On the formation of trapped surfaces

In a recent important breakthrough D. Christodoulou has solved a long standing problem of General Relativity of evolutionary formation of trapped surfaces in the Einstein-vacuum space-times. He has identified an open set of regular initial conditions on an outgoing null hypersurface (both finite and at past null infinity) leading to a formation a trapped surface in the corresponding vacuum space-time to the future of the initial outgoing hypersurface and another incoming null hypersurface with the prescribed Minkowskian data. In this paper we give a simpler proof for a finite problem by enlarging the admissible set of initial conditions and, consistent with this, relaxing the corresponding propagation estimates just enough that a trapped surface still forms. We also reduce the number of derivatives needed in the argument from two derivatives of the curvature to just one. More importantly, the proof, which can be easily localized with respect to angular sectors, has the potential for further developments.     

Super-Luminal Effects for Finsler Branes as a Way to Preserve the Paradigm of Relativity Theories

Using Finsler brane solutions [see details and methods in: S. Vacaru, Class. Quant. Grav. 28:215001, 2011], we show that neutrinos may surpass the speed of light in vacuum which can be explained by trapping effects from gravity theories on eight dimensional (co) tangent bundles on Lorentzian manifolds to spacetimes in general and special relativity. In nonholonomic variables, the bulk gravity is described by Finsler modifications depending on velocity/momentum coordinates. Possible super-luminal phenomena are determined by the width of locally anisotropic brane (spacetime) and induced by generating functions and integration functions and constants in coefficients of metrics and nonlinear connections. We conclude that Finsler brane gravity trapping mechanism may explain neutrino super-luminal effects and almost preserve the paradigm of Einstein relativity as the standard one for particle physics and gravity.     

Fractional Dynamics from Einstein Gravity,General Solutions,and Black Holes

We study the fractional gravity for spacetimes with non-integer fractional derivatives. Our constructions are based on a formalism with the fractional Caputo derivative and integral calculus adapted to nonholonomic distributions. This allows us to define a fractional spacetime geometry with fundamental geometric/physical objects and a generalized tensor calculus all being similar to respective integer dimension constructions. Such models of fractional gravity mimic the Einstein gravity theory and various Lagrange–Finsler and Hamilton–Cartan generalizations in nonholonomic variables. The approach suggests a number of new implications for gravity and matter field theories with singular, stochastic, kinetic, fractal, memory etc processes. We prove that the fractional gravitational field equations can be integrated in very general forms following the anholonomic deformation method for constructing exact solutions. Finally, we study some examples of fractional black hole solutions, ellipsoid gravitational configurations and imbedding of such objects in solitonic backgrounds.     

Heteronuclear (Co-Ca, Co-Ba) 2,3-pyridinedicarboxylate complexes: synthesis, structure and physico-chemical properties

Three pyridine 2,3-dicarboxylate complexes have been synthesized and characterized by IR spectroscopy, thermal analysis and single crystal X-ray diffractometry. Their magnetic properties have also been studied by EPR and magnetisation measurements. The decomposition of such complexes in air leads to the generation of mixed metal oxides, as confirmed by powder X-ray diffraction.     

Nonlinear resonant periodic problems with concave terms

We consider a nonlinear periodic problem, driven by the scalar p-Laplacian with a concave term and a Caratheodory perturbation. We assume that this perturbation f(t,x) is (p−1)-linear at ±∞, and resonance can occur with respect to an eigenvalue λm+1, m?2, of the negative periodic scalar p-Laplacian. Using a combination of variational techniques, based on the critical point theory, with Morse theory, we establish the existence of at least three nontrivial solutions. Useful in our considerations is an alternative minimax characterization of λ₁>0 (the first nonzero eigenvalue) that we prove in this work.     

TiO2 nanotube layers: Flexible and electrically active flow-through membranes

In the present work we demonstrate the fabrication and use of a new generation of TiO₂ nanotube membranes. We show that anodic oxide nanotube growth can be performed through a patterned Ti foil into an underlying Al metal layer. After the selective dissolution of the Al/alumina layer, a very well defined both side open suspended TiO₂ nanotube layer can be obtained. Using lithographic patterning of the anodization area allows to achieve very large scale, flexible and well electrically connected nanotubular flow-through membranes with fast electrical switching features over the entire membrane.     

