Lyapunov numbers and the local structure of attractors

We examine an M-dimensional mapping defined by a system of broken linear equations, whose Lyapunov numbers may be prespecified, and whose directions of stretching and compression are the coordinate directions. With K positive and M-K negative Lyapunov exponents, the attractor is locally the product of a K-dimensional continuum and an (M-K)-dimensional Cantor set; the latter is found to be a pseudo-product of Cantor sets or continua or Cantor sets and continua. When seen with finite resolution a pseudo-product may look like a true product, but its fractional dimension is less than the sum of the dimensions of its projections on the coordinate axes. Transitions in the number of Cantor sets and continua involved in the pseudo-product need not correspond to transitions in the integral part of the fractional dimension of the attractor. We speculate as to whether the attractors of continuous mappings and flows have similar structures.     

Laser-driven plasma loader for shockless compression and acceleration of samples in the solid state

A new method for shockless compression and acceleration of solid materials is presented. A plasma reservoir pressurized by a laser-driven shock unloads across a vacuum gap and piles up against an Al sample thus providing the drive. The rear surface velocity of the Al was measured with a line VISAR, and used to infer load histories. These peaked between approximately 0.14 and 0.5 Mbar with strain rates approximately 10(6)-10(8) s(-1). Detailed simulations suggest that apart from surface layers the samples can remain close to the room temperature isentrope. The experiments, analysis, and future prospects are discussed.     

Sub-shot-noise phase quadrature measurement of intense light beams

We present a setup for performing sub-shot-noise measurements of the phase quadrature of intense pulsed light without the use of a separate local oscillator. A Mach-Zehnder interferometer with an unbalanced arm length is used to detect the fluctuations of the phase quadrature at a single sideband frequency. With this setup, the nonseparability of a pair of quadrature-entangled beams is demonstrated experimentally.     

Design of a constant adiabaticity pulse for selective population inversion

A new adiabatic pulse for population inversion and the principles of its design are presented. The pulse shape is characterized by the combination of two constraints. (i) Adiabatic following of the central isochromat of the spectral region of interest occurs with constant, possibly small adiabaticity parameter; thereby, the center isochromat gets most efficiently inverted. (ii) Frequency and amplitude modulations obey the principle of offset-independent adiabaticity; thus, the inversion dynamics of the center isochromat is extended over the desired bandwidth. Selective population inversion can be achieved rather independently of spatial radio frequency field inhomogeneities and with significantly reduced peak RF amplitude in comparison with the well-known sech/tanh adiabatic pulse.     

Explosive thermal interactions between molten lava and water

The most effective volcanic eruptions are the phreatomagmatic explosions. In such eruptions, magma and groundwater come into contact with each other, leading to explosions. A reproduction of such explosive interactions between lava (produced by remelting of volcanic rocks) and water in the laboratory was carried out, in which water was injected into molten lava. The amount of lava that was involved in the interactions, the so-called interactive lava mass, was determined. The influences of chemical composition and temperature of the melt and the injection velocity of water were also investigated.

Experiments show that an enhancement of the injection velocity of the water leads to more violent explosions. This is obviously due to an enlargement of the mixing region between water and molten lava in the crucible. Raising the temperature of the lava melt leads also to a greater impulse but not to an increase in the interactive masses as is found in connection with the water injection velocity. That means that the conversion ratio will be larger for higher lava temperatures than for lower ones.

By a fitting calculation with the measured curve of the force history of an explosive thermal interaction, the mass of water that was evaporated by the thermal interaction was estimated. In the same calculation the superheating temperature of this evaporated water can be determined. Furthermore, the amount of energy released by the explosive thermal interactions was calculated by using the measured impulse and determined fragment mass in fragmentation analysis.     

[Rh2(MEPY)4] and [BiRh(MEPY)4]: Convenient Syntheses and Computational Analysis of Strikingly Dissimilar Siblings

[Rh₂(MEPY)₄] is a versatile catalyst for asymmetric synthesis but its preparation requires purification by chromatography on surface-modified silica. A higher yielding procedure based on a more convenient work-up is presented herein. Moreover, a much improved method for the preparation of [BiRh(OTfa)₄] is described, which makes this heterobimetallic complex readily available. Subsequent exchange of the trifluoroacetate ligands opens access to a so far underappreciated family of (chiral) paddlewheel complexes. While [BiRh] complexes comprising four carboxylate ligands are highly adequate for intermolecular asymmetric cyclopropanation reactions, [BiRh(MEPY)₄] as the heterobimetallic cousin of [Rh₂(MEPY)₄] was found to be surprisingly unreactive; DFT calculations uncover the reasons for this inertia.     

Pivotal Role of Holes in Photocatalytic CO2 Reduction on TiO2

Evidence is provided that in a gas-solid photocatalytic reaction the removal of photogenerated holes from a titania (TiO₂) photocatalyst is always detrimental for photocatalytic CO₂ reduction. The coupling of the reaction to a sacrificial oxidation reaction hinders or entirely prohibits the formation of CH₄ as a reduction product. This agrees with earlier work in which the detrimental effect of oxygen-evolving cocatalysts was demonstrated. Photocatalytic alcohol oxidation or even overall water splitting proceeds in these reaction systems, but carbon-containing products from CO₂ reduction are no longer observed. H₂ addition is also detrimental, either because it scavenges holes or because it is not an efficient proton donor on TiO₂. The results are discussed in light of previously suggested reaction mechanisms for photocatalytic CO₂ reduction. The formation of CH₄ from CO₂ is likely not a linear sequence of reduction steps but includes oxidative elementary steps. Furthermore, new hypotheses on the origin of the required protons are suggested.     

The ladder towards understanding the oxygen evolution reaction

Understanding the atomic-scale mechanistic details of the oxygen evolution reaction (OER) remains an unresolved challenge in electrochemistry owing to the complexity of the OER. In this short review we discuss how, with the advent of new experimental and computational methodologies, the OER can be treated with increasingly sophisticated models to aid in our complete understanding. For the case of steady state catalyst surfaces, we define a six-rung ladder of complexity to frame how far this understanding reaches and in which aspects our understanding could still improve.     

In Situ Formation of a MoS2‐Based Inorganic–Organic Nanocomposite by Directed Thermal Decomposition

Nanocomposites based on molybdenum disulfide (MoS₂) and different carbon modifications are intensively investigated in several areas of applications due to their intriguing optical and electrical properties. Addition of a third element may enhance the functionality and application areas of such nanocomposites. Herein, we present a facile synthetic approach based on directed thermal decomposition of (Ph₄P)₂MoS₄ generating MoS₂ nanocomposites containing carbon and phosphorous. Decomposition at 250 °C yields a composite material with significantly enlarged MoS₂ interlayer distances caused by in situ formation of Ph₃PS bonded to the MoS₂ slabs through Mo?S bonds and (Ph₄P)₂S molecules in the van der Waals gap, as was evidenced by ³¹P solid‐state NMR spectroscopy. Visible‐light‐driven hydrogen generation demonstrates a high catalytic performance of the materials.