Criticality and convergence in Newtonian collapse

We study through numerical simulation the spherical collapse of isothermal gas in Newtonian gravity. We observe a critical behavior which occurs at the threshold of gravitational instability leading to core formation. For a given initial density profile, we find a critical temperature, which is of the same order as the virial temperature of the initial configuration. For the exact critical temperature, the collapse converges to a self-similar form, the first member in Hunter's family of self-similar solutions. For a temperature close to the critical value, the collapse first approaches this critical solution. Later on, in the supercritical case, the collapse converges to another self-similar solution, which is called the Larson-Penston solution. In the subcritical case, the gas bounces and disperses to infinity. We find two scaling laws: one for the collapsed mass in the supercritical case and the other for the maximum density reached before dispersal in the subcritical case. The value of the critical exponent is measured to be $\simeq 0.11$ in the supercritical case, which agrees well with the predicted value $\simeq 0.10567$. These critical properties are quite similar to those observed in the collapse of a radiation fluid in general relativity. We study the response of the system to temperature fluctuation and discuss astrophysical implications for the insterstellar medium structure and for the star formation process. Newtonian critical behavior is important not only because it provides a simple model for general relativity but also because it is relevant for astrophysical systems such as molecular clouds.Comment: 15 pages, 8 figures, accepted for publication in PRD, figures 1 and 3 at lower resolution than in journal version, typos correcte

Neuronal migration defects in the Loa dynein mutant mouse

<p>Abstract</p> <p>Background</p> <p>Cytoplasmic dynein and its regulatory proteins have been implicated in neuronal and non-neuronal cell migration. A genetic model for analyzing the role of cytoplasmic dynein specifically in these processes has, however, been lacking. The Loa (Legs at odd angles) mouse with a mutation in the dynein heavy chain has been the focus of an increasing number of studies for its role in neuron degeneration. Despite the location of this mutation in the tail domain of the dynein heavy chain, we previously found a striking effect on coordination between the two dynein motor domains, resulting in a defect in dynein run length <it>in vitro </it>and <it>in vivo</it>.</p> <p>Results</p> <p>We have now tested for effects of the Loa mutation on neuronal migration in the developing neocortex. Loa homozygotes showed clear defects in neocortical lamination and neuronal migration resulting from a reduction in the rate of radial migration of bipolar neurons.</p> <p>Conclusions</p> <p>These results present a new genetic model for understanding the dynein pathway and its functions during neuronal migration. They also provide the first evidence for a link between dynein processivity and somal movement, which is essential for proper development of the brain.</p

Singularity in 2+1 dimensional AdS-scalar black hole

We study the spacetime singularity in 2+1 dimensional AdS-scalar black hole with circular symmetry using a quasi-homogeneous model. We show that this is a spacelike, scalar curvature, deformationally strong singularity.Comment: 4 pages, RevTeX, submitted to PRD (brief report

Convergence to a self-similar solution in general relativistic gravitational collapse

We study the spherical collapse of a perfect fluid with an equation of state $P=k\rho$ by full general relativistic numerical simulations. For 0, it has been known that there exists a general relativistic counterpart of the Larson-Penston self-similar Newtonian solution. The numerical simulations strongly suggest that, in the neighborhood of the center, generic collapse converges to this solution in an approach to a singularity and that self-similar solutions other than this solution, including a ``critical solution'' in the black hole critical behavior, are relevant only when the parameters which parametrize initial data are fine-tuned. This result is supported by a mode analysis on the pertinent self-similar solutions. Since a naked singularity forms in the general relativistic Larson-Penston solution for 0, this will be the most serious known counterexample against cosmic censorship. It also provides strong evidence for the self-similarity hypothesis in general relativistic gravitational collapse. The direct consequence is that critical phenomena will be observed in the collapse of isothermal gas in Newton gravity, and the critical exponent $\gamma$ will be given by $\gamma\approx 0.11$, though the order parameter cannot be the black hole mass.Comment: 22 pages, 15 figures, accepted for publication in Physical Review D, reference added, typos correcte

Numerical investigation of black hole interiors

Gravitational perturbations which are present in any realistic stellar collapse to a black hole, die off in the exterior of the hole, but experience an infinite blueshift in the interior. This is believed to lead to a slowly contracting lightlike scalar curvature singularity, characterized by a divergence of the hole's (quasi-local) mass function along the inner horizon. The region near the inner horizon is described to great accuracy by a plane wave spacetime. While Einstein's equations for this metric are still too complicated to be solved in closed form it is relatively simple to integrate them numerically. We find for generic regular initial data the predicted mass inflation type null singularity, rather than a spacelike singularity. It thus seems that mass inflation indeed represents a generic self-consistent picture of the black hole interior.Comment: 6 pages LaTeX, 3 eps figure

