The dynamics of spatiotemporal modulations

The modulational instability of traveling waves is often thought to be a crucial point in the mechanism of transition to space-time disorder and turbulence. The aim of this paper is to study the effect of spatiotemporal modulations on some dynamics u(0)(x,t), which may occur as an instability process when a control parameter varies, for instance. We analyze the properties of the modulated dynamics of the form g(1)(x)g(2)(t)u(0)(x,t) compared to those of the reference dynamics u(0)(x,t), using operator theory. We show that, if the reference dynamics is invariant under some space-time symmetry in the sense of Ref. [J. Nonlinear Sci. 2, 183 (1992)], the modulation has the effect of either deforming this symmetry or breaking it, depending on whether the corresponding operator remains unitary or not. We also demonstrate that the smallest Euclidean space containing the modulated dynamics has a dimension smaller than or equal to the smallest Euclidean space containing u(0)(x,t). The previous results are then applied to the case of modulated uniformly traveling waves. While the spatiotemporal translation invariance of the wave never persists in the presence of a modulation, the existence of a spatiotemporal symmetry depends on the resonance of the Fourier sidebands due to the modulation. In case of nonresonance, a spatiotemporal symmetry exists and is explicitly determined. In this situation, the modulated wave and the carrier wave have the same spectrum (up to a normalization factor), the same entropy, and the spatial (resp., temporal) two-point correlation is deformed only by the spatial (resp., temporal) modulation. (c) 1995 American Institute of Physics.     

Addition conjuguee d'equivalents d'acyles aux cyclohexen-2 ones et a la Δ1(9) octalone-2: Synthese de dicetones 1–4.

The synthesis of 3-acetylcyclohexanones $\text{11}$, $\text{12}$, $\text{13}$ has been realized by conjugate addition of lithiated cyanohydrin ether $\text{1a}$ to 2-cyclohexenones $\text{2}$, $\text{3}$, $\text{4}$ in THF-HMPA, even if 3-substituted. 3-benzoylcyclohexanones $\text{14}$, $\text{15}$, $\text{16}$ are obtained from $\text{1b}$ and $\text{2}$, $\text{3}$, $\text{4}$ in THF with excellent yields.     

Alternierende Copolymerisation von Styrol und Benzylmethacrylat in Gegenwart von Ethylaluminiumsesquichlorid

Zusammenfassung Die alternierende Copolymerisation von Styrol und Benzylmethacrylat in Gegenwart von Ethylaluminiumsesquichlorid als Katalysator zeigt im Anfangsstadium der Reaktion ein vom weiteren Verlauf abweichendes Verhalten. So nehmen die Zusammensetzung und die Grenzviskositäten der Produkte sowie die Reaktionsgeschwindigkeit erst nach der Anfangsphase konstante Werte an.Die¹H-NMR-Spektren von alternierenden und statistischen Copolymeren gleicher Bruttozusammensetzung zeigen deutliche Unterschiede. Das Spektrum des alternierenden Copolymeren bestätigt die alternierende Struktur und spricht gleichzeitig für einen ataktischen Kettenaufbau.

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The alternating copolymerization of styrene and benzylmethacrylate shows a different behaviour at the beginning of the reaction and later on. Thus the composition and the intrinsic viscosity of the products as well as the reaction rate become constant only after the initial stage.The¹H-NMR-spectra of alternating and statistical copolymers with equal composition show distinct differences. The spectrum of the alternating copolymer confirms the alternating structure as well as an atactic chain configuration.

     

Analysis of thermal behaviour of high power semiconductor laser arrays by means of the finite element method (FEM)

New results of steady-state two-dimensional finite-element computations of temperature distributions of high power semiconductor laser arrays are presented. The influence of different thermal loads on the 2D temperature distribution in AlGaAs/GaAs gain-guided laser arrays is investigated. TheFEM model is tested by comparing it with analytical solutions. For numerical convenience, the latter is rewritten in a novel form, which is free of overflow problems. The maximum temperatures calculated by both methods agree within 1%. Several factors determining the thermal resistance of the device are quantitatively examined: the ratio of light emitting to non-emitting areas along the active zone, the amount of Joule losses, the current spreading, the solder thickness, and voids in the solder. This yields design rules for optimum thermal performance.     

Fragmentation dynamics of ammonia cluster ions after single photon ionisation

A reflecting time of flight mass spectrometer (RETOF) is used to study unimolecular and collision induced fragmentation of ammonia cluster ions. Synchrotron radiation from the BESSY electron storage ring is used in a range of photon energies from 9.08 up to 17.7 eV for single photon ionisation of neutral clusters in a supersonic beam. The threshold photoelectron photoion coincidence technique (TPEPICO) is used to define the energy initially deposited into the cluster ions. Metastable unimolecular decay (µs range) is studied using the RETOF's capacity for energy analysis. Under collision free conditions the by far most prominent metastable process is the evaporation of one neutral NH₃ monomer from protonated clusters (NH₃) _{n ? 2}NH ₄ ⁺ . Abundance of homogeneous vs. protonated cluster ions and of metastable fragments are reported as a function of photon energy and cluster size up ton=10.     

Electrochemistry and photoelectron spectroscopy of oxomolybdenum(V) complexes with phenoxide ligands: effect of para substituents on redox potentials,heterogeneous electron transfer rates,and ionization energies

Complexes of the form (Tp*)MoOCl(p-OC(6)H(4)X) and (Tp*)MoO(p-OC(6)H(4)X)(2) (Tp* = hydrotris(3,5-dimethyl-1-pyrazolyl)borate and X = OEt, OMe, Et, Me, H, F, Cl, Br, I, and CN) were examined by electrochemical techniques and gas-phase photoelectron spectroscopy to probe the effect of the remote substituent (X) on electron-transfer reactions at the oxomolybdenum core. Cyclic voltammetry revealed that all of these neutral Mo(V) compounds undergo a quasireversible one-electron oxidation (Mo(VI)/Mo(V)) and a quasireversible one-electron reduction (Mo(V)/Mo(IV)) at potentials that linearly depend on the electronic influence (Hammett sigma(p) parameter) of X. The first ionization energies for (Tp*)MoO(p-OC(6)H(4)X)(2) (X = OEt, OMe, H, F, and CN) were determined by photoelectron spectroscopy. A nearly linear correlation was found for the Mo(VI)/Mo(V) oxidation potentials in solution and the gas-phase ionization energies. Calculated heterogeneous electron-transfer rate constants show a slight systematic dependence on the substituent.     

The first enantiomerically pure [n]triangulanes and analogues: sigma-[n]helicenes with remarkable features

(M)-(-)- and (P)-(+)-Trispiro[2.0.0.2.1.1]nonanes [(M)- and (P)-3] as well as (M)-(-)- and (P)-(+)-tetraspiro[2.0.0.0.2.1.1.1]undecanes [(M)- and (P)-4]-enantiomerically pure unbranched [4]- and [5]triangulanes-have been prepared starting from racemic bicyclopropylidenecarboxylic [(1RS)-12] and exo-dispiro[2.0.2.1]heptane-1-carboxylic [(1RS,3SR)-13] acids. The optical resolutions of rac-12 and rac-13 furnished enantiomerically pure acids (S)-(+)-12, (R)-(-)-12, (1R,3S)-(-)-13, and (1S,3R)-(+)-13. The ethyl ester (R)-25 of the acid (R)-(-)-12 was cyclopropanated to give carboxylates (1R,3R)-26 and (1R,3S)-26. The ester (1R,3S)-26 and acids (1R,3S)-13 and (1S,3R)-13 were converted into enantiomerically pure methylene[3]triangulanes (S)-(-)- and (R)-(+)-28. An alternative approach consisted of an enzymatic deracemization of endo-[(1SR,3SR)-dispiro[2.0.2.1]heptyl]methanol (rac-20) or anti-[(1SR,3RS)-4-methylenespiropentyl]methanol (rac-18). This afforded (S)-(-)- and (R)-(+)-28 (starting from rac-20), as well as enantiomerically pure (M)-(-)- and (P)-(+)-1,4-dimethylenespiropentanes [(M)- and (P)-23] starting from rac-18. The methylenetriangulanes (S)-(-)- and (R)-(+)-28 were cyclopropanated furnishing (M)- and (P)-3. The rhodium-catalyzed cycloaddition of ethyl diazoacetate onto (S)-(-)- and (R)-(+)-28 yielded four diastereomeric ethyl trispiro[2.0.0.2.1.1]nonane-1-carboxylates in approximately equal proportions. The enantiomerically pure esters (1R,3S,4S)- and (1S,3R,4R)-30 were isolated by careful distillation and then transformed into [5]triangulanes (M)- and (P)-4 using the same sequence of reactions as applied for (M)- and (P)-3. The structures of the key intermediates (R)-12 and rac-31 were confirmed by X-ray analyses. Although [4]- and [5]triangulanes have no chromophore which would lead to any significant absorption above 200 nm, they have remarkably high specific rotations even at 589 nm with [alpha](20)D=-192.7 [(M)-3, c=1.18, CHCl(3))] or +373.0 [(P)-4, c=1.18, CHCl(3))]. This remarkable optical rotatation is in line with their helical arrangement of sigma bonds, as confirmed by a full valence space single excitation configuration interaction treatment (SCI) in conjunction with DFT computations at the B3LYP/TZVP//B3LYP/6-31+G(d,p) level of theory which reproduce the ORD very well. Thus, it is appropriate to call the helically shaped unbranched [n]triangulanes the "sigma-[n]helicenes", representing the sigma-bond analogues of the aromatic [n]helicenes.     

1,2,4,5‐Tetrazines vs. Carboxylic Acid Dimers: Molecular Chemistry vs. Supramolecular Chemistry

The structures of six new tetrazines have been determined and their molecular packing has been compared to the supermolecular architecture observed in related carboxylic acid dimers. In the tetrazines, covalent N? N bonds are considered to replace the intermolecular O? H???O hydrogen bonds of the carboxylic acids. In the systems investigated, it is apparent that, in the majority of cases, the covalent six‐membered ring of the tetrazine is an appropriate replacement for the carboxylic acid synthon. This apparent interplay between molecular and supramolecular units may have applications in the crystal engineering of new materials.     

SCF-Xα-SW model calculations for metal clusters of nickel,copper, and silver and for the oxygen chemisorption on these metals

The oxygen chemisorption on Ni, Cu and Ag is studied by comparing PE spectra of these systems and SCF-Xα scattered-wave cluster models. Consideration of octahedral clusters M₆ (M = Ni, Cu, Ag) shows that they are large enough to reproduce trends in energy differences, such as the width of the d-bands and the distance from the top of the d-bands to the Fermi level, as found in experiment and in bulk energy band calculations. Substrate model clusters for the interaction of oxygen with different metal surfaces are derived from an octahedron by removing one ((100) face) or two adjacent metal atoms ((110) face). Comparing the UPS difference spectrum for O/Ag (110) with several Ag₄O cluster models makes it possible to interpret the peaks above the Ag d-band as O-Ag anti-bonding levels. These peaks are caused by O 2p-Ag 4d and O 2p-Ag 5s interaction. The corresponding bonding levels fall in the Ag d-bands and cannot therefore be identified with confidence in the spectra. The decreasing intensity of the oxygen derived peak below the metal d-band in the UPS spectra when going from Ni to Cu to Ag, and the simultaneously increasing O peaks above the d-band correlate with the changes of the localization of the corresponding bonding and anti-bonding levels in the oxygen sphere and the decreasing strength of the chemisorption bond.