Resonances in a Chaotic Attractor Crisis of the Lorenz Flow

Local bifurcations of stationary points and limit cycles have successfully been characterized in terms of the critical exponents of these solutions. Lyapunov exponents and their associated covariant Lyapunov vectors have been proposed as tools for supporting the understanding of critical transitions in chaotic dynamical systems. However, it is in general not clear how the statistical properties of dynamical systems change across a boundary crisis during which a chaotic attractor collides with a saddle. This behavior is investigated here for a boundary crisis in the Lorenz flow, for which neither the Lyapunov exponents nor the covariant Lyapunov vectors provide a criterion for the crisis. Instead, the convergence of the time evolution of probability densities to the invariant measure, governed by the semigroup of transfer operators, is expected to slow down at the approach of the crisis. Such convergence is described by the eigenvalues of the generator of this semigroup, which can be divided into two families, referred to as the stable and unstable Ruelle–Pollicott resonances, respectively. The former describes the convergence of densities to the attractor (or escape from a repeller) and is estimated from many short time series sampling the state space. The latter is responsible for the decay of correlations, or mixing, and can be estimated from a long times series, invoking ergodicity. It is found numerically for the Lorenz flow that the stable resonances do approach the imaginary axis during the crisis, as is indicative of the loss of global stability of the attractor. On the other hand, the unstable resonances, and a fortiori the decay of correlations, do not flag the proximity of the crisis, thus questioning the usual design of early warning indicators of boundary crises of chaotic attractors and the applicability of response theory close to such crises.     

Correction of wandering smoothing effects on static measurements of a wing-tip vortex

Wandering is a typical feature of wing-tip vortices and it consists in random fluctuations of the vortex core. Consequently, vortices measured by static measuring techniques appear to be more diffuse than in reality, so that a correction method is needed. In the present paper statistical simulations of the wandering of a Lamb-Oseen vortex are first performed by representing the vortex core locations through bi-variate normal probability density functions. It is found that wandering amplitudes smaller than 60% of the core radius are well predicted by using the ratio between the RMS value of the mean cross-velocity and its slope measured at the mean vortex center. Furthermore, the principal axes of wandering can be accurately evaluated from the opposite of the cross-correlation coefficient between the spanwise and the normal velocities measured at the mean vortex center. The correction of the wandering smoothing effects is then carried out through four different algorithms that perform the deconvolution of the mean velocity field with the probability density function that represents the wandering. The corrections performed are very accurate for the simulations with wandering amplitudes smaller than 60% of the core radius, whereas errors become larger with increasing wandering amplitudes. Subsequently, the whole procedure to evaluate wandering and to correct the mean velocity field is applied to static measurements, carried out with a fast-response five-hole pressure probe, of a tip vortex generated from a NACA 0012 half-wing model. It is found that the wandering is predominantly in the upward-outboard to downward-inboard direction. Furthermore, the wandering amplitude grows with increasing streamwise distance from the wing, whereas it decreases with increasing angle of attack and free-stream velocity.     

Temperature and potential-dependent structural changes in a Pt cathode electrocatalyst viewed by in situ XAFS

The paper presents an X-ray absorption fine structure (XAFS) investigation of Pt supported on Vulcan XC-72 operating as a cathode catalyst in a polymer electrolyte membrane fuel cell (PEM FC). XAFS spectroscopy was performed in situ using a cell developed by the authors and optimized for absorption measurements. Low-noise spectra were obtained using the transmission mode over the Pt L₃ XAFS range, enabling multiple-scattering XAFS data-analysis for the Pt nanocrystalline system under operating conditions. Accurate measurements of the local structure were performed at various potentials and working temperatures. Changes in the near-edge structures reflecting variations in the Pt electronic structure were observed for various potential values in the cathode activation region. The Pt average local geometric structure was found to be practically potential-independent. The increase in structural disorder caused by the higher working FC temperature was not found to affect the catalyst’s performance in the kinetically controlled region.     

Crystal Structures of a Series of Bis{(2-Aminobenzoyl-)amino}alkanes

Abstract  The crystal structures of 1,2-bis-{(2-aminobenzoyl-)amino}ethane(1), 1,4-bis-{(2-aminobenzoyl-)amino}butane(2) and 2,2-dimethyl-1,3-bis-{(2-aminobenzoyl-)amino}-propane(3) have been determined by single crystal X-ray diffraction analysis. 1 and 2 are centrosymmetric molecules which lie on crystallographic centers of symmetry and adopt extended conformations. On the other hand, owing to the odd number of carbon atoms in the spacer unit, 3 does not show centrosymmetry, but crystallizes in a non-centrosymmetric space group and assumes a folded conformation. The crystal structures of 1, 2 and 3 are compared with the known structures of anthranilamide (7) and the N-alkyl anthranilamide derivative 8. Crystal data: 1 C₁₆H₁₈N₄O₂, monoclinic, space group P2₁/a, a = 9.5262(8) ?, b = 5.4200(5) ?, c = 15.3821(14) ?, β = 105.980(5)° and V = 763.52(12) ?³, for Z = 2. 2 C₁₈H₂₂N₄O₂, monoclinic, space group C2/c, a = 32.0710(17) ?, b = 5.4732(4) ?, c = 9.7326(5) ?, β = 102.570(4)° and V = 1667.42(17) ?³, for Z = 4. 3 C₁₉H₂₄N₄O₂, orthorhombic, space group Pca2₁, a = 16.7676(4) ?, b = 10.1847(2) ?, c = 10.5338(5) ?, and V = 1798.89(7) ?³, for Z = 4. Index Abstract  The crystal structures of 1,2-bis-{(2-aminobenzoyl-)amino}ethane(1), 1,4-bis-{(2-aminobenzoyl-)amino}butane(2) and 2,2-dimethyl-1,3-bis-{(2-aminobenzoyl-)amino}-propane(3) have been determined by single crystal X-ray diffraction analysis. 1 and 2 are centrosymmetric molecules which lie on crystallographic centers of symmetry and adopt extended conformations, whereas 3 does not show centrosymmetry, but crystallizes in a non-centrosymmetric space group and assumes a folded conformation.      

Superbroadband fluorescence fiber fabricated with granulated oxides

We demonstrate a single-core multiply doped fiber that, when pumped with a single pump source of approximately 800 nm, emits a more than two-octaves-spanning fluorescence spectrum ranging from 365 to 2300 nm. The fiber preform is manufactured from granulated oxides, and the core is doped with five different rare earths. At a pump power of 250 mW the total emitted power is 34 microW; given a core diameter of 6.5 microm and a numerical aperture of 0.1, the radiance exceeds 3 kW sr(-1) cm(-2). We also demonstrate direct diode pumping of the fiber.     

THz spectrum of monodeuterated methane

We report new measurements of the rotational spectrum of monodeuterated methane (CH₃D) in the range of 690-1200 GHz which allow for an accurate prediction of all lines in the range of the high-resolution spectrometer of the Herschel Space Observatory. Comparison is also made with the previous analysis based on infrared combination differences. Three lines of ¹³CH₃D were measured in natural abundance.     

Synthesis and Characterization of New Boron Compounds Using Reaction of Diazonium Tetraphenylborate with Enaminoamides

A family of oxazaborines, diazaborinones, triazaborines, and triazaborinones was prepared by reaction of polarized ethylenes, such as β-enaminoamides, with 4-methylbenzenediazonium tetraphenylborates. The reaction conditions (stirring in CH₂Cl₂ at room temperature (Method A) or stirring with CH₃COONa in CH₂Cl₂ at room temperature (Method B) or refluxing in the CH₂Cl₂/toluene mixture (Method C)) controlled the formation and relative content of these compounds in the reaction mixtures from one to three products. Substituted oxazaborines gradually rearranged into diazaborinones at 250 °C. The prepared compounds were characterized by ¹H NMR, ¹³C NMR, IR, and UV–Vis spectroscopy, HRMS, or microanalysis. The structure of individual compounds was confirmed by ¹¹B NMR, ¹⁵N NMR, 1D NOESY, and X-ray analysis. The mechanism of reaction of enaminoamides with 4-methylbenzenediazonium tetraphenylborate was proposed.     

Thermal degradation kinetics of carotenoids: Acrocomia aculeata oil in the context of nutraceutical food and bioprocess technology

Journal of Thermal Analysis and Calorimetry - In the present study, the kinetics of β-carotene and β-cryptoxanthin degradation were investigated in edible oil mechanically extracted from...     

Frustrated Lewis Pair Mediated 1,2-Hydrocarbation of Alkynes

Frustrated Lewis pair (FLP) chemistry enables a rare example of alkyne 1,2-hydrocarbation with N-methylacridinium salts as the carbon Lewis acid. This 1,2-hydrocarbation process does not proceed through a concerted mechanism as in alkyne syn-hydroboration, or through an intramolecular 1,3-hydride migration as operates in the only other reported alkyne 1,2-hydrocarbation reaction. Instead, in this study, alkyne 1,2-hydrocarbation proceeds by a novel mechanism involving alkyne dehydrocarbation with a carbon Lewis acid based FLP to form the new C−C bond. Subsequently, intermolecular hydride transfer occurs, with the Lewis acid component of the FLP acting as a hydride shuttle that enables alkyne 1,2-hydrocarbation.     

Evidence of mechanisms occurring in thermally induced phase separation of polymeric systems

Thermally induced phase separation is a fabrication technique for porous polymeric structures. By means of easy‐to‐tune processing parameters, such as system composition and demixing temperature, a vast latitude of average pore dimensions, pore size distributions, and morphologies can be obtained. The relation between demixing temperature and morphology was demonstrated via cloud point curve measurement and foams fabrication with controlled thermal protocols, for the model system poly‐l ‐lactide–dioxane–water. The morphologies obtained at a temperature lower than cloud point showed a closed‐pore architecture, suggesting a “nucleation‐and‐growth” separation mechanism, which produced larger pores at higher holding times. Conversely, the porous structures attained when holding the sample above the cloud point exhibited open pores with dimensions independent of time, denoting a phase separation occurring during sample freezing. Finally, the influence of the cooling rate on final morphology was investigated, showing a clear correlation with microstructure and pore size. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 979–983