Optimal state space reconstruction via Monte Carlo decision tree search

Nonlinear Dynamics - A novel idea for an optimal time delay state space reconstruction from uni- and multivariate time series is presented. The entire embedding process is considered as a game, in...     

Theoretical analysis of bonding properties in 1,1-dicyanocyclopentane and 1,1-dichlorocyclopentane by applying the AIM and NBO approaches

Using Bader’s quantum-topological theory of atoms in molecules (AIM) and Weinhold’s Natural Bond Orbital (NBO) analysis we could rationalize the impact of the geminal substitution by C≡N and Cl on the geometry and electronic structure of the cyclopentane ring in 1,1-dicyanocyclopentane (DCCP) and 1,1-dichlorocyclopentane (DClCP). Among the crucial results we obtained are: 1. The topological quantities, particularly the bond ellipticity of 0.035 for the C–CN bond, indicate that this bond possesses higher bond order than a single bond. This conclusion is clearly supported by the NBO results. 2. The AIM theory as well as the NBO analysis confirm uniformly the non-linearity of the C–C≡N moiety. 3. Regardless the quantum mechanical method that has been employed for a variety of nitriles the sign of the Laplacian of the charge density, ∇²ρ(r), of the C≡N group changes its sign from negative to positive upon moving from the triple zeta to the double zeta basis set. A possible explanation for this striking behavior has been provided. By invoking the AIM and NBO approaches the different endocyclic C–C bond lengths in DCCP and DClCP as a consequence of the geminal substitution could be explained. Also the variations of these bond lengths upon moving from the more stable C _s to the energetically less favorable C ₂ conformer of both compounds could be rationalized. For the purpose of comparison and verification of some findings of this work, we also carried out AIM and NBO calculations on various related cyclic and non-cyclic compounds.     

The gas-phase molecular structure of 1,1-diethynylsilacyclobutane as determined by means of electron diffraction and ab initio calculations

As a continuation of our systematic investigation of the effect of substituents on the ring geometry and dynamics in silacyclobutanes and in order to explore the role of the silicon atom as a mediator for electronic interactions between the attached fragments, we studied the molecular structure of 1,1-diethynylsilacyclobutane (DESCB) by means of gas-phase electron diffraction and ab initio calculations. The structural refinement of the electron diffraction data yielded the following bond lengths (r_a) and bond angles (uncertainties are 3σ): r(Si–C)=1.874(2) Å, r(Si–C)=1.817(1) Å, (C–Si–C)=79.2(6)°, (C–Si–C)=106.5(6)°. The geminal Si–CC moieties were found to be bent outwards by 3.1(15)° and the puckering angle was determined to be 30.0(15)°. The evidently short Si–C bond length, which was also reproduced by the ab initio calculations, could be rationalized as being the consequence of the electronic interaction between the outer π charges of the triple bond and the 3pπ orbitals at the silicon atom. It is also likely that the conjugation of the geminal ethynyl groups leads to an enhancement of this bond contraction. Electrostatic interactions and the subsequent reduction of the covalent radius of the silicon atom may also contribute to this bond shortening. It has been found that the endocyclic Si–C bond length fits nicely within a scheme describing a monotonous decrease of the Si–C bond length with the increase of the electronegativity of the substituent in various geminally substituted silacyclobutanes.A series of related silacyclobutanes and acyclic diethynylsilanes have been studied by applying various ab initio methods and their optimized structures were compared to the structure of DESCB. Among these compounds are 1,1-dicyanosilacyclobutane (DCYSCB), which is isoelectronic to DESCB, 1,1-diethynylcyclobutane (DECB) which is isovalent to DESCB, monoethynylsilacyclobutane (MESCB) and monocyanosilacyclobutane (MCYSCB). Searching for reasonable support for the explanation of the structural results of DESCB we performed detailed natural population analysis as well as Mulliken population analysis (MPA) on DESCB and other related molecules. In contrast to the Mulliken charges, the natural atomic charges provided helpful information concerning the bonding properties in DESCB and the corresponding compounds. By varying the size of some basis sets, we could demonstrate the validity of the repeatedly discussed dependency of the Mulliken MPA on the basis set.For the performance of the quantum mechanical calculations we employed the following methods and basis sets: HF/6-31G(d,p), DFT/B3PW91/6-31G(d), DFT/B3PW91/6-311++G(d,p), MP2/6-31G(d,p) and MP2/6-311++G(d,p).     

