Synchronization Analysis of Coupled Noncoherent Oscillators

We present two different approaches to detect and quantify phase synchronization in the case of coupled non-phase coherent oscillators. The first one is based on the general idea of curvature of an arbitrary curve. The second one is based on recurrences of the trajectory in phase space. We illustrate both methods in the paradigmatic example of the R?ssler system in the funnel regime. We show that the second method is applicable even in the case of noisy data. Furthermore, we extend the second approach to the application of chains of coupled systems, which allows us to detect easily clusters of synchronized oscillators. In order to illustrate the applicability of this approach, we show the results of the algorithm applied to experimental data from a population of 64 electrochemical oscillators.     

Resonances and microlocal analysis

In this paper we outline briefly how microlocal analysis can be applied to give a general approach to the mathematical theory of resonances in the semiclassical limit. We also describe recent results about the asymptotic behavior of resonances generated by closed trajectories and stationary points in the classical flow.     

Thermal analysis by EMF-measurements on solid electrolytes

Galvanic cells of the type (C+Cl₂)(NaCl_(s))(MCl_2(s))(C+Cl₂) give e. m. f. 's above 280°, which are due to the formation of ternary chlorides Na_nMCl_n+2. By the change in slope of continuously measured e.m.f.vs. T curves, the temperatures of solid-state reactions in systems NaCl-MCl₂ can be found. This method was applied for the systems of NaCl with NiCl₂, CoCl₂ and CdCl₂, and for KCl-NiCl₂. With the exception of the system NaCl-NiCl₂, all phase diagrams must be corrected.

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Zusammenfassung Mit galvanischen Zellen des Typs (C+Cl₂)/NaCl_(s)/MCl_2(s)/(C+Cl₂) lassen sich oberhalb 280° EMK's messen, die auf der Bildung ternärer Chloride Na_nMCl_n+2 beruhen. Durch die Änderung der Steigung kontinuierlich gemessener EMK- gegen T-Kurven lassen sich in Systemen NaCl/MCl₂ die Temperaturen von Festkörperreaktionen nachweisen. Diese Methode wurde auf die Systeme des NaCl mit NiCl₂, CoCl₂ und CdCl₂ sowie auf das System KCl-NiCl₂ angewendet. Alle Phasendiagramme, mit Ausnahme des Systems NaCl-NiCl₂, mußten auf Grund dieser Messungen revidiert werden.

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(C+Cl₂)/NaCl./MCl₂./(C +Cl₂) 280 °C . . , Na_nMCl_n+2. . . , NaCl-MCl₂. NaCl NiCl₂, CoCl₂, CdCl₂ KCl-NiCl₂. NaCl-NiCl₂,ce .

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This work was supported by the Deutsche Forschungsgemeinschaft and the Fonds der Chemischen Industrie.     

The Donor-Acceptor-Acceptor Purine Analog: Transformation of 5-aza-7-deaza-1H-isoguanine (=4-aminoimidazo-[1,2-a]-1,3,5-triazin-2(1H)-one) to 2′-deoxy-5-aza-7-deaza-isoguanosine using purine nucleoside phosphorylase

A new synthesis is reported for 4-aminoimidazo[1,2-a]-1,3,5-triazin-2(1H)-one ( =5-aza-7-deaza-isoguanosine; 8 ), a purine analog that, when incorporated into an oligonucleotide chain, presents a H-bond donor-acceptor-acceptor pattern to a complementary pyrimidine analog. A protected ribose derivative was coupled to 8 to yield 4-amino-8-(β-D -ribofuranosyl)imidazo[1,2-a]-1,3,5-triazin-2(8H)-one ( =5-aza-7-deaza-isoguanosine; 11 ) after deprotection, Alternatively, direct synthesis of both the ribo derivative 11 and the corresponding deoxyribo derivative 17 as the β-D -anomers was achieved using the enzyme purine nucleoside phosphorylase in a one-pot reaction. This adapts a known synthetic approach to yield a new strategy for obtaining diastereoisomerically pure deoxyribonucleoside analogs on 1-gram scales.     

Successive coordination of palladium(II)-ions and terpyridine-ligands to a pyridyl-terminated self-assembled monolayer on gold

The deposition of palladium on a novel, reversibly protonatable, pyridyl-terminated self-assembled monolayer on gold substrates has been studied by X-ray photoelectron spectroscopy (XPS), near-edge X-ray absorption fine structure spectroscopy (NEXAFS spectroscopy) and time of flight-secondary ion mass spectrometry (ToF-SIMS). For this purpose, 12-(pyridin-4-yl)dodecane-1-thiol, consisting of a surface-active head group, an unfunctionalized hydrocarbon backbone and a terminal pyridyl group, has been synthesized and deposited on gold surfaces. Coordination of Pd(II) ions to the pyridyl group was examined. Furthermore, a reversible protonation/deprotonation cycle has been applied, and the relation between protonation and the amount of complexed palladium was studied. Investigation of the SAM by angle-resolved NEXAFS spectroscopy revealed the aliphatic backbone to be preferentially upright oriented with the aromatic head group being not preferentially oriented. The palladium layer was further coordinated with a CF₃-labeled terpyridine ligand in order to prove the accessibility of the Pd(II) ions to further complexation and the platform useful for deposition of further layers toward a multi-layered system.     

Traveling Salesman Problem with Clustering

In the original traveling salesman problem, the traveling salesman has the task to find the shortest closed tour through a proposed set of nodes, touching each node exactly once and returning to the initial node at the end. For the sake of the tour length to be minimized, nodes close to each other might not be visited one after the other but separated in the tour. However, for some practical applications, it is useful to group nodes to clusters, such that all nodes of a cluster are visited contiguously. Here we present an approach which leads to an automatic clustering with a clustering parameter governing the sizes of the clusters.