Dynamical and statistical features of soliton interactions in the focusing Gardner equation.

In this paper, the dynamical properties of soliton interactions in the focusing Gardner equation are analyzed by the conventional two-soliton solution and its degenerate cases. Using the asymptotic expressions of interacting solitons, it is shown that the soliton polarities depend on the signs of phase parameters, and that the degenerate solitons in the mixed and rational forms have variable velocities with the time dependence of attenuation. By means of extreme value analysis, the interaction points in different interaction scenarios are presented with exact determination of positions and occurrence times of high transient waves generated in the bipolar soliton interactions. Next, with all types of two-soliton interaction scenarios considered, the interactions of two solitons with different polarities are quantitatively shown to have a greater contribution to the skewness and kurtosis than those with the same polarity. Specifically, the ratios of spectral parameters (or soliton amplitudes) are determined when the bipolar soliton interactions have the strongest effects on the skewness and kurtosis. In addition, numerical simulations are conducted to examine the properties of multi-soliton interactions and their influence on higher statistical moments, especially confirming the emergence of the soliton interactions described by the mixed and rational solutions in a denser soliton ensemble.

Integrable turbulence and statistical characteristics of chaotic wave field in the Kundu-Eckhaus equation.

Integrable turbulence, as an irregular behavior in dynamic systems, has attracted a lot of attention in integrable and Hamiltonian systems. This article focuses on the studies of integrable turbulence phenomena of the Kundu-Eckhaus (KE) equation as well as the generation of rogue waves from the numerical and statistical viewpoints. First, via the Fourier collocation method, we obtain the spectral portraits of different analytical solutions. Second, we perform the numerical simulation on the KE equation under the initial condition of a plane wave with random noise to simulate the chaotic wave fields. Then, we analyze the influences of standard deviation and correlation length on the integrable turbulence and amplitude of wave field. It's found that both of the two parameters have positive effects on the generation probability of rogue wave caused by the interactions. But only the variation of standard deviation can lead to the transition from the breather turbulence to soliton turbulence. Furthermore, by analyzing the effects of additional higher-order nonlinear terms on the chaotic wave field, we find that those two higher-order nonlinear effects in the KE equation can lead to a larger amplitude of the chaotic wave field and a higher probability of generating rouge waves compared with the NLS equation.

2,2'-Diamino-6,6'-diboryl-1,1'-binaphthyl: A Versatile Building Block for Temperature-Dependent Dual Fluorescence and Switchable Circularly Polarized Luminescence.

Temperature-dependent dual fluorescence and switchable circularly polarized luminescence (CPL) are two highly pursued but challenging properties for small organic molecules (SOMs). We herein disclose a triarylborane π-system based on a 2,2'-diamino-6,6'-diboryl-1,1'-binaphthyl scaffold that can serve as a versatile building block for achieving these two properties by simply choosing different amino groups. BNMe2 -BNaph with less bulky dimethylamino groups displays temperature-dependent dual fluorescence, and can thus be used as a highly sensitive ratiometric fluorescence thermometer. On the other hand, BNPh2 -BNaph with bulky diphenylamino groups exhibits intense fluorescence in both solution and in the solid state. A change of solvent from nonpolar cyclohexane to highly polar MeCN not only shifts the CPL position to much longer wavelength but also inverts the CPL sign. In addition, the complexation of BNPh2 -BNaph with fluoride greatly enhances the CPL intensity.

Solid-state emissive B,S-bridged p-terphenyls: synthesis, properties, and utility as bifunctional fluorescent sensor for Hg2+ and F- ions.

The efficient synthesis has been disclosed to achieve a new class of ladder-type molecules, B,S-bridged p-terphenyls (BS-TPs). Their properties were fully characterized by UV-vis and fluorescence spectroscopy in both solution and solid state, time-resolved fluorescence spectroscopy, DFT theoretical calculations, and cyclic voltammetry. A detailed comparison between anti-BS-TP and its analogue B,N-bridged p-terphenyl (BN-TP) was made to elucidate the effect of displacement of bridging N with S atom on the properties. The introduction of S rather than N atom as bridging atom leads to increased fluorescence efficiency in both solution and solid state as well as enhanced reduction stability. And thus this new class of ladder-type molecules are highly emissive in both solution and solid state and display reversible reduction wave in cyclic voltammograms, denoting their promising potentials as electron-transporting solid-state emitters. In addition, this new class of molecules are capable of detecting F(-) and Hg(2+) with different fluorescence responses, owing to the high Lewis acidity of the B center to coordinate with F(-) anions and the great mercury-philicity of the S center to complex with Hg(2+) cations.

Synthesis, structure, and binding property of pentiptycene-based rigid tweezer-like molecules.

A series of pentiptycene-derived rigid tweezer-like molecules have been efficiently synthesized, and their structures have been determined by NMR, MS spectra, and X-ray analysis. Moreover, it was also found that molecular tweezer 15 showed efficient binding ability toward C(60).

Efficient synthesis of a chiral [4]pseudocatenane and its derivatives: a novel ship's wheel-like interlocked structure.

A novel chiral[4]pseudocatenane 5H(3)[PF(6)](3) was synthesized efficiently by treatment of a solution of chiral triptycene-based tri(crown ether) 1 and three equivalents of a bis[p-(but-3-enyloxy)benzyl]ammonium salt in CH(2)Cl(2) with a Grubbs II catalyst, followed by hydrogenation. It was found that the ammonium groups in 5H(3)[PF(6)](3) could be deprotonated by 1,8-diazabicyclo[5.4.0]undec-7-ene (DBU) in acetonitrile or dimethyl sulfoxide (DMSO). Consequently, N-acylation of the ammonium groups was easily performed in the presence of DBU, which resulted in a new class of neutