The formation of CDM haloes II: collapse time and tides

We use two cosmological simulations of structure formation in the LambdaCDM scenario to study the evolutionary histories of dark-matter haloes and to characterize the Lagrangian regions from which they form. We focus on haloes identified at redshift z_id=0 and show that the classic ellipsoidal collapse model systematically overestimates their collapse times. If one imposes that halo collapse takes place at z_id, this model requires starting from a significantly lower linear density contrast than what is measured in the simulations at the locations of halo formation. We attempt to explain this discrepancy by testing two key assumptions of the model. First, we show that the tides felt by collapsing haloes due to the surrounding large-scale structure evolve non-linearly. Although this effect becomes increasingly important for low-mass haloes, accounting for it in the ellipsoidal collapse model only marginally improves the agreement with N-body simulations. Second, we track the time evolution of the physical volume occupied by forming haloes and show that, after turnaround, it generally stabilizes at a well-defined redshift, z_c>z_id, contrary to the basic assumption of extended Press-Schechter theory based on excursion sets. We discuss the implications of this result for understanding the origin of the mass-dependence and scatter in the linear threshold for halo formation. Finally, we show that, when tuned for collapse at z_c, a modified version of the ellipsoidal collapse model that also accounts for the triaxial nature of protohaloes predicts their linear density contrast in an unbiased way.Comment: 15 pages, 11 figures, MNRAS in pres

Article 14 of the Universal Declaration of Human Rights, Africa and the non-application of the verb ‘enjoy’?

My contribution focuses on Article 14 of the Universal Declaration of Human Rights (UDHR) on the right ‘to seek and to enjoy […] asylum’ (14(1)) –subject to exceptions (14(2)) and how this right has been translated into the domestic legislation of African countries and is applied into practice. This is because the correct application of this article by states would help to construct and develop a better future for refugees in Africa. The first regional legal instrument to adopt a formula similar to Article 14 is the African Charter on Human and Peoples’ Rights (Banjul Charter), whose Article 12(3), recalls the right enshrined in Article 14(1) of the UDHR, which stipulates that every individual persecuted shall have the right of ‘seeking and obtaining asylum’. Although the second verb used (after ‘seeking’) is different, it is clear that the ‘attainment’ of the right mentioned in Article 12(3) of the Banjul Charter seems in some way preparatory to the ‘enjoyment’ of the same right mentioned in Article 14(1). Thus, I analyse the theory and practice of refugee law in Africa to discover if there is a piece of sub-regional and/or domestic legislation and/or one or more adjudicated cases/s on the continent where the right to ‘enjoy’ asylum has been reaffirmed in a way that renders the UDHR applicable in this regard. Linked to this argument I also reflect whether political shifts caused by decolonization have given rise to a real, non-imperial world, in the way that refugee law in Africa would reflect changes in political systems. This is order to better assess if the enjoyment of asylum is concrete on the continent. In converse, I am also wondering whether decolonization is a perpetually unfinished process since the goal of achieving sovereignty is contingent beyond the powers of the African state. This is because it is clear that, if my response to the above question will be positive, I could not be surprised if the attainment of the right to enjoy asylum is substantially not practicable in Africa

The braking index of millisecond magnetars

We make the first measurement of the braking index $n$ of two putative millisecond magnetars born in short gamma-ray bursts. We measure $n=2.9\pm0.1$ and $n=2.6\pm0.1$ for millisecond magnetars born in GRB 130603B and GRB 140903A respectively. The neutron star born in GRB 130603B has the only known braking index consistent with the fiducial $n=3$ value. This value is ruled out with 99.95\% confidence for GRB 140903A. We discuss possible causes of $n<3$ braking indices in millisecond magnetars, showing that several models can account for the measurement of the braking index in GRB 140903A, while it is more difficult to account for a braking index consistent with $n=3$.Comment: ApJ

Perturbation of matrices and non-negative rank with a view toward statistical models

In this paper we study how perturbing a matrix changes its non-negative rank. We prove that the non-negative rank is upper-semicontinuos and we describe some special families of perturbations. We show how our results relate to Statistics in terms of the study of Maximum Likelihood Estimation for mixture models.Comment: 13 pages, 3 figures. A theorem has been rewritten, and some improvements in the presentations have been implemente

The AU Convention on Refugees and the Concept of Asylum

This article analyzes several specific aspects of the current refugee legal regime in Sub-Saharan Africa in order to assess how the institution of asylum, considered the traditional solution for both individuals and groups who are obliged to flee their countries of citizenship, is legally perceived and applied. The analysis will focus on the 1969 African Union Convention Governing the Specific Aspects of Refugee Problems in Africa, the pillar for refugee protection in SSA and considered the most generous and flexible international agreement on refugee protection

Quantum squeezing generation versus photon localization in a disordered microcavity

We investigate theoretically the nonlinear dynamics induced by an intense pump field in a disordered planar microcavity. Through a self-consistent theory, we show how the generation of quantum optical noise squeezing is affected by the breaking of the in-plane translational invariance and the occurrence of photon localization. We find that the generation of single-mode Kerr squeezing for the ideal planar case can be prevented by disorder as a result of multimode nonlinear coupling, even when the other modes are in the vacuum state. However, the excess noise is a non-monotonous function of the disorder amplitude. In the strong localization limit, we show that the system becomes protected with respect to this fundamental coupling mechanism and that the ideal quadrature squeezing generation can be obtained

Stochastic properties of systems controlled by autocatalytic reactions II

We analyzed the stochastic behavior of systems controlled by autocatalytic reaction A+X -> X+X, X+X -> A+X, X -> B provided that the distribution of reacting particles in the system volume is uniform, i.e. the point model of reaction kinetics introduced in arXiv:cond-mat/0404402 can be applied. Assuming the number of substrate particles A to be kept constant by a suitable reservoir, we derived the forward Kolmogorov equation for the probability of finding n=0,1,... autocatalytic particles X in the system at a given time moment. We have shown that the stochastic model results in an equation for the mean value of autocatalytic particles X which differs strongly from the kinetic rate equation. It has been found that not only the law of the mass action is violated but also the bifurcation point is disappeared in the well-known diagram of X particle- vs. A particle-concentration. Therefore, speculations about the role of autocatalytic reactions in processes of the "natural selection" can be hardly supported.Comment: 17 pages, 6 figure