A unification in the theory of linearization of second order nonlinear ordinary differential equations

In this letter, we introduce a new generalized linearizing transformation (GLT) for second order nonlinear ordinary differential equations (SNODEs). The well known invertible point (IPT) and non-point transformations (NPT) can be derived as sub-cases of the GLT. A wider class of nonlinear ODEs that cannot be linearized through NPT and IPT can be linearized by this GLT. We also illustrate how to construct GLTs and to identify the form of the linearizable equations and propose a procedure to derive the general solution from this GLT for the SNODEs. We demonstrate the theory with two examples which are of contemporary interest.Comment: 8 page

Stellar populations in superclusters of galaxies

A catalogue of superclusters of galaxies is used to investigate the influence of the supercluster environment on galaxy populations, considering galaxies brighter than M$_r<$-21+5$\log$ h. Empirical spectral synthesis techniques are applied to obtain the stellar population properties of galaxies which belong to superclusters and representative values of stellar population parameters are attributed to each supercluster. We show that richer superclusters present denser environments and older stellar populations. The galaxy populations of superclusters classified as filaments and pancakes are statistically similar, indicating that the morphology of superclusters does not have a significative influence on the stellar populations. Clusters of galaxies within superclusters are also examined in order to evaluate the influence of the supercluster environment on their galaxy properties. Our results suggest that the environment affects galaxy properties but its influence should operate on scales of groups and clusters, more than on the scale of superclusters.Comment: 7 pages, 4 figures; accepted to MNRA

Solving 1ODEs with functions

Here we present a new approach to deal with first order ordinary differential equations (1ODEs), presenting functions. This method is an alternative to the one we have presented in [1]. In [2], we have establish the theoretical background to deal, in the extended Prelle-Singer approach context, with systems of 1ODEs. In this present paper, we will apply these results in order to produce a method that is more efficient in a great number of cases. Directly, the solving of 1ODEs is applicable to any problem presenting parameters to which the rate of change is related to the parameter itself. Apart from that, the solving of 1ODEs can be a part of larger mathematical processes vital to dealing with many problems.Comment: 31 page

Explaining Jupiter's magnetic field and equatorial jet dynamics

Spacecraft data reveal a very Earth-like Jovian magnetic field. This is surprising since numerical simulations have shown that the vastly different interiors of terrestrial and gas planets can strongly affect the internal dynamo process. Here we present the first numerical dynamo that manages to match the structure and strength of the observed magnetic field by embracing the newest models for Jupiter's interior. Simulated dynamo action primarily occurs in the deep high electrical conductivity region while zonal flows are dynamically constrained to a strong equatorial jet in the outer envelope of low conductivity. Our model reproduces the structure and strength of the observed global magnetic field and predicts that secondary dynamo action associated to the equatorial jet produces banded magnetic features likely observable by the Juno mission. Secular variation in our model scales to about 2000 nT per year and should also be observable during the one year nominal mission duration.Comment: 7 pages, 4 figures, accepted for publication in Geophysical Research Letter

A Method to Tackle First Order Differential Equations with Liouvillian Functions in the Solution - II

We present a semi-decision procedure to tackle first order differential equations, with Liouvillian functions in the solution (LFOODEs). As in the case of the Prelle-Singer procedure, this method is based on the knowledge of the integrating factor structure.Comment: 11 pages, late

Constraining Elko Dark Matter at the LHC with Monophoton Events

A mass dimension one fermion, also known as Elko, constitutes a dark matter candidate which might interact with photons at the tree level in a specific fashion. In this work, we investigate the constraints imposed by unitarity and LHC data on this type of interactions using the search for new physics in monophoton events. We found that Elkos which can explain the dark matter relic abundance mainly through electromagnetic interactions are excluded at the 95\%CL by the 8 TeV LHC data for masses up to 1 TeV.Comment: 6 pages, 4 figure

Liquid mixtures involving fluorinated alcohols: The equation of state (p, r, T, x) of (Ethanol + Trifluoroethanol) Experimental and Simulation

