Self-similar optical wave collapse: observation of the Townes profile

Analyses of many different types of nonlinear wave equations indicate that a collapsing wave will transform into a universal blowup profile regardless of its initial shape; that is, the amplitude of the wave increases as the spatial extent decreases in a self-similar fashion. We show experimentally that the spatial profile of a collapsing optical wave evolves to a specific circularly symmetric shape, known as the Townes profile, for elliptically shaped or randomly distorted input beams. These results represent the first experimental confirmation of this universal collapsing behavior and provide deeper insight into the high-power filamentation of femtosecond laser pulses in air.     

The bireflections of a permutation

A bireflection of a permutation θ is an ordered pair (φ, ψ) of permutations satisfying φ² = ψ² = 1, θ = φψ. The family of bireflections of a permutation is studied. As a corollary an expression for the number of dihedral groups over θ in S_A is obtained.     

Self-starting ultralow-jitter pulse source based on coupled optoelectronic oscillators with an intracavity fiber parametric amplifier

A self-starting optical pulse source based on mutually coupled optoelectronic oscillators is described. The system employs a phototransistor-based microwave oscillator that is coupled to a fiber cavity optoelectronic oscillator with an intracavity fiber parametric amplifier. It self-starts and exhibits 3 ps pulses at a rate of 10 GHz with extremely low jitter of 30, 29, and 40 fs (for integration bandwidths of 100 Hz-15 kHz, 500 Hz-1 MHz, and 100 Hz-1 MHz, respectively).     

The Ti3AlC2 MAX Phase as an Efficient Catalyst for Oxidative Dehydrogenation of n‐Butane

Dehydrogenation or oxidative dehydrogenation (ODH) of alkanes to produce alkenes directly from natural gas/shale gas is gaining in importance. Ti₃AlC₂, a MAX phase, which hitherto had not been used in catalysis, efficiently catalyzes the ODH of n‐butane to butenes and butadiene, which are important intermediates for the synthesis of polymers and other compounds. The catalyst, which combines both metallic and ceramic properties, is stable for at least 30 h on stream, even at low O₂:butane ratios, without suffering from coking. This material has neither lattice oxygens nor noble metals, yet a unique combination of numerous defects and a thin surface Ti_1?yAl_yO_2?y/2 layer that is rich in oxygen vacancies makes it an active catalyst. Given the large number of compositions available, MAX phases may find applications in several heterogeneously catalyzed reactions.     

An experimental approach for controlling confinement effects at catalyst interfaces

Catalysts are conventionally designed with a focus on enthalpic effects, manipulating the Arrhenius activation energy. This approach ignores the possibility of designing materials to control the entropic factors that determine the pre-exponential factor. Here we investigate a new method of designing supported Pt catalysts with varying degrees of molecular confinement at the active site. Combining these with fast and precise online measurements, we analyse the kinetics of a model reaction, the platinum-catalysed hydrolysis of ammonia borane. We control the environment around the Pt particles by erecting organophosphonic acid barriers of different heights and at different distances. This is done by first coating the particles with organothiols, then coating the surface with organophosphonic acids, and finally removing the thiols. The result is a set of catalysts with well-defined “empty areas” surrounding the active sites. Generating Arrhenius plots with >300 points each, we then compare the effects of each confinement scenario. We show experimentally that confining the reaction influences mainly the entropy part of the enthalpy/entropy trade-off, leaving the enthalpy unchanged. Furthermore, we find this entropy contribution is only relevant at very small distances (<3 Å for ammonia borane), where the “empty space” is of a similar size to the reactant molecule. This suggests that confinement effects observed over larger distances must be enthalpic in nature.

Designable materials help pinpoint the role of steric confinement in catalysis.     

Ordinals and scattered compact ordered spaces

Scattered Compact Ordered Spaces (SCOS) are studied with respect to their well ordered images and preimages. Typical results:

1. A SCOS is homeomorphic to an ordinal iff it has no pit point (a pit in an ordered space is one with infinite left and right cofinalities, one of which is uncountable).
2. A SCOS of characteristic <μ,m> is mappable onto and includes ω^μ·m+1; it is also an image of ω^μ·(2m)+1. The SCOSs are characterized by: Theorem 5: Let K be a Hausdorff space. The following conditions are equivalent:
3. K is homeomorphic to a compact scattered ordered space.
4. K is an order-two image of a compact ordinal. A.M.S. (MOS) Subject Classification: Primary: 54F05, 54F65, 06A45 Secondary: 54D30.

     

Comprehensive study of the macropore and mesopore size distributions in polymer monoliths using complementary physical characterization techniques and liquid chromatography

Poly(styrene‐co‐divinylbenzene) monolithic stationary phases with two different domain sizes were synthesized by a thermally initiated free‐radical copolymerization in capillary columns. The morphology was investigated at the meso‐ and macroscopic level using complementary physical characterization techniques aiming at better understanding the effect of column structure on separation performance. Varying the porogenic solvent ratio yielded materials with a mode pore size of 200 nm and 1.5 μm, respectively. Subsequently, nano‐liquid chromatography experiments were performed on 200 μm id × 200 mm columns using unretained markers, linking structure inhomogeneity to eddy dispersion. Although small‐domain‐size monoliths feature a relatively narrow macropore‐size distribution, their homogeneity is compromised by the presence of a small number of large macropores, which induces a significant eddy‐dispersion contribution to band broadening. The small‐domain size monolith also has a relatively steep mass‐transfer term, compared to a monolith containing larger globules and macropores. Structural inhomogeneity was also studied at the mesoscopic level using gas‐adsorption techniques combined with the non‐local‐density‐function‐theory. This model allows to accurately determine the mesopore properties in the dry state. The styrene‐based monolith with small domain size has a distinctive trimodal mesopore distribution with pores of 5, 15, and 25 nm, whereas the monolith with larger feature sizes only contains mesopores around 5 nm in size.     

Insights into Sonogashira cross-coupling by high-throughput kinetics and descriptor modeling

A method is presented for the high-throughput monitoring of reaction kinetics in homogeneous catalysis, running up to 25 coupling reactions in a single reaction vessel. This method is demonstrated and validated on the Sonogashira reaction, analyzing the kinetics for almost 500 coupling reactions. First, one-pot reactions of phenylacetylene with a set of 20 different meta- and para-substituted aryl bromides were analyzed in the presence of 17 different Pd-phosphine complexes. In addition, the temperature-dependent Sonogashira reactions were examined for 21 different ArX (X=Cl, Br, I) substrates, and the corresponding activation enthalpies and entropies were determined by means of Eyring plots: ArI (DeltaH(not equal)=48-62 kJ mol(-1); DeltaS(not equal)=-71--39 J mol(-1) K; NO(2)-->OMe), ArBr (DeltaH(not equal)=54-82 kJ mol(-1), DeltaS(not equal)=-55-11 J mol(-1) K), and ArCl (DeltaH(not equal)=95-144 kJ mol(-1), DeltaS(not equal)=-6-100 J mol(-1) K). DFT calculations established a linear correlation of DeltaH( not equal) and the Kohn-Sham HOMO energies of ArX (X=Cl, Br, I) and confirmed their involvement in the rate-limiting step. However, despite different C--X bond energies, aryl iodides and electron-deficient aryl bromides showed similar activation parameters.