Primordial black hole formation in the early universe: critical behaviour and self-similarity

Following on after three previous papers discussing the formation of primordial black holes during the radiative era of the early universe, we present here a further investigation of the critical nature of the process involved, aimed at making contact with some of the basic underlying ideas from the literature on critical collapse. We focus on the intermediate state, which we have found appearing in cases with perturbations close to the critical limit, and examine the connection between this and the similarity solutions which play a fundamental role in the standard picture of critical collapse. We have derived a set of self-similar equations for the null-slicing form of the metric which we are using for our numerical calculations, and have then compared the results obtained by integrating these with the ones coming from our simulations for collapse of cosmological perturbations within an expanding universe. We find that the similarity solution is asymptotically approached in a region which grows to cover both the contracting matter and part of the semi-void which forms outside it. Our main interest is in the situation relevant for primordial black hole formation in the radiative era of the early universe, where the relation between the pressure $p$ and the energy density $e$ can be reasonably approximated by an expression of the form $p = we$ with $w=1/3$. However, we have also looked at other values of $w$, both because these have been considered in previous literature and also because they can be helpful for giving further insight into situations relevant for primordial black hole formation. As in our previous work, we have started our simulations with initial supra-horizon scale perturbations of a type which could have come from inflation.Comment: 23 pages, 8 figures, new abstract, submitted to Classical and Quantum Gravity. This new version of the paper has been completely rewritten with respect the previous one, with several changes and substantial additional wor

Causal Nature and Dynamics of Trapping Horizons in Black Hole Collapse

In calculations of gravitational collapse to form black holes, trapping horizons (foliated by marginally trapped surfaces) make their first appearance either within the collapsing matter or where it joins on to a vacuum exterior. Those which then move outwards with respect to the matter have been proposed for use in defining black holes, replacing the global concept of an "event horizon" which has some serious drawbacks for practical applications. We here present results from a study of the properties of both outgoing and ingoing trapping horizons, assuming strict spherical symmetry throughout. We have investigated their causal nature (i.e. whether they are spacelike, timelike or null), making contact with the Misner-Sharp- Hernandez formalism, which has often been used for numerical calculations of spherical collapse. We follow two different approaches, one using a geometrical quantity related to expansions of null geodesic congruences, and the other using the horizon velocity measured with respect to the collapsing matter. After an introduction to these concepts, we then implement them within numerical simulations of stellar collapse, revisiting pioneering calculations from the 1960s where some features of the emergence and subsequent behaviour of trapping horizons could already be seen. Our presentation here is aimed firmly at "real world" applications of interest to astrophysicists and includes the effects of pressure, which may be important for the asymptotic behaviour of the ingoing horizon.Comment: 33 pages, 11 figure

Assessing urban system vulnerabilities to flooding to improve resilience and adaptation in spatial planning

Fluvial, pluvial and coastal flooding are the most frequent and costly natural hazard. Cities are social hubs and life in cities is reliant on a number of services and functions such as housing, healthcare, education and other key daily facilities. Urban flooding can cause significant disruption to these services and wider impacts on the population. These impacts may be short or long with a variably spatial scale: urban systems are spatially distributed and the nature of this can have significant effects on flood impacts. From an urban-planning perspective, measuring this disruption and its consequences is fundamental in order to develop more resilient cities. Whereas the assessment of physical vulnerabilities and direct damages is commonly addressed, new methodologies for assessing the systemic vulnerability and indirect damages at the urban scale are required. The proposed systemic approach recognizes the city as a collection of sub-systems or functional units (such as neighborhoods and suburbs), interconnected through the road network, providing key daily services to inhabitants (e.g., healthcare facilities, schools, food shops, leisure and cultural services). Each city is part of broader systems—which may or may not match administrative boundaries—and, as such, needs to be connected to its wider surroundings in a multi-scalar perspective. The systemic analysis, herein limited to residential households, is based on network-accessibility measures and evaluates the presence, the distribution among urban units and the redundancy of key daily services. Trying to spatially sketch the existence of systemic interdependences between neighborhoods, suburbs and municipalities, the proposed method highlights how urban systemic vulnerability spreads beyond the flooded areas. The aim is to understand which planning patterns and existing mixed-use developments are more flood resilient, thereby informing future urban development and regeneration projects. The methodology has been developed based on GIS and applied to an Italian municipality (Noale) in the metropolitan area of Venice, NE Italy