Stability criterion for self-similar solutions with a scalar field and those with a stiff fluid in general relativity

A stability criterion is derived in general relativity for self-similar solutions with a scalar field and those with a stiff fluid, which is a perfect fluid with the equation of state $P=\rho$. A wide class of self-similar solutions turn out to be unstable against kink mode perturbation. According to the criterion, the Evans-Coleman stiff-fluid solution is unstable and cannot be a critical solution for the spherical collapse of a stiff fluid if we allow sufficiently small discontinuity in the density gradient field in the initial data sets. The self-similar scalar-field solution, which was recently found numerically by Brady {\it et al.} (2002 {\it Class. Quantum. Grav.} {\bf 19} 6359), is also unstable. Both the flat Friedmann universe with a scalar field and that with a stiff fluid suffer from kink instability at the particle horizon scale.Comment: 15 pages, accepted for publication in Classical and Quantum Gravity, typos correcte

Cauchy horizon singularity without mass inflation

A perturbed Reissner-Nordstr\"om-de Sitter solution is used to emphasize the nature of the singularity along the Cauchy horizon of a charged spherically symmetric black hole. For these solutions, conditions may prevail under which the mass function is bounded and yet the curvature scalar $R_{\alpha\beta\gamma\delta} R^{\alpha\beta\gamma\delta}$ diverges.Comment: typeset in RevTex, 13 page

Effects of Pair Creation on Charged Gravitational Collapse

We investigate the effects of pair creation on the internal geometry of a black hole, which forms during the gravitational collapse of a charged massless scalar field. Classically, strong central Schwarzschild-like singularity forms, and a null, weak, mass-inflation singularity arises along the Cauchy horizon, in such a collapse. We consider here the discharge, due to pair creation, below the event horizon and its influence on the {\it dynamical formation} of the Cauchy horizon. Within the framework of a simple model we are able to trace numerically the collapse. We find that a part of the Cauchy horizon is replaced by the strong space-like central singularity. This fraction depends on the value of the critical electric field, $E_{\rm cr}$, for the pair creation.Comment: LaTex, 27 pages, including 14 figures. Some points are clarified, typos corrected. Version accepted for publication in Phys.Rev.

Effectiveness of prehabilitation for patients undergoing orthopaedic surgery: protocol for a systematic review and meta-analysis.

INTRODUCTION: Undergoing major surgery can induce physical and functional decline. Prehabilitation programmes aim to improve physical fitness and function preoperatively and could enhance postoperative recovery and outcomes. Prehabilitation interventions have been utilised across a range of orthopaedic populations of all ages and can be multimodal in nature. The aim of this study is to evaluate the effectiveness of prehabilitation for patients undergoing orthopaedic surgery including day surgery procedures. It will also investigate the components of prehabilitation to understand optimum duration and frequency of programmes. METHODS/DESIGN: Systematic review and meta-analysis designed in accordance with Preferred Reporting Items for Systematic Review and Meta-Analysis Protocols. A comprehensive electronic search will be performed in MEDLINE, CINAHL, AMED, Embase, PEDro and Cochrane CENTRAL databases in order to identify randomised control trials published between January 2000 to 25 March 2019. ISI Web of Science, System for information on grey literature and the European Union clinical trials registry will identify studies that are underway or unpublished. Two independent reviewers will carry out the searches, study selection (title and abstract and full text stages), data extraction, risk of bias assessment (Cochrane Risk of Bias tool 2.0) and evaluation of overall strength of evidence. Meta-analyses will be used for data which demonstrates homogeneity, otherwise a narrative synthesis will be performed for groups of studies of high heterogeneity (I2 >50%). The overall strength of the body of evidence will be assessed using Grading of Recommendations Assessment, Development and Evaluation. ETHICS AND DISSEMINATION: This study raises no ethical issues. This study aims to identify the effectiveness of prehabilitation interventions and may assist clinicians in determining which components, duration, frequency and the method of delivery would form the most effective prehabilitation intervention for patients undergoing an orthopaedic surgical procedure. The findings will be disseminated through publication in a peer-reviewed journal and conference presentations. PROSPERO REGISTRATION NUMBER: CRD42019123268