A data-based stability-preserving model order reduction method for hyperbolic partial differential equations

Nonlinear Dynamics - This paper proposes a data-based approach for model order reduction that preserves incremental stability properties. Existing data-based approaches do typically not preserve...     

Effect of power-law nonlinearity on ${ \mathcal P }{ \mathcal T }$-symmetric optical system with fourth-order diffraction

Gaussian-type soliton solutions of the nonlinear Schrödinger (NLS) equation with fourth order dispersion, and power law nonlinearity in the novel parity-time (${ \mathcal P }{ \mathcal T }$)-symmetric quartic Gaussian potential are derived analytically and numerically. The exact analytical expressions of the solutions are obtained in the first two-dimensional (1D and 2D) power law NLS equations. By means of the linear stability analysis, the effect of power law nonlinearity on the stability of Gauss type solitons in different nonlinear media is carried out. Numerical investigations do confirm the stability of our soliton solutions in both focusing and defocusing cases, specially around the propagation parameters.     

Network dimensionality and ligand flexibility in lanthanide terephthalate hydrates

Various lanthanide open framework materials incorporating the terephthalate (TP) entity were prepared using hydrothermal synthesis methods at a moderate temperature of 170 °C. The compounds Nd₂(TP)₃(H₂O)₄(1), Er₂(TP)₃(H₂O)₄(2), Yb₂(TP)₃(H₂O)₂(3), Yb₂(TP)₃(H₂O)₆(4), and Yb₂(TP)₃(H₂O)₈·2H₂O (5), were characterized by single crystal structural analysis and FT-IR spectroscopy. While compounds 1 and 2 have been reported before on the basis of powder X-ray diffraction, the structural characterization of any ytterbium terephthalate species is unprecedented. Compounds 1-5 crystallize in triclinic settings with space group P-1. The compounds are compared with their previously reported Er and Tb-counterparts and the reduction of the dimensionality of the resulting networks from 3D over 2D to 1D with increasing level of hydration is discussed. Compounds 1, 2, and 3 with the lowest water content assemble in three-dimensional network lattices. Compounds 4 and 5, however, form 2D layered systems and 1D rod like chains, respectively, which are held together by hydrogen bonds originating from coordinating H₂O. The crystal lattices of the 3D networks experience higher levels of tension as can be seen by increasing out-of-plane torsion with regard to the terephthalate carboxylate groups. Moreover, there seems to be a correlation between the level of strain on the aromatic ligands and the reduction of the number of carboxylate oxygen atoms that are part of the coordination polyhedra.     

Highly Active Electrocatalysis of the Hydrogen Evolution Reaction by Cobalt Phosphide Nanoparticles

Nanoparticles of cobalt phosphide, CoP, have been prepared and evaluated as electrocatalysts for the hydrogen evolution reaction (HER) under strongly acidic conditions (0.50 M H₂SO₄, pH 0.3). Uniform, multi‐faceted CoP nanoparticles were synthesized by reacting Co nanoparticles with trioctylphosphine. Electrodes comprised of CoP nanoparticles on a Ti support (2 mg cm^?2 mass loading) produced a cathodic current density of 20 mA cm^?2 at an overpotential of ?85 mV. The CoP/Ti electrodes were stable over 24 h of sustained hydrogen production in 0.50 M H₂SO₄. The activity was essentially unchanged after 400 cyclic voltammetric sweeps, suggesting long‐term viability under operating conditions. CoP is therefore amongst the most active, acid‐stable, earth‐abundant HER electrocatalysts reported to date.     

The pyridyl-tag strategy applied to the hydrocarbon/perfluorocarbon phase-switching of a porphyrin and a fullerene

A new hydrocarbon/perfluorocarbon phase-switching strategy based on coordination of pyridyl-tagged molecules to a highly fluorinated dicopper-carboxylate complex possessing two accessible axial coordination sites is described. When a chloroform solution of the tetrapyridyl-substituted porphyrin 3 (0.1 mM, 2 mL) is layered on a perfluorodecalin solution of 2 (3.25 mM, 1.5 mL), complete extraction of the porphyrin into the fluorous phase is observed after 30 min of stirring. Quantitative release of both the porphyrin and 2 is achieved simply by adding excess THF to the biphasic system, the THF acting as a pyridine competing ligand. The recovered perfluorocarbon solution containing 2 can be reused for another complexation with the same efficiency. The scope of this approach is emphasized by the phase-switching of a dipyridyl-substituted fullerene, another example of a molecule for which solubilization in perfluorocarbons is very challenging.     

Use of a microelectromechanical mirror for adaptive optics in the human eye

Ophthalmic instrumentation equipped with adaptive optics offers the possibility of rapid and automated correction of the eye's optics for improving vision and for improving images of the retina. One factor that limits the widespread implementation of adaptive optics is the cost of the wave-front corrector, such as a deformable mirror. In addition, the large apertures of these elements require high pupil magnification, and hence the systems tend to be physically large. We present what are believed to be the first closed-loop results when a compact, low-cost, surface micromachined, microelectromechanical mirror is used in a vision adaptive-optics system. The correction performance of the mirror is shown to be comparable to that of a Xinetics mirror for a 4.6-mm pupil size. Furthermore, for a pupil diameter of 6.0-mm, the residual rms error is reduced from 0.36 to 0.12 microm and individual photoreceptors are resolved at a pupil eccentricity of 1 degrees from the fovea.