A numerical fit of analytical to simulated density profiles in dark matter haloes

Analytical and geometrical properties of generalized power-law (GPL) density profiles are investigated in detail. In particular, a one-to-one correspondence is found between mathematical parameters and geometrical parameters. Then GPL density profiles are compared with simulated dark haloes (SDH) density profiles, and nonlinear least-absolute values and least-squares fits involving the above mentioned five parameters (RFSM5 method) are prescribed. More specifically, the sum of absolute values or squares of absolute logarithmic residuals is evaluated on a large number of points making a 5-dimension hypergrid, through a few iterations. The size is progressively reduced around a fiducial minimum, and superpositions on nodes of earlier hypergrids are avoided. An application is made to a sample of 17 SDHs on the scale of cluster of galaxies, within a flat $\Lambda$CDM cosmological model (Rasia et al. 2004). In dealing with the mean SDH density profile, a virial radius, averaged over the whole sample, is assigned, which allows the calculation of the remaining parameters. Using a RFSM5 method provides a better fit with respect to other methods. No evident correlation is found between SDH dynamical state (relaxed or merging) and asymptotic inner slope of the logarithmic density profile or (for SDH comparable virial masses) scaled radius. Mean values and standard deviations of some parameters are calculated, and a comparison with previous results is made with regard to the scaled radius. A certain degree of degeneracy is found in fitting GPL to SDH density profiles. If it is intrinsic to the RFSM5 method or it could be reduced by the next generation of high-resolution simulations, still remains an open question.Comment: 44 pages, 6 figures, updated version with recent results from high-resolution simulations (Diemand et al. 2004; Reed et al. 2005) included in the discussion; accepted for publication on SAJ (Serbian Astronomical Journal

Dark matter haloes: an additional criterion for the choice of fitting density profiles

Simulated dark matter haloes are fitted by self-similar, universal density profiles, where the scaled parameters depend only on a scaled (truncation) radius which, in turn, is supposed to be independent on the mass and the formation redshift. A criterion for the choice of the best fitting density profile is proposed, with regard to a set of high-resolution simulations, where some averaging procedure on scaled density profiles has been performed, in connection with a number of fitting density profiles. An application is made to a pair of sets each made of a dozen of high-resolution simulations, which are available in literature, in connection with two currently used fitting density profiles, where the dependence of the scaled radius on the mass and the formation redshift, may be neglected to a first extent. Some features of the early evolution of dark matter haloes represented by fitting density profiles, are discussed in the limit of the spherical top-hat model.Comment: 62 pages, 9 figures, accepted for publication on SAJ (Serbian Astronomical Journal), paragraph and reference added for section

The Schwinger Representation of a Group: Concept and Applications

The concept of the Schwinger Representation of a finite or compact simple Lie group is set up as a multiplicity-free direct sum of all the unitary irreducible representations of the group. This is abstracted from the properties of the Schwinger oscillator construction for SU(2), and its relevance in several quantum mechanical contexts is highlighted. The Schwinger representations for $SU(2), SO(3)$ and SU(n) for all $n$ are constructed via specific carrier spaces and group actions. In the SU(2) case connections to the oscillator construction and to Majorana's theorem on pure states for any spin are worked out. The role of the Schwinger Representation in setting up the Wigner-Weyl isomorphism for quantum mechanics on a compact simple Lie group is brought out.Comment: Latex, 17 page

Non-symplectic symmetries and bi-Hamiltonian structures of the rational Harmonic Oscillator

The existence of bi-Hamiltonian structures for the rational Harmonic Oscillator (non-central harmonic oscillator with rational ratio of frequencies) is analyzed by making use of the geometric theory of symmetries. We prove that these additional structures are a consequence of the existence of dynamical symmetries of non-symplectic (non-canonical) type. The associated recursion operators are also obtained.Comment: 10 pages, submitted to J. Phys. A:Math. Ge

FORMAÇÃO E REMOÇÃO DE TRIHALOMETANOS EM ÁGUAS DE ABASTECIMENTO TRATADAS, NA PRÉOXIDAÇÃO, COM CLORO.

