Universality of level spacing distributions in classical chaos

We suggest that random matrix theory applied to a matrix of lengths of classical trajectories can be used in classical billiards to distinguish chaotic from non-chaotic behavior. We consider in 2D the integrable circular and rectangular billiard, the chaotic cardioid, Sinai and stadium billiard as well as mixed billiards from the Limaçon/Robnik family. From the spectrum of the length matrix we compute the level spacing distribution, the spectral auto-correlation and spectral rigidity. We observe non-generic (Dirac comb) behavior in the integrable case and Wignerian behavior in the chaotic case. For the Robnik billiard close to the circle the distribution approaches a Poissonian distribution. The length matrix elements of chaotic billiards display approximate GOE behavior. Our findings provide evidence for universality of level fluctuations—known from quantum chaos—to hold also in classical physics.     

Direct α-hydroxylation of ketones using iodosobenzene

Ketones are converted smoothly into the corresponding acyloin with a high degree of selectivity upon treatment with iodosobenzene or phenyliodosodiacetate in methanolic sodium hydroxide.     

Ion chromatograph with three-dimensional printed absorbance detector for indirect ultraviolet absorbance detection of phosphate in effluent and natural waters

An ion chromatography system employing a low-cost three-dimensional printed absorbance detector for indirect ultraviolet detection towards portable phosphate analysis of environmental and industrial waters has been developed. The optical detection cell was fabricated using stereolithography three-dimensional printing of nanocomposite material. Chromatographic analysis and detection of phosphate were carried out using a CS5A 4 × 250 mm analytical column with indirect ultraviolet detection using a 255 nm light-emitting diode. Isocratic elution using a 0.6 mM potassium phthalate eluent combined with 1.44 mM sodium bicarbonate was employed at a flow rate of 0.75 mL/min. A linear calibration range of 0.5 to 30 mg/L PO₄³⁻ applicable to environmental and wastewater analysis was achieved. For retention time and peak area repeatability, relative standard deviation values were 0.68 and 4.09%, respectively. Environmental and wastewater samples were analyzed with the optimized ion chromatography platform and the results were compared to values obtained by an accredited ion chromatograph. For the analysis of environmental samples, relative errors of <14 % were achieved. Recovery analysis was also carried out on both freshwater and wastewater samples and recovery results were within the acceptable range for water analysis using standard ion chromatography methods.     

Possible role of Lewis acid catalysis in the oxidation of alkenes and α,β-unsaturated ketones using bleomycin-zn(ii) and bleomycin-fe(iii)-iodosylbenzene in aqueous methanol

C₆H₅IO in CH₃OH-H₂0 is activated towards electrophilic attack upon various alkenes by Fe(ClO₄).9H₂O, FE(III) bleomycin and ZN(II) bleomycin. The results imply that direct transfer of oxygen from an Fe(V)=0 intermediate is not required in the mechanism of oxygenation by iron-containing species, and that much earlier work is questionable as models for biological oxygenation.     

Synthesis of 1,4-annulated cyclooctatetraenophanes based on a novel cubane building block approach

A general synthetic approach to strained 1,4-annulated cyclooctatetraene-based cyclophanes is described. A key feature in this approach is exploitation of the cubane core as a masked cyclooctatetraene synthon. Thus, 1,4-disubstituted cubanes 3 and 4 used as precursors to cyclooctatetraenophanes have been prepared in four steps from the readily available 1,4-cubanedicarboxaldehyde (5). The synthesis of 3 was effected by palladium/copper-mediated coupling of 1,4-bis[(Z,Z)-2-iodovinyl]cubane (6) and 1,4-bis[(Z,Z)-but-1-en-3-ynyl]cubane (8). For the synthesis of 4, on the other hand, modified Eglington-Glaser coupling was applied for the macrocyclization step. The general characteristic of Rh(I) to induce [2 + 2] cycloreversion of the cubane core to syn-tricyclo[4.2.0.0(2,5)]octa-3,7-diene followed by thermal rearrangement to cyclooctatetraene was applied as a key structural transformation toward targeted cyclooctatetraenophanes 1 and 2.     

A Conventient Synthesis of 3-Hydroxy-4-chromanone Using Iodobenzene Diacetate

A useful synthesis of 3-hydroxy-4-chromanone (6) is not currently available. Lead tetraacetate oxidation of 4-chromanone (4) yields the C(3) acetoxy derivative but this compound could not be deacetylated to 6.¹ Recently Donnelly and Maloney reported² that the Algar-Flynn-Oyamada reaction (H₂O₂/CH₃OH/NaOH), which is commonly used for the conversion of o-hydroxychalcones (1) into 3-hydroxyflavanone (2) and 3-hydroxyflavones (3), does not yield 6 when applied to o-hydroxya-crylophenone 1 (R = H). The authors found that under less basic conditions using K₂CO₃ some 6 is formed but the major product is catechol. These observations clearly indicate the necessity of developing a method for making 6. The present note describes a staightforward way of preparing 3-hydroxy-4-chromanone (6) in good yield.     

alpha-thiocyanation of carbonyl and beta-dicarbonyl compounds using (dichloroiodo)benzene-lead(II) thiocyanate

The combination reagent (dichloroiodo)benzene and lead(II) thiocyanate in dichloromethane effects oxidation of various enol silyl ethers, ketene silyl acetals, and beta-dicarbonyl compounds, thereby providing an efficient and convenient method for alpha-thiocyanation of carbonyl and beta-dicarbonyl compounds.     

Robust Damping in Self-Excited Mechanical Systems

A technique to optimize the stability of a general mechanical system is outlined. The method relies on decomposing the damping matrix into several component matrices, which may have some special structure or physical relevance. An optimization problem can then be formulated where the ratio of these are varied to either stabilize or make more stable the equilibrium state subject to sensible constraints. For the purpose of this study, we define a system to be more stable if its eigenvalue with largest real part is as negative as possible. The technique is demonstrated by applying it to an introduced non-dimensionalized variant of a known minimal wobbling disc brake model. In this case, it is shown to be beneficial to shift some damping from the disc to the pins for a system optimized for stability. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)