Straighten out coordinates for volume-preserving actions

Archiv der Mathematik - In this short note we obtain a canonical form for commuting divergence-free vector fields.     

Influence of the Mg-content on the cation distribution in cubic MgxFe3−xO4 nanoparticles

The influence of the Mg-content on the structural and magnetic properties of cubic Mg_xFe_3−xO₄ nanoparticles prepared by combustion reaction was investigated using X-ray diffraction, transmission electron microscopy (TEM), Mössbauer spectroscopy, and Raman spectroscopy. Lattice parameter, nanoparticle size, and cation (Mg²⁺, Fe³⁺) distribution were quantified as a function of the Mg-content in the range 0.5≤x≤1.5. We found a mixed-like spinel structure at the smaller x-value end whereas the inverse-like spinel structure dominates samples with larger x-values. Moreover, in the x-value range investigated (0.5≤x≤1.5) we found no change in the quadrupole splitting and isomer shift values, though the hyperfine field decreases as the x-value increases. The splitting of the A_1g Raman mode was used to both quantify the Mg²⁺/Fe³⁺ contents in the tetrahedral site and obtain the cation distribution in the Mg_xFe_3−xO₄ structure. The cation distribution obtained from the Raman data is in very good agreement with the cation distribution obtained from the Mössbauer data.     

Preference modeling experiments with surrogate weighting procedures for the PROMETHEE method

One of the main tasks in a multi-criteria decision-making process is to define weights for the evaluation criteria. However, in many situations, the decision-maker (DM) may not be confident about defining specific values for these weights and may prefer to use partial information to represent the values of such weights with surrogate weights. Although for the additive model, the use of surrogate weighting procedures has been already explored in the literature, there is a gap with regard to experimenting with such kind of preference modeling in outranking based methods, such as PROMETHEE, for which there already are applications with surrogate weights in the literature. Thus, this paper presents an experimental study on preference modeling based on simulation so as to increase understanding and acceptance of a recommendation obtained when using surrogate weights within the PROMETHEE method. The main approaches to surrogate weights in the literature (EW, RS, RR and ROC) have been evaluated for choice and ranking problematics throughout statistical procedures, including Kendall's tau coefficient. The surrogate weighting procedure that most faithfully represents a DM's value system according to this analysis is the ROC procedure.     

Determination of cocaine and cocaethylene in urine by solid-phase microextraction and gas chromatography-mass spectrometry

In order to evaluate recent cocaine exposure or its coingestion with ethanol, a simple and sensitive solid-phase microextraction (SPME) procedure for determination of cocaine and cocaethylene in urine was developed and validated. A polydimethylsiloxane fibre (100 microm) was submersed in the urine sample for 20 min under magnetic stirring after alkalinization with solid buffer (NaHCO(3):K(2)CO(3), 2:1). Gas chromatography-mass spectrometry (GC-MS) was used to identify and quantify the analytes in selected ion monitoring mode (SIM). The limits of quantification were 5.0 ng/mL for both analytes. Good inter- and intra-assay precision was also observed (coefficient of variation <9%).     

Bosonization approach for bilayer quantum Hall systems at nu(T)=1

We develop a nonperturbative bosonization approach for bilayer quantum Hall systems at nu(T)=1, which allows us to systematically study the existence of an exciton condensate in these systems. An effective boson model is derived and the excitation spectrum is calculated in both the Bogoliubov and the Popov approximations. In the latter case, we show that the ground state of the system is an exciton condensate only when the distance between the layers is very small compared to the magnetic length, indicating that the system possibly undergoes another phase transition before the incompressible-compressible one. The effect of a finite electron interlayer tunneling is included and a quantitative phase diagram is proposed.     

Improved thermogravimetric system for processing of oil sludge using HY zeolite catalyst

The oil sludge residue presents an aggregate of hydrocarbons, organic and inorganic impurities, and water. The microporous and mesoporous zeolites are considered promising catalysts for processing of petroleum residues generated in refining processes. The aim of this work was to study the degradation of petroleum sludge obtained from primary processing, with applications of an improved thermogravimetry system and HY zeolite, at specific temperature ranges and degradation times, in order to obtain light gases and distillate fuels. The NaY zeolite was synthesized under hydrothermal treatment of a gel containing sodium silicate, sodium aluminate, and water. The obtained solid material was filtered, dried and calcined, and then ion-exchanged with ammonium chloride and calcined in order to obtain its protonic acid form (HY). The samples’ characterization by TG/DTG, XRD, and SEM proved that the crystalline structure of the faujasite zeolite was obtained. The thermal and catalytic degradation of the petroleum sludge was performed with 1.0 g of sample containing 10% of HY zeolite in the temperatures of 100, 200, 300, 400, and 500 °C, varying the time from 0 to 60 min to each temperature, using an oven with temperature program system, adapted with a Shimadzu precision balance. The curves obtained with this system evidenced that the presence of HY zeolite improves the degradation of the residue, with decreasing of the activation energy for the processes, as determined using the Arrhenius model.

     

Gravitational pressure,apparent horizon and thermodynamics of FLRW universe in the teleparallel gravity

In the context of the teleparallel equivalent of general relativity the concept of gravitational pressure and gravitational energy-momentum arisen in a natural way. In the case of a Friedmann–Lemaitre–Robertson–Walker space FLRW we obtain the total energy contained inside the apparent horizon and the radial pressure over the apparent horizon area. We use these definitions to written a thermodynamics relation \(T_{A}dS_{A} = dE_{A}+P_{A}dV_{A}\) at the apparent horizon, where \(E_{A}\) is the total energy inside the apparent horizon, \(V_{A}\) is the areal volume of the apparent horizon, \(P_{A}\) is the radial pressure over the apparent horizon area, \(S_{A}\) is the entropy which can be assumed as one quarter of the apparent horizon area only for a non stationary apparent horizon. We identify \(T_{A}\) as the temperature at the surface of the apparent horizon. We shown that for all expanding accelerated FLRW model of universe the radial pressure is positive.     

Stability conditions for fermionic Ising spin-glass models in the presence of a transverse field

The stability of a spin-glass (SG) phase is analyzed in detail for a fermionic Ising SG (FISG) model in the presence of a magnetic transverse field Γ. The fermionic path integral formalism, replica method and static approach have been used to obtain the thermodynamic potential within one step replica symmetry breaking ansatz. The replica symmetry (RS) results show that the SG phase is always unstable against the replicon. Moreover, the two other eigenvalues λ_± of the Hessian matrix (related to the diagonal elements of the replica matrix) can indicate an additional instability to the SG phase, which enhances when Γ is increased. Therefore, this result suggests that the study of the replicon cannot be enough to guarantee the RS stability in the present quantum FISG model, especially near the quantum critical point. In particular, the FISG model allows changing the occupation number of sites, so one can get a first order transition when the chemical potential exceeds a certain value. In this region, the replicon and the λ_± indicate instability problems for the SG solution close to all ranges of a first order boundary.     

Staggered-vortex superfluid of ultracold bosons in an optical lattice

We show that the dynamics of cold bosonic atoms in a two-dimensional square optical lattice produced by a bichromatic light-shift potential is described by a Bose-Hubbard model with an additional effective staggered magnetic field. In addition to the known uniform superfluid and Mott insulating phases, the zero-temperature phase diagram exhibits a novel kind of finite-momentum superfluid phase, characterized by a quantized staggered rotational flux. An extension for fermionic atoms leads to an anisotropic Dirac spectrum, which is relevant to graphene and high-T(c) superconductors.