Fractional damping enhances chaos in the nonlinear Helmholtz oscillator

Nonlinear Dynamics - The main purpose of this paper is to study both the underdamped and the overdamped dynamics of the nonlinear Helmholtz oscillator with a fractional-order damping. For that...     

1/N-Expansion for the Dicke model and the decoherence program

An analysis of the Dicke model, N two-level atoms interacting with a single radiation mode, is done using the Holstein-Primakoff transformation. The main aim of the paper is to show that, changing the quantization axis with respect to the common usage, it is possible to prove a general result either for N or the coupling constant going to infinity for the exact solution of the model. This completes the analysis, known in the current literature, with respect to the same model in the limit of N and volume going to infinity, keeping the density constant. For the latter the proper axis of quantization is given by the Hamiltonian of the two-level atoms and for the former the proper axis of quantization is defined by the interaction. The relevance of this result relies on the observation that a general measurement apparatus acts using electromagnetic interaction and so, one can state that the thermodynamic limit is enough to grant the appearance of classical effects. Indeed, recent experimental results give first evidence that superposition states disappear interacting with an electromagnetic field having a large number of photons.     

An adaptive filter for gravitational-wave antennas

Summary We report on the development of an adaptive optimum filter for processing the data of a resonant bar gravitational-wave detector. This filter, based on the matched-filter theory, is adaptive in the sense that the function it realizes is derived from the actual noise spectrum of the data being analysed (instead from an idealized model of the noise). Its implementation is mostly based on frequency domain techniques. We also report on the application of the new filter to the data of the cryogenic antenna Explorer of the Rome group, with particular reference to the comparison between its performance and that of an otpimum filter with fixed values of the parameters.     

Solid-state photodimerization of steroid enones

Androst-4-ene-3,17-dione (1) and 17alpha-methyltestosterone (2) are dimerized in the solid-state by UV radiation. These substances were selected by a search in the CSD among the steroid enones presenting in the crystalline state an intermolecular short contact between a hydrogen alpha to a carbonyl group and the oxygen of an enone system. Dimerization occurs by transfer of the hydrogen to the oxygen and connection between the two involved carbons. Androst-4-ene-3,17-dione (1) affords dimer 3 and trimer 4, both formed by connection of the C-16 of a molecule with the C-3 of a near one. Irradiation of 17alpha-methyltestosterone (2) gives the isomeric trienones 5 and 6. These compounds are reasonably formed by dehydration of unisolated intermediate products 7 and/or 8 obtained by coupling of two molecules through a linkage between the C-2 and the C-3' carbons. The formation mechanisms of the photoproducts are satisfactory explained on the basis of the molecular arrangement of the monomers in the crystal state. Modeling of the dimeric molecules was done using molecular mechanics calculations. A single-crystal X-ray of the dimer of androst-4-ene-3,17-dione confirms the structural interpretation of spectral data. The conformer found in the solid-state agrees well with the results of molecular mechanics calculations.     

Dimer asymmetry in superoxide dismutase studied by molecular dynamics simulation

Summary Molecular dynamics (MD) simulations of 100 ps have been carried out to study the active-site behaviour of the Cu,Zn superoxide dismutase dimer (SOD) in water. The active site of each subunit was monitored during the whole simulation by calculating the distances between functional residues and the catalytic copper. The results indicate that charge orientation is maintained at each active site but the solvent accessibility varies. Analysis of the MD simulation, carried out by using the atomic displacement covariance matrix, has shown a different intra-subunit correlation pattern for the two monomers and the presence of inter-subunit correlations. The MD simulation presented here indicates an asymmetry in the two active sites and different dynamic behaviour of the two SOD subunits.     

The photoconversion R-CH3 → R-CHO in indazole derivatives

The UV irradiation of 1-(p-nitrophenyl)-3-methyl-indazole leads to the formation of the corresponding 3-formyl derivative as product of the photooxidation R-CH₃ → R-CHO. This method was applied to a series of substituted indazoles and the same reaction was observed with methyl groups attached to the pyrazole and to the benzene ring of the indazole.     

On the reaction of Ph2PNHPPh2 with RNCS (R=Et, Ph, p-NO2C6H4): preparation of the zwitterionic ligand EtNHC(S)Ph2P==NPPh2C(S)NEt (HSNS) and the zwitterionic metalate [(SNS)Rh(CO)

The reaction of Ph(2)PNHPPh(2) (PNP) with RNCS (Et, Ph, p-NO(2)(C(6)H(4))) gives addition products resulting from the attack of the P atoms of PNP on the electrophilic carbon atom of the isothiocyanate. When PNP is reacted with EtNCS in a 1:2 molar ratio, the zwitterionic molecule EtNHC(S)PPh(2)==NP(+)Ph(2)C(S)N(-)Et (HSNS) is obtained in high yield. HSNS can be protonated (H(2)SNS(+)) or deprotonated (SNS(-)), behaving in the latter form as an S,N,S-donor pincer ligand. The reaction of HSNS with [(acac)Rh(CO)(2)] (acac=acetylacetonate) affords the zwitterionic metalate [(SNS)Rh(CO)]. Other products can be obtained depending on the R group, the PNP/RNCS ratio (1:1 or 1:2), and the reaction temperature. The proposed product of the primary attack of PNP on RNCS, Ph(2)PN==PPh(2)C(S)NHR (A), cannot be isolated. Reaction of A with another RNCS molecule leads to 1:2 addition compounds of the general formula RNHC(S)PPh(2)==NP(+)Ph(2)C(S)N(-)R (1), which can rearrange into the non-zwitterionic product RNHC(S)PPh(2)==NP(S)Ph(2) (2) by eliminating a molecule of RNC. Two molecules of A can react together, yielding 1:1 PNP/RNCS zwitterionic products of the formula RNHCH[PPh(2)==NP(S)Ph(2)]PPh(2)==NP(+)Ph(2)C(S)N(-)R (3). Compound 3 can then rearrange into RNHCH[PPh(2)==NP(S)Ph(2)](2) (4) by losing a RNC molecule. When R=Et (a), compounds 1 a, 2 a (HSNS), and 4 a have been isolated and characterized. When R=Ph (b), compounds 2 b and 4 b can be prepared in high yield. When R=p-NO(2)C(6)H(4) (c), only compound 3 c is observed and isolated in high yield. The crystal structures of HSNS, [(SNS)Rh(CO)], and of the most representative products have been determined by X-ray diffraction methods.     

Hetero Diels-Alder reactions (HDAR) of α,α′-dioxothiones on solid support

Solid-supported α,α′-dioxothiones are easily obtained starting from β-ketoester modified Wang and hydroxymethylated polystyrene resins. The hetero Diels-Alder reactions (HDAR) of these species, used either as electron-poor dienes or dienophiles, followed by a simple cleavage of the products from the resin by trans-esterification with sodium methoxide, allowed the isolation of the desired cycloadducts in overall yields up to 90%.