Behavioural responses of the colonial sea squirt botrylloides violaceus oka to suspended food micro‐ particles in laboratory cultures

Violet sea squirts are noteworthy model organisms, because they provide insights into various physiologic processes, including cell senescence, ageing, apoptosis and allorecognition. Consequently, their culture is critical to permit experimental studies. Most papers refer to short periods of rearing using various feeds, both living and conserved, missing a formal justification for their use or indications of their actual nutritional value. Here, we use two behavioural responses— the percentage of open siphons and the frequency of zooid contractions—as compared to the abundance of suspended microparticles during feeding tests, to identify feeds able to promote filter-feeding. The results will enable to formulate compound diets that maximise positive physiological responses. Our tests demonstrated that plant items, such as dry microalgae and cyanobacteria (Arthrospira platensis, commercially known as Spirulina), along with living planktonic Haptophyta (Isochrysis galbana), trigger clear positive reactions, represented by a higher frequency of zooid contractions and larger proportions of open siphons. These responses correspond to decreases in the concentrations of suspended microparticles during the experiment and indicate higher filter-feeding activity. In contrast, feeds commonly administered to colonies, such as milk powder, dried eggs and artificial plankton, triggered negative behavioural responses, and their intake was lower during the feeding trials

Critical Phenomena in Neutron Stars I: Linearly Unstable Nonrotating Models

We consider the evolution in full general relativity of a family of linearly unstable isolated spherical neutron stars under the effects of very small, perturbations as induced by the truncation error. Using a simple ideal-fluid equation of state we find that this system exhibits a type-I critical behaviour, thus confirming the conclusions reached by Liebling et al. [1] for rotating magnetized stars. Exploiting the relative simplicity of our system, we are able carry out a more in-depth study providing solid evidences of the criticality of this phenomenon and also to give a simple interpretation of the putative critical solution as a spherical solution with the unstable mode being the fundamental F-mode. Hence for any choice of the polytropic constant, the critical solution will distinguish the set of subcritical models migrating to the stable branch of the models of equilibrium from the set of subcritical models collapsing to a black hole. Finally, we study how the dynamics changes when the numerically perturbation is replaced by a finite-size, resolution independent velocity perturbation and show that in such cases a nearly-critical solution can be changed into either a sub or supercritical. The work reported here also lays the basis for the analysis carried in a companion paper, where the critical behaviour in the the head-on collision of two neutron stars is instead considered [2].Comment: 15 pages, 9 figure

Mener des démarches d'enquête et de conceptualisation en univers social au primaire

Titin, also known as connectin, is a giant modular protein specifically found in vertebrate striated muscle. Since the huge size of titin does not allow a direct structure determination, we have started a long-term project to characterize the protein by cutting it into smaller domains or structural units. The major part of the titin sequence is assembled by modules approximately 100 amino acids long that belong to two major protein superfamilies. Most of these modules are linked together by stretches of variable length with unique sequence. No direct structural characterization has been achieved so far for any of these linkers. We present here a study of a stretch located in the titin N-terminus and part of a linker between two modules. Our attention was drawn toward this region because it shows 100% probability to form a coiled coil when analyzed by a prediction program. A synthetic 38 amino acid peptide spanning such a sequence was studied in aqueous solution by circular dichroism, nuclear magnetic resonance, and analytical ultracentrifugation at various pH, salt, and peptide concentrations. Under all conditions, it shows a strong tendency to form alpha-helical structures. In the presence of salt, this conformation is associated with the formation of helical bundles below pH 5. Above pH 5, any aggregate breaks, and the titin peptide is a monomeric helix in equilibrium with its random coil conformation. We discuss the factors which stabilize the helical conformation and the possible role of this stretch in vivo