Exterior and interior metrics with quadrupole moment

We present the Ernst potential and the line element of an exact solution of Einstein’s vacuum field equations that contains as arbitrary parameters the total mass, the angular momentum, and the quadrupole moment of a rotating mass distribution. We show that in the limiting case of slowly rotating and slightly deformed configuration, there exists a coordinate transformation that relates the exact solution with the approximate Hartle solution. It is shown that this approximate solution can be smoothly matched with an interior perfect fluid solution with physically reasonable properties. This opens the possibility of considering the quadrupole moment as an additional physical degree of freedom that could be used to search for a realistic exact solution, representing both the interior and exterior gravitational field generated by a self-gravitating axisymmetric distribution of mass of perfect fluid in stationary rotation.     

Reversibly Switchable Fluorescent Molecular Systems Based on Metallacarborane–Perylenediimide Conjugates

Icosahedral metallacarboranes are θ-shaped anionic molecules in which two icosahedra share one vertex that is a metal center. The most remarkable of these compounds is the anionic cobalt-based metallacarborane [Co(C₂B₉H₁₁)₂]⁻, whose oxidation-reduction processes occur via an outer sphere electron process. This, along with its low density negative charge, makes [Co(C₂B₉H₁₁)₂]⁻ very appealing to participate in electron-transfer processes. In this work, [Co(C₂B₉H₁₁)₂]⁻ is tethered to a perylenediimide dye to produce the first examples of switchable luminescent molecules and materials based on metallacarboranes. In particular, the electronic communication of [Co(C₂B₉H₁₁)₂]⁻ with the appended chromophore unit in these compounds can be regulated upon application of redox stimuli, which allows the reversible modulation of the emitted fluorescence. As such, they behave as electrochemically-controlled fluorescent molecular switches in solution, which surpass the performance of previous systems based on conjugates of perylendiimides with ferrocene. Remarkably, they can form gels by treatment with appropriate mixtures of organic solvents, which result from the self-assembly of the cobaltabisdicarbollide-perylendiimide conjugates into 1D nanostructures. The interplay between dye π-stacking and metallacarborane electronic and steric interactions ultimately governs the supramolecular arrangement in these materials, which for one of the compounds prepared allows preserving the luminescent behavior in the gel state.     

Magnetic and structural properties of as-milled and heat-treated bcc-Fe70Cu30 alloy

A ferromagnetic solid solution with a nominal atomic composition Fe₇₀Cu₃₀ and a body-centered structure has been obtained by high-energy ball milling. The decomposition of the system is monitored by X-ray diffraction (XRD), magnetic measurements and Mössbauer spectroscopy. According to XRD, for healing temperatures below 723 K there is only a bcc phase in the material, while for heating temperatures above 723 K a new phase, with a fcc structure, appears, suggesting that the solid solution has decomposed into bcc-Fe and fcc-Cu. However, the magnetic behavior observed during the decomposition process indicates that this evolution is more complex than the simple decomposition into the equilibrium phases. This behavior can be summarized in two points: (1) a decrease in the magnetization at 5 K, and (2) drastic changes in the coercive field with the thermal treatment, soft magnetic behavior for the material in the as-milled state, superparamagnetism for low heating temperatures and a hardening of the material heated to above 723 K, for which the values of the coercive field at room temperature are several times higher than those for the as-milled sample. The Mössbauer spectroscopy performed at room temperature shows that for the heat-treated samples the Fe atoms are in two different phases: a ferromagnetic phase, which evolves to bcc-Fe, and a paramagnetic phase.     

On the exterior gravitational field of a mass with a multipole moment

Recently, Gutsunaev and Manko [6] presented a procedure for obtaining new static axisymmetric solutions of Einstein's vacuum field equations from a known one. We show that this procedure is based on the property that the derivatives of a harmonic function are harmonic. The special case of a metric with mass and quadrupole moment is investigated and compared with the Erez-Rosen metric.     

Magnetization process in twisted uniaxial polycrystals

A single model has been developed to obtain the general features of the Matteucci, ME, and the inverse Wiedemann, IWE, effects. The model will be confined to polycrystalline tubes and thin wires whose uniaxial crystals are arbitrarily oriented. The domain arrangement is expressed as a function of applied twist in order to determine the remanent magnetization of the M_z-M_ø and M_ø-H_z hysteresis loops. Theory shows that, for certain values of the applied magnetic field, the ME and IWE decrease and vanish with torsion. The relation between the symmetry properties of the ME and IWE and the symmetry of the initial domain structure of the sample is discussed.     

Synthesis and characterization of long perylenediimide polymer fibers: from bulk to the single-molecule level

The synthesis and characterization of perylenediimide polyisocyanides is reported. In addition to short oligomers, our synthetic approach results in the formation of extremely long, well-defined, and rigid perylenediimide polymers. Ordering and close-packing of the chromophores in these long polymers is guaranteed by attachment to a polyisocyanide backbone with amino acid side chains. Hydrogen bonding interactions between those groups stabilize and rigidify the helical polymer structure. The rodlike nature of the synthesized long perylenediimide pendant polyisocyanides as well as the helical arrangement of the chromophores is demonstrated by means of atomic force microscopy. Remarkably, polymer fibers up to 1 mum in length have been visualized, containing several thousands of perylenediimide molecules. Circular dichroism spectroscopy reveals the chiral organization of the chromophore units in the polymer, whereas absorption and emission measurements prove the occurrence of excited-state interactions between those moieties due to the close packing of the chromophore groups. However, an intricate optical behavior is encountered in bulk as a result of the coexistence of short oligomers and long polymers of perylenediimide, a situation subsequently uncovered by means of single-molecule experiments. Individual long helical perylenediimide polyisocyanides exhibit a typical red-shifted fluorescence spectrum, which, together with depolarized emission continuously decreasing in time, demonstrate that fluorescence arises from multiple excimer-like species in the polymer. Upon continuous irradiation of these long polymers, a fast decay in fluorescence lifetime is observed, a situation explained by photoinduced creation of quenching sites. Radical/ion formation by intramolecular electron transfer between close-by perylenediimide moieties is the most probable mechanism for this process. Appropriate control of the electron-transfer process might open the possibility of applying these polymers as perylenediimide-based supramolecular nanowires.     

Geometrothermodynamics of higher dimensional black holes

We study the thermodynamics and geometrothermodynamics of different black hole configurations in more than four spacetime dimensions. We use the response functions to find the conditions under which second order phase transitions occur in higher-dimensional static Reissner–Nordström and stationary Kerr black holes. Our results indicate that the equilibrium manifold of all these black hole configurations is in general curved and that curvature singularities appear exactly at those places where second order phase transitions occur.     

Congruences and Closure Endomorphisms of Hilbert Algebras

In this paper we describe the congruences of a finite Hilbert algebra in terms of its closure endomorphisms. We use this result to give a necessary and sufficient condition under which two finite Hilbert algebras share the same monoid of endomorphisms.     

Microstructural and magnetic characterization of Nd2Fe17 ball milled alloys

Microstructural and magnetic changes induced by ball milling in Nd₂Fe₁₇ alloy have been investigated. X-ray and neutron powder diffraction studies have shown that the main crystalline phase present in the as-cast Nd₂Fe₁₇ compound is the rhombohedral Th₂Zn₁₇-type crystal structure. Contrary to other materials, the crystal structure does not change after milling, and the crystal lattice parameters slightly increases while the induced strain is less than 0.1%. It has been observed from SEM and TEM images that the microstructure consists of agglomerates of nanoparticles with a mean size around 20 nm, and from magnetic measurements a broadening of the temperature range in which ferromagnetic to paramagnetic transition takes place.