Studying noise-induced intermittency in multistable systems on the basis of reference systems

The noise-induced intermittent behavior of multistable systems is studied using the example of a reference system (a Chua generator). It is shown that upon exposing the Chua generator to external noise, a noise-induced intermittency is observed at certain values of the control parameters. The statistical characteristics obtained for this type of behavior are compared to the appropriate theoretical formulas.     

Rotating bound states of dissipative solitons in systems of reaction-diffusion type

We report on the formation of stable rotating bound states consisting of self-organized well localized solitary structures with particle-like behaviour in systems of reaction-diffusion type. These dissipative solitons are detected in an experimental planar d.c. gas-discharge system with a high ohmic barrier, as well as in numerical solutions of related three-component reaction-diffusion equations where the formation of rotating bound states is investigated in the context of a particle ansatz.Received: 15 July 2003, Published online: 15 March 2004PACS: 89.75.Fb Structures and organization in complex systems - 82.40.Ck Pattern formation in reactions with diffusion, flow and heat transfer - 52.80.Tn Other gas discharges     

Apparent two-dimensional behavior of TiO2 nanotubes revealed by light absorption and luminescence

Optical absorption and photoluminescence (PL) properties of colloidal TiO(2) nanotubes, produced by the alkali hydrothermal method, were studied at room temperature in the range 300-700 nm. Nanotubes having an internal diameter in the range 2.5-5 nm have very similar optical properties, in contrast to the expected behavior for quasi-1-D systems. This is explained by the complete thermal smearing of all 1-D effects, due to the large effective mass of charge carriers in TiO(2), resulting in an apparent 2-D behavior of TiO(2) nanotubes.     

Reaction of acetyl- and 1,1′-diacetylferrocene with isatin (Pfitzinger reaction)

An efficient method for the synthesis of 2-ferrocenyl-substituted quinoline-4-carboxylic acids via the reaction of acetyl- and 1,1′-diacetylferrocene with isatin under the conditions of the Pfitzinger reaction was developed. Starting from the obtained acids methyl esters, amides, N-methyl-N-methoxyamides, and oximes (at one of the free acetyl groups) of some of these compounds were synthesized.     

Choosing the state of a spatially distributed system in calculating a spectrum of Lyapunov exponents

The problem of choosing the set of parameters that determine the state of a spatially distributed system when calculating a spectrum of Lyapunov exponents is considered. The possibility of reducing the number of necessary quantities due to the features of the employed mathematical model is discussed. The proposed method is successfully applied to a hydrodynamic model of a Piers diode.     

Diagram analysis of the Hubbard model: Stationarity property of the thermodynamic potential

The diagram approach proposed many years ago for the strongly correlated Hubbard model is developed with the aim to analyze the thermodynamic potential properties. A new exact relation between renormalized quantities such as the thermodynamic potential, the one-particle propagator, and the correlation function is established. This relation contains an additional integration of the one-particle propagator with respect to an auxiliary constant. The vacuum skeleton diagrams constructed from the irreducible Green’s functions and tunneling propagator lines are determined and a special functional is introduced. The properties of this functional are investigated and its relation to the thermodynamic potential is established. The stationarity property of this functional with respect to first-order variations of the correlation function is demonstrated; as a consequence, the stationarity property of the thermodynamic potential is proved.     

Reaction of acetylferrocene with dimethylformamide dimethyl acetal and some transformations of the reaction product

1-Dimethylamino-3-ferrocenyl-3-oxoprop-1-ene was synthesized by the reaction of acetylferrocene with dimethylformamide dimethyl acetal. Its reactivity in the reactions with mononucleophilic (sodium salts of phenol, thiophenol, benzenesulfinate, diethylphosphorous acid) and binucleophilic reagents (hydrazine hydrate, hydroxylamine, amidines, 1,2-diaminobenzene, 2-aminophenol, 2-aminothiophenol) and methyl iodide was studied. As a result, we obtained new ferrocene-containing α-keto-unsaturated compounds and heterocycles of pyrazole, isoxazole, pyrimidine, and benzazepine series. In the reaction with CH₃I formed ferrocenoylacetylene which in the presence of dicarbonyl-bis(triphenylphosphine)nickel catalyst easily trimerized to give a mixture of 1,2,4- and 1,3,5-triferrocenoylbenzene.