Liquid mixtures involving fluorinated alcohols: The equation of state (p, r, T, x) of (Ethanol + Trifluoroethanol) Experimental and Simulation Pedro Duartea, Djêide Rodriguesa, Marcelo Silvaa, Pedro Morgadoa, Luís Martinsa,b and Eduardo J. M. Filipea* aCentro de Química Estrutural, Instituto Superior Técnico, 1049-001 Lisboa, Portugal bCentro de Química de Évora, Universidade de Évora, 7000-671 Évora, Portugal Fluorinated alcohols are substances with unique properties and high technological value in the pharmaceutical and chemical industries. Trifluoroethanol (TFE), in particular, displays a number of unusual properties as a solvent. For example, it dissolves nylon at room temperature and is effectively used as solvent in bioengineering. The presence of the three fluorines atoms gives the alcohol a high ionization constant, strong hydrogen bonding capability and stability at high temperatures. In the pharmaceutical industry, TFE finds use as the major raw material for the production of inhalation anesthetics. Mixtures of TFE and water (known as Fluorinols®) are used as working fluids for Rankine cycle heat engines for terrestrial and space applications, as a result of a unique combination of physical and thermodynamic properties such as high thermal efficiency and excellent turbine expansion characteristics. Environmentally, TFE is a CFC substitute with an acceptable short lifetime and with small ozone depletion potential. Additionally, TFE is known to induce conformational changes in proteins and it is used as a co-solvent to analyze structural features of partially folded states. The (ethanol + TFE) system displays an interesting and peculiar behaviour, combining a negative azeotrope with high positive excess volumes. In this work, liquid mixtures of (ethanol + TFE) were investigated. The densities of the mixtures were measured as a function of composition between 278K and 338K and at pressures up to 700 bar. The corresponding excess volumes as a function of temperature and pressure, the isothermal compressibilities and thermal expansivities were calculated from the experimental results. The mixtures are highly non-ideal with excess volumes ranging from 0.8 - 1.0 cm3mol-1. Finally, molecular dynamic simulations were performed to model and interpret the experimental results. The Trappe force field was used to simulate the (TFE + ethanol) mixtures and calculate the corresponding excess volumes. The simulation results are able to reproduce the correct sign and order of magnitude of the experimental VE without fitting to the experimental data. Furthermore, the simulations suggest the presence of a particular type of hydrogen bridge between ethanol and TFE, that can help to rationalize the experimental results

Retired galaxies: not to be forgotten in the quest of the star formation -- AGN connection

We propose a fresh look at the Main Galaxy Sample of the Sloan Digital Sky Survey by packing the galaxies in stellar mass and redshift bins. We show how important it is to consider the emission-line equivalent widths, in addition to the commonly used emission-line ratios, to properly identify retired galaxies (i.e. galaxies that have stopped forming stars and are ionized by their old stellar populations) and not mistake them for galaxies with low-level nuclear activity. We find that the proportion of star-forming galaxies decreases with decreasing redshift in each mass bin, while that of retired galaxies increases. Galaxies with $M_\star > 10^{11.5} M_\odot$ have formed all their stars at redshift larger than 0.4. The population of AGN hosts is never dominant for galaxy masses larger than $10^{10} M_\odot$. We warn about the effects of stacking galaxy spectra to discuss galaxy properties. We estimate the lifetimes of active galactic nuclei (AGN) relying entirely on demographic arguments --- i.e. without any assumption on the AGN radiative properties. We find upper-limit lifetimes of about 1--5 Gyr for detectable AGN in galaxies with masses between $10^{10}$--$10^{12} M_\odot$. The lifetimes of the AGN-dominated phases are a few $10^8$ yr. Finally, we compare the star-formation histories of star-forming, AGN and retired galaxies as obtained by the spectral synthesis code STARLIGHT. Once the AGN is turned on it inhibits star formation for the next $\sim$ 0.1 Gyr in galaxies with masses around $10^{10} M_\odot$, $\sim$ 1 Gyr in galaxies with masses around $10^{11} M_\odot$.Comment: accepted for MNRAS figure resolution has been degraded with respect to what will be published in MNRA