Theoretical study on the reaction of the phenoxy radical with O2, OH,and NO2

Unlike the chemistry underlying the self‐coupling of phenoxy (C₆H₅O) radicals, there are very limited kinetics data at elevated temperatures for the reaction of the phenoxy radical with other species. In this study, we investigate the addition reactions of O_2, OH, and NO₂ to the phenoxy radical. The formation of a phenoxy‐peroxy is found to be very slow with a rate constant fitted to k = 1.31 × 10^?20T^2.49 exp (?9300/T) cm³/mol/s in the temperature range of (298–2,000 K) where the addition occurs predominantly at the ortho site. Our rate constant is in line with the consensus of opinions in the literature pointing to the observation of no discernible reaction between the oxygen molecule and the resonance‐stabilized phenoxy radical. Addition of OH at the ortho and para sites of the phenoxy radical is found to afford adducts with sizable well depths of 59.8 and 56.0 kcal/mol, respectively. The phenoxy‐NO₂ bonds are found to be among the weakest known phenoxy‐radical bonds (1.7–8.7 kcal/mol). OH‐ and O₂‐initiated mechanisms for the degradation of atmospheric phenoxy appear to be negligible and the fate of atmospheric phenoxy is found to be controlled by its reaction with NO₂. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

On interrelations of recurrences and connectivity trends between stock indices

Financial data has been extensively studied for correlations using Pearson’s cross-correlation coefficient ρ$\rho$ as the point of departure. We employ an estimator based on recurrence plots — the correlation of probability of recurrence (CPR$CPR$) — to analyze connections between nine stock indices spread worldwide. We suggest a slight modification of the CPR$CPR$ approach in order to get more robust results. We examine trends in CPR$CPR$ for an approximately 19-month window moved along the time series and compare them to trends in ρ$\rho$. Binning CPR$CPR$ into three levels of connectedness (strong, moderate, and weak), we extract the trends in number of connections in each bin over time. We also look at the behavior of CPR$CPR$ during the dot-com bubble by shifting the time series to align their peaks. CPR$CPR$ mainly uncovers that the markets move in and out of periods of strong connectivity erratically, instead of moving monotonically towards increasing global connectivity. This is in contrast to ρ$\rho$, which gives a picture of ever-increasing correlation. CPR$CPR$ also exhibits that time-shifted markets have high connectivity around the dot-com bubble of 2000. We use significance tests using twin surrogates to interpret all the measures estimated in the study.     

Effect of emergent carrying capacity in an eco‐epidemiological system

The paper explores an eco‐epidemiological model of a predator–prey type, where the prey population is subject to infection. The model is basically a combination of S‐I type model and a Rosenzweig–MacArthur predator–prey model. The novelty of this contribution is to consider different competition coefficients within the prey population, which leads to the emergent carrying capacity. We explicitly separate the competition between non‐infected and infected individuals. This emergent carrying capacity is markedly different to the explicit carrying capacities that have been considered in many eco‐epidemiological models. We observed that different intra‐class and inter‐class competition can facilitate the coexistence of susceptible prey‐infected prey–predator, which is impossible for the case of the explicit carrying capacity model. We also show that these findings are closely associated with bi‐stability. The present system undergoes bi‐stability in two different scenarios: (a) bi‐stability between the planner equilibria where susceptible prey co‐exists with predator or infected prey and (b) bi‐stability between co‐existence equilibrium and the planner equilibrium where susceptible prey coexists with infected prey; have been discussed. The conditions for which the system is to be permanent and the global stability of the system around disease‐free equilibrium are worked out. Copyright © 2015 John Wiley & Sons, Ltd.     

250 W single-crystal fiber Yb:YAG laser

We demonstrate an Yb:YAG single-crystal fiber laser with 251 W output power in continuous-wave and an optical efficiency of 44%. This performance can be explained by the high overlap between pump and signal beams brought by the pump guiding and by the good thermal management provided by the single-crystal fiber geometry. The oscillator performance with a reflectivity of the output coupler as low as 20% also shows high potential for power amplification.     

Border effect corrections for diagonal line based recurrence quantification analysis measures

Recurrence Quantification Analysis (RQA) defines a number of quantifiers, which base upon diagonal line structures in the recurrence plot (RP). Due to the finite size of an RP, these lines can be cut by the borders of the RP and, thus, bias the length distribution of diagonal lines and, consequently, the line based RQA measures. In this letter we investigate the impact of the mentioned border effects and of the thickening of diagonal lines in an RP (caused by tangential motion) on the estimation of the diagonal line length distribution, quantified by its entropy. Although a relation to the Lyapunov spectrum is theoretically expected, the mentioned entropy yields contradictory results in many studies. Here we summarize correction schemes for both, the border effects and the tangential motion and systematically compare them to methods from the literature. We show that these corrections lead to the expected behavior of the diagonal line length entropy, in particular meaning zero values in case of a regular motion and positive values for chaotic motion. Moreover, we test these methods under noisy conditions, in order to supply practical tools for applied statistical research.     

