LHCb detector at the Large Hadron Collider. The state is consistent with the ground isoscalar T+cc tetraquark with a quark content of ccu⎯⎯⎯d⎯⎯⎯ and spin-parity quantum numbers JP = 1+. Study of the DD mass spectra disfavours interpretation of the resonance as the isovector state. The decay structure via intermediate off-shell D*+ mesons is consistent with the observed D0π+ mass distribution. To analyse the mass of the resonance and its coupling to the D*D system, a dedicated model is developed under the assumption of an isoscalar axial-vector T+cc state decaying to the D*D channel. Using this model, resonance parameters including the pole position, scattering length, effective range and compositeness are determined to reveal important information about the nature of the T+cc state. In addition, an unexpected dependence of the production rate on track multiplicity is observed

Intracranial Aneurysm Classifier Using Phenotypic Factors: An International Pooled Analysis.

Intracranial aneurysms (IAs) are usually asymptomatic with a low risk of rupture, but consequences of aneurysmal subarachnoid hemorrhage (aSAH) are severe. Identifying IAs at risk of rupture has important clinical and socio-economic consequences. The goal of this study was to assess the effect of patient and IA characteristics on the likelihood of IA being diagnosed incidentally versus ruptured. Patients were recruited at 21 international centers. Seven phenotypic patient characteristics and three IA characteristics were recorded. The analyzed cohort included 7992 patients. Multivariate analysis demonstrated that: (1) IA location is the strongest factor associated with IA rupture status at diagnosis; (2) Risk factor awareness (hypertension, smoking) increases the likelihood of being diagnosed with unruptured IA; (3) Patients with ruptured IAs in high-risk locations tend to be older, and their IAs are smaller; (4) Smokers with ruptured IAs tend to be younger, and their IAs are larger; (5) Female patients with ruptured IAs tend to be older, and their IAs are smaller; (6) IA size and age at rupture correlate. The assessment of associations regarding patient and IA characteristics with IA rupture allows us to refine IA disease models and provide data to develop risk instruments for clinicians to support personalized decision-making

Some people and some problems met in half a century of commitment to mathematical physics

Personnal recollection of half a century of Mathematical Physics

Management of phenylketonuria in Europe: Survey results from 19 countries

To gain better insight in the most current diagnosis and treatment practices for phenylketonuria (PKU) from a broad group of experts, a European PKU survey was performed. The questionnaire. consisting of 33 questions, was sent to 243 PKU professionals in 165 PKU centers in 23 European countries. The responses were compiled and descriptive analyses were performed. One hundred and one questionnaires were returned by 93/165 centers (56%) from 19/23 European countries (83%). The majority of respondents (77%) managed patients of all age groups and more than 90% of PKU teams included physicians or dieticians/nutritionists. The greatest variability existed especially in the definition of PKU phenotypes, therapeutic blood phenylalanine (Phe) target concentrations, and follow-up practices for PKU patients. The tetrahydrobiopterin (BH4: sapropterin) loading test was performed by 54% of respondents, of which 61% applied a single dose test (20 mg/kg over 24 h). BH4 was reported as a treatment option by 34%. This survey documents differences in diagnostic and treatment practices for PKU patients in European centers. In particular, recommendations for the treatment decision varied greatly between different European countries. There is an urgent need to pool long-term data in PKU registries in order to generate an evidence-based international guideline