A presente pesquisa avaliou, em escala de laboratório, a formação de trihalometanos (THM) produzidos em reações de oxidação, com cloro livre, de amostras de água contendo ácidos húmicos, sob diferentes concentrações e tempos de contato. O estudo também abrangeu a presença do íon brometo, como forma de se avaliar, qualitativa e quantitativamente, as diferentes espécies de THM produzidas. A detecção dos trihalometanos formados foi realizada, comparativamente, através de duas técnicas analíticas. A cromatografia gasosa, indicada para a análise de tais moléculas, permitiu a quantificação dos compostos clorofórmio, diclorobromometano, dibromoclorometano e bromofórmio. A espectrofotometria foi avaliada como metodologia alternativa à primeira, permitindo a expressão dos resultados apenas em THM totais. Foram realizados ensaios de remoção de THM por adsorção em diferentes concentrações de carvão ativado em pó (CAP), seguido de processos de coagulação com sulfato de alumínio, floculação, sedimentação e filtração, em reatores estáticos. Os resultados obtidos indicaram que a formação de THM é diretamente proporcional às concentrações de cloro, ácidos húmicos, íon brometo e ao tempo de contato das reações. Os procedimentos de adsorção em CAP, seguido de processos convencionais de tratamento de água, demonstraram remoções de THM das amostras da ordem de até 89%. O aumento da concentração de CAP de 10 para 150 mg/L, e do tempo de contato de adsorção de 60 para 120 minutos, contribuiu para os melhores desempenhos nos experimentos realizados. As técnicas de detecção de THM por cromatografia gasosa e por espectrofotometria apresentaram resultados diferentes nas condições destes ensaioOrientador: Prof. Dr. Rubens Bresaola Júnior

Abandoned places, complexes and parts of cities. Regeneration and enhancement of monumental hospitals in the historic centre of Naples

Even before Covid - 19 although in the very center of the old town and historic center of Naples there were abandoned buildings and complexes, uninhabited and unused for decades. The cause is attributed to multiple reasons such as functional obsolescence, failure to adapt to intervening European standards in terms of hospital construction, technological facilities to standards, etc. The health crisis which strongly affected European societies revealed the fragilities of our healthcare systems. In Italy, a large number of COVID-19 patients congested hospitals while the continuity of essential services was interrupted at the expense of other needs. At the same time, the process of abandonment of historic buildings affects different monumental hospitals, such as the “San Giacomo degli Incurabili” and the “Carlo Forlanini” in Rome, or the “Gesù e Maria” Hospital, “San Gennaro dei Poveri” and the “Santa Maria del Popolo degli Incurabili” in Naples. This paper reports three case studies of Neapolitan historical hospitals regeneration proposals with the goal of strengthening the existing community healthcare system and developing energy efficiency and seismic improvement strategies in the spirit of sustainable development. Leveraging the flexibility of monumental hospitals, the proposed light retrofit interventions restore the historial healthcare functional destination ensuring also the reuse of such an heritage. The current research delineates an approach to the recovery and enhancement for social and cultural purposes of unused and abandoned historical hospitals. This approach can positively affect the quality of life of citizens and the use of health services, while recovering historical cultural heritage buildings

A variational principle for volume-preserving dynamics

We provide a variational description of any Liouville (i.e. volume preserving) autonomous vector fields on a smooth manifold. This is obtained via a ``maximal degree'' variational principle; critical sections for this are integral manifolds for the Liouville vector field. We work in coordinates and provide explicit formulae

Hamilton-Jacobi Theory and Information Geometry

Recently, a method to dynamically define a divergence function $D$ for a given statistical manifold $(\mathcal{M}\,,g\,,T)$ by means of the Hamilton-Jacobi theory associated with a suitable Lagrangian function $\mathfrak{L}$ on $T\mathcal{M}$ has been proposed. Here we will review this construction and lay the basis for an inverse problem where we assume the divergence function $D$ to be known and we look for a Lagrangian function $\mathfrak{L}$ for which $D$ is a complete solution of the associated Hamilton-Jacobi theory. To apply these ideas to quantum systems, we have to replace probability distributions with probability amplitudes.Comment: 8 page

Qubit-portraits of qudit states and quantum correlations

The machinery of qubit-portraits of qudit states, recently presented, is consider here in more details in order to characterize the presence of quantum correlations in bipartite qudit states. In the tomographic representation of quantum mechanics, Bell-like inequalities are interpreted as peculiar properties of a family of classical joint probability distributions which describe the quantum state of two qudits. By means of the qubit-portraits machinery a semigroup of stochastic matrices can be associated to a given quantum state. The violation of the CHSH inequalities is discussed in this framework with some examples, we found that quantum correlations in qutrit isotropic states can be detected by the suggested method while it cannot in the case of qutrit Werner states.Comment: 12 pages, 4 figure