Blow-up profile of rotating 2D focusing Bose gases

We consider the Gross-Pitaevskii equation describing an attractive Bose gas trapped to a quasi 2D layer by means of a purely harmonic potential, and which rotates at a fixed speed of rotation $\Omega$. First we study the behavior of the ground state when the coupling constant approaches $a\_*$ , the critical strength of the cubic nonlinearity for the focusing nonlinear Schr{\"o}dinger equation. We prove that blow-up always happens at the center of the trap, with the blow-up profile given by the Gagliardo-Nirenberg solution. In particular, the blow-up scenario is independent of $\Omega$, to leading order. This generalizes results obtained by Guo and Seiringer (Lett. Math. Phys., 2014, vol. 104, p. 141--156) in the non-rotating case. In a second part we consider the many-particle Hamiltonian for $N$ bosons, interacting with a potential rescaled in the mean-field manner $--a\_N N^{2\beta--1} w(N^{\beta} x), with$w$a positive function such that$\int\_{\mathbb{R}^2} w(x) dx = 1$. Assuming that$\beta < 1/2$and that$a\_N \to a\_*$sufficiently slowly, we prove that the many-body system is fully condensed on the Gross-Pitaevskii ground state in the limit$N \to \infty$

Occupation times of long-range exclusion and connections to KPZ class exponents

With respect to a class of long-range exclusion processes on \ZZ^d, with single particle transition rates of order $|\cdot|^{-(d+\alpha)}$, starting under Bernoulli invariant measure $\nu_\rho$ with density $\rho$, we consider the fluctuation behavior of occupation times at a vertex and more general additive functionals. Part of our motivation is to investigate the dependence on $\alpha$, $d$ and $\rho$ with respect to the variance of these functionals and associated scaling limits. In the case the rates are symmetric, among other results, we find the scaling limits exhaust a range of fractional Brownian motions with Hurst parameter $H\in [1/2,3/4]$. However, in the asymmetric case, we study the asymptotics of the variances, which when $d=1$ and $\rho=1/2$ points to a curious dichotomy between long-range strength parameters $03/2$. In the former case, the order of the occupation time variance is the same as under the process with symmetrized transition rates, which are calculated exactly. In the latter situation, we provide consistent lower and upper bounds and other motivations that this variance order is the same as under the asymmetric short-range model, which is connected to KPZ class scalings of the space-time bulk mass density fluctuations.The research of CB was supported in part by the French Ministry of Education through the grant ANR JCJC EDNHS. PG thanks FCT (Portugal) for support through the research project PTDC/MAT/109844/2009 and CNPq (Brazil) for support through the research project 480431/2013-2. PG thanks CMAT for support by "FEDER" through the "Programa Operacional Factores de Competitividade COMPETE" and by FCT through the project PEst-C/MAT/UI0013/2011. SS was supported in part by ARO grant W911NF-14-1-0179

Other-Condemning Anger = Blaming Accountable Agents for Frustrated Intentions

National audienceThis paper provides a formalization of the other-condemning anger emotion which is a social type of anger triggered by the behaviour of other agents. Other-condemning anger responds to frustration of committed goals by others, and motivates goal-congruent behavior towards the blameworthy agents. Understanding this type of anger is crucial for modelling human behavior in social settings as well as designing socially aware artificial systems. We utilize existing psychological theories on other-condemning anger and propose a logical framework to formally specify this emotion. The logical framework is based on dynamic multi-agent logic with graded cognitive attitudes

How much time? Indigenous status and the sentenced imprisonment term decision in New South Wales

Using administrative data from the higher and lower courts of New South Wales, this study examines whether Indigeneity: (a) exerts a direct effect on length of imprisonment term once other relevant sentencing variables are taken into account; (b) interacts with other relevant sentencing variables to influence prison length. Results show that being Indigenous significantly reduces the length of sentenced prison term in the lower courts but has no significant effect at the higher court level. Further, evidence of interactive effects by Indigenous status was scant. Only age differed significantly between Indigenous and non-Indigenous offenders at both court levels. In this case age had no effect on the length of sentence imposed on Indigenous defendants in the lower courts or higher courts but increased sentence length for non-Indigenous offenders at both court levels.No Full Tex