Surface analysis of polymers and catalysts

Summary The use of solid-state mass spectrometry for studying polymers is evaluated. Structural differences between polymers can be obtained by laser mass spectrometry by observing fingerprint-like spectra in the range m/z<250. Secondary-ion mass spectra (SIMS) revealed fragments that show the spacing of the repeat unit of the polymer up to m/ z 3,500. Oligomer distributions of low molecular weight polymers can be estimated by laser mass spectrometry. The order of monomer addition can be estimated by measuring three-carbon fragment ions in polyvinylidene fluoride. The value of SIMS for studying surface reactions is reviewed. Detection of surface impurities on polymer surfaces is possible using the laser microprobe LAMMA-1000. The specific example discussed involves detecting dye molecules on polystyrenes.The use of X-ray photoelectron spectroscopy (ESCA) for the study of supported catalysts is evaluated. Variations of the surface structure and reactivity of the deposited phase, brought about by changing the active phase loading, some preparation variables or by modifying the carrier, were monitored by ESCA. The results were compared to those obtained from classical methods such as transmission electron microscopy, chemisorption and gravimetric measurements; they correlated with catalytic behavior.

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Oberflächenanalyse von Polymeren und Katalysatoren

Zusammenfassung Der Einsatz der Festkörper-Massenspektrometrie zur Untersuchung von Polymeren wird bewertet. Strukturunterschiede bei Polymeren können durch Laser-Massenspektrometrie erhalten werden, indem fingerprintähnliche Spektren im Bereich m/z < 250 beobachtet werden. Sekundärionen-Massenspektren (SIMS) offenbaren Fragmente, welche die Länge der Basiszellen bei Polymeren bis zu m/z-Werten von 3500 anzeigen. Oligomerverteilungen von Polymeren mit kleinerem Molekulargewicht können durch Laser-Massenspektrometrie beurteilt werden. Der Grad einer Monomerenaddition kann durch Messung von C₃-Fragment-Ionen in Polyvinylidenfluorid erkannt werden. Ein Überblick über die Bedeutung von SIMS für die Untersuchung von Oberflächenreaktionen wird gegeben. Der Nachweis von Verunreinigungen auf Polymer-Oberflächen gelingt durch den Einsatz der Laser-Mikrosonde LAMMA-1000. Das angeführte Beispiel enthält auch den Nachweis von Farbstoffmolekülen auf Polystyrolen.Die Anwendung der Röntgen-Photoelektronenspektroskopie (ESCA) zur Untersuchung von Trägerkatalysatoren wird ebenfalls bewertet. Änderungen der Oberflächenstruktur und der Reaktivität der aufgebrachten Phase, die durch Änderungen der Phasenbeschichtung oder gewisser Präparationsparameter oder durch Trägermodifizierung verursacht wurden, sind mit Hilfe von ESCA kontrolliert worden. Die Ergebnisse wurden mit denen verglichen, die mit Hilfe klassischer Methoden gewonnen wurden, wie Transmissionselektronenmikroskopie, Chemiesorption und gravimetrische Bestimmungen; sie korrelieren mit dem katalytischen Verhalten.

     

Measurement of the surface coverage of V/Al2O3 catalysts by infrared spectroscopy, CO2 chemisorption and ion scattering spectroscopy

Quantitative FTIR studies of alumina hydroxyl groups have been used to measure the surface coverage of V/Al₂O₃ catalysts. The IR spectra show a preferential consumption of the most basic hydroxyls (3769 cm^–1) with the initial V uptake. The integrated area of the hydroxyl region was used to calculate the surface coverage of the catalysts. The surface coverage increased to 0.63 as the V loading increased to 6.7 wt%. The surface coverage results obtained from IR were compared to those measured by ion scattering spectroscopy (ISS) and CO₂ chemisorption. The surface coverages measured by ISS were comparable to those obtained by IR. In contrast, CO₂ chemisorption appears to overestimate the surface coverage of the catalysts. The overestimation of the surface coverage by the CO₂ chemisorption method is attributed to the preferential adsorption of the V phase onto the most basic hydroxyls, the same sites which interact with CO₂.Dedicated to Professor Dr. Dieter Klockow on the occasion of his 60th birthday