TiO2 nanotubes in dye-sensitized solar cells: Higher efficiencies by well-defined tube tops

Aligned self-organized TiO₂ nanotubes of 15–20 µm length proved to be very promising for application in dye-sensitized solar cells. Conventional anodic nanotube layers usually show an irregular structure (nanograss) or a thin nucleation layer at the top of the nanotube array. In the present paper, we demonstrate that by a simple photoresist based method, well-defined and open TiO₂ nanotube tops can be obtained which significantly enhances their performance when used in DSSCs. In fact, the layers show the highest reported solar energy conversion efficiency up to now for a pristine (particle-free) nanotube layer.     

Structural similarities and diversity in a series of crystalline solids composed of 2-aminopyridines and glutaric acid

Structural Chemistry - A solvent co-crystallization of three 2-aminopyridine derivatives, 2-aminopyridine (AP), 2-amino-6-methylpyridine (AMP), and 2,6-diaminopyridine (DAP) with the odd-membered...     

Hydrogen‐bonded supramolecular polymers containing dimethylsilane groups: Synthesis,crystal structure,and characterization

Bis[N‐(4‐carboxyphenyl)phtalimidyl]dimethylsilane prepared by the reaction between bis(3,4‐dicarboxyphenyl)dimethylsilane anhydride and p‐aminobenzoic acid has been used to built three novel hydrogen‐bonded supramolecular polymers as a result of cocrystallization with pyridine derivatives: 4,4′‐bipyridyl ( SP1 ), 1,2‐bis(4‐pyridyl)ethylene ( SP2 ), and 4,4′‐azopyridine ( SP3 ). The structures of the dianhydride, diacid, and derived supramolecular polymers were investigated by Fourier transform infrared (FTIR) and proton magnetic resonance (¹H NMR) spectroscopy. Self‐assembling was proved by the presence of the IR absorption bands around 1900 and 2400 cm^?1 specific for hydrogen bond. The association constant values were estimated by using FTIR spectroscopy in solid state. According to X‐ray diffraction study, the bis(3,4‐dicarboxyphenyl)dimethylsilane anhydride ( 1 ) has an isolated molecular structure. Bis[N‐(4‐carboxyphenyl)phtalimidyl]dimethylsilane ( 2 ) molecules are associated in the crystal structure via dimeric O? H … O hydrogen bonds resulting in the wavy 1D supramolecular chain. The main packing motif for SP1 and SP3 is represented by wavy chain formed by alternating sequences of 4,4′‐bipyridyl or 4,4′‐azopyridine and bis[N(4‐carboxyphenyl)phtalimidyl]dimethylsilane molecules linked by O? H … N hydrogen bonds. Thermal behavior was studied by differential scanning calorimetry and thermogravimetric analysis. The ability for the structuration in film was emphasized by atomic force microscopy. The molecular transport ability of the reversible associations was estimated by dynamic water vapor sorption (DVS) analysis. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Does the Sign of the Cu–Gd Magnetic Interaction Depend on the Number of Atoms in the Bridge?

Several theoretical investigations with CASSCF methods confirm that the magnetic behavior of Cu–Gd complexes can only be reproduced if the 5d Gd orbitals are included in the active space. These orbitals, expected to be unoccupied, do present a low spin density, which is mainly due to a spin polarization effect. This theory is strengthened by the experimental results reported herein. We demonstrate that Cu–Gd complexes characterized by Cu–Gd interactions through single‐oxygen and three‐atom bridges consisting of oxygen, carbon, and nitrogen atoms, present weak ferromagnetic exchange interactions, whereas complexes with bridges made of two atoms, such as the nitrogen–oxygen oximato bridge, are subject to weak antiferromagnetic exchange interactions. Therefore, a bridge with an odd number of atoms induces a weak ferromagnetic exchange interaction, whereas a bridge with an even number of atoms supports a weak antiferromagnetic exchange interaction, as observed in pure organic compounds and also, as in this case, in metal–organic compounds with an active spin polarization effect.