Bright‐Dark Rogue Waves

During the last two decades, revealing mechanisms of origin waves with anomalous amplitude (rogue waves) have been in the focus of researchers from different fields ranging from oceanography to laser physics. Mode‐locked lasers, as a test bed system, provide a unique opportunity to collect more data on rogue waves in the form of random pulses (soliton rain) and to clarify the mechanisms of rogue‐wave emergence caused by soliton–soliton and soliton–dispersive wave interactions. Here, for the first time, for an Er‐doped mode‐locked laser, a new type of vector rogue waves is demonstrated experimentally and theoretically, which is driven by desynchronization of the orthogonal linear states of polarization, so leading to output power oscillations in the form of anomalous spikes‐dips (bright‐dark rogue waves). The results can pave the way to unlocking the universal nature of the origin of rogue waves and thus can be of interest to the broad scientific community.     

Steric effects on the mechanism of reaction of nucleophilic substitution of β‐substituted alkoxyvinyl trifluoromethyl ketones with four secondary amines

The kinetics of the reaction of β‐substituted β‐alkoxyvinyl trifluoromethyl ketones R¹O‐CR²?CH‐COCF₃ ( 1a – e ) [( 1a ), R¹?C₂H₅, R²?H; ( 1b ), R¹?R²?CH₃; ( 1c ), R¹?C₂H₅, R²?C₆H₅; ( 1d ), R¹?C₂H₅, R²?V^?pNO₂C₆H₄; ( 1e ), R¹?C₂H₅, R²?C(CH₃)₃] with four aliphatic amines ( 2a – d ) [( 2a ), (C₂H₅)₂NH; ( 2b ), (i‐C₃H₇)₂NH; ( 2c ), (CH₂)₅NH; ( 2d ), O(CH₂CH₂)₂NH] was studied in two aprotic solvents, hexane and acetonitrile. The least reactive stereoisomeric form of ( 1a – d ) was the most populated ( E‐s‐Z‐o‐Z ) form, whereas in ( 1e ), the more reactive form ( Z‐s‐Z‐o‐Z ) dominated. The reactions studied proceeded via common transition state formation whose decomposition occurred by ‘uncatalyzed’ and/or ‘catalyzed’ route. Shielding of the reaction centre by bulky β‐substituents lowered abruptly both k′ (‘uncatalyzed’ rate constant) and k″ (‘catalyzed’ rate constant) of this reaction. Bulky amines reduced k″ to a greater extent than k′ as a result of an additional steric retardation to the approach of the bulky amine to its ammonium ion in the transition state. An increase in the electron‐withdrawing ability of the β‐substituent increased ‘uncatalyzed’ k′ due to the acceleration of the initial nucleophile attack (k₁) and ‘uncatalyzed’ decomposition of transition state (k₂) via promoting electrophilic assistance (through transition state 8 ). The amine basicity determined the route of the reaction: the higher amine basicity, the higher k₃/k₂ ratio (a measure of the ‘catalyzed’ route contribution as compared to the ‘uncatalyzed’ process) was. ‘Uncatalyzed’ route predominated for all reactions; however in polar acetonitrile the contribution of the ‘catalyzed’ route was significant for amines with high pK_a and small bulk. Copyright © 2007 John Wiley & Sons, Ltd.     

Stochastic phenomena in a fiber Raman amplifier

The interplay of such cornerstones of modern nonlinear fiber optics as a nonlinearity, stochasticity and polarization leads to variety of the noise induced instabilities including polarization attraction and escape phenomena harnessing of which is a key to unlocking the fiber optic systems specifications required in high resolution spectroscopy, metrology, biomedicine and telecommunications. Here, by using direct stochastic modeling, the mapping of interplay of the Raman scattering‐based nonlinearity, the random birefringence of a fiber, and the pump‐to‐signal intensity noise transfer has been done in terms of the fiber Raman amplifier parameters, namely polarization mode dispersion, the relative intensity noise of the pump laser, fiber length, and the signal power. The obtained results reveal conditions for emergence of the random birefringence‐induced resonance‐like enhancement of the gain fluctuations (stochastic anti‐resonance) accompanied by pulse broadening and rare events in the form of low power output signals having probability heavily deviated from the Gaussian distribution.

     

Synthesis, characterization, and controlled aggregation of biotemplated polystyrene nanodisks

Cross-linked polystyrene nanodisks were prepared by controlled polymerization of styrene and divinylbenzene in the interior of bicelles, discoidal lipid aggregates. Aggregation behavior of polymer nanodisks was studied in water, organic solvents, and solid phase. Nanodisks form stable dispersions in aqueous solutions of surfactants, such as sodium dodecyl sulfate (SDS). Varying SDS/nanodisk ratio allowed us to control the size of nanodisk aggregates. Nanodisks are readily solubilized in nonpolar organic solvents, such as toluene and carbon tetrachloride, to yield stable monodisperse suspensions. These findings open opportunities for creating nanodisk-based nanocomposite materials. Stable nanodisk suspension in toluene enabled small angle neutron scattering (SANS) measurements. SANS data confirmed the nanodisk diameter and allowed accurate measurement of nanodisk thickness (19.5 ± 1.0 Å). In solid phase, nanodisks aggregate in sub-micron platelets.     

Physical properties of SrSn(4) single crystals

We present detailed thermodynamic and transport measurements on single crystals of the recently discovered binary intermetallic superconductor, SrSn(4). We find this material to be a slightly anisotropic three-dimensional, strongly coupled, possibly multiband, superconductor. Hydrostatic pressure causes a decrease in the superconducting transition temperature at the rate of ≈?-?0.068?K?kbar(-1). Band structure calculations are consistent with experimental data on the Sommerfeld coefficient and upper superconducting critical field anisotropy, and suggest a complex, multi-sheet Fermi surface formed by four bands.     

Instability of Fabry-Perot interferometer with a multilayered paramagnetic filling

The results of the analysis of the stability of stationary solutions of wave equations discribing a behavior of the nonlinear Fabry-Perot interferometer with a saturated paramagnetic filling are presented in this paper. The cases when paramagnetic medium is characterized by a homogeneously and nonhomogeneously broadened line of the magnetic resonance have been considered. Areas of unstable behavior of these characteristics of the resonance structure have been found.     

Formulae and continuity for the index of subfactors

Let be an inclusion of -factors, the trace state of , and , the set of projections in and , respectively. We prove that the Jones index for the inclusion is

This formula is exploited to obtain continuity results for the index. In particular, we obtain a formula for the index which expresses in terms of the positions of and , in , when and are finite-dimensional -subalgebras with dense union in and , respectively.

     

The Variational Principle for a Class of Asymptotically Abelian C*-Algebras

Let (A,α) be a C^*-dynamical system. We introduce the notion of pressure P _α(H) of the automorphism α at a self-adjoint operator H∈A. Then we consider the class of AF-systems satisfying the following condition: there exists a dense α-invariant *-subalgebra ? of A such that for all pairs a,b∈? the C^*-algebra they generate is finite dimensional, and there is p=p(a,b)∈ℕ such that [α ^j (a),b]= 0 for |j|≥p. For systems in this class we prove the variational principle, i.e. show that P _α(H) is the supremum of the quantities h _φ(α) −φ(H), where h _φ(α) is the Connes–Narnhofer–Thirring dynamical entropy of α with respect to the α-invariant state φ. If H∈A, and P _α(H) is finite, we show that any state on which the supremum is attained is a KMS-state with respect to a one-parameter automorphism group naturally associated with H. In particular, Voiculescu's topological entropy is equal to the supremum of h _φ(α), and any state of finite maximal entropy is a trace. Received: 19 April 2000 / Accepted: 14 June 2000     

Numerical solution of the problem of computational time reversal in a quadrant

The problem of computational time reversal is posed as the inverse problem of the determination of an unknown initial condition with a finite support in a hyperbolic equation, given the Cauchy data at the lateral surface. Two such two-dimensional inverse problems are solved numerically in the case when the domain is a quadrant and the Cauchy data are given at finite parts of the coordinate axes. The previously obtained Lipschitz stability estimate implies refocusing of the time-reversed wave field in the case of a small amount of noise in the data. It also indicates the possibility of good performance of a proper numerical method. Such performance is demonstrated in this paper for a particular problem and a particular numerical method.     

19F+27Al耗散反应中双核系统的转动与形变

测量了¹⁹F+²⁷Al耗散反应产物B,C,N,O,F和Ne的激发函数,入射束流的能量从110.25MeV到118.75MeV, 能量步长为250keV. 从产物的 能量自关联函数中提取了反应中所形成的中间双核系统的转动惯量, 与相粘模型计算的刚体转动惯量相比较, 结果表明形成的双核系统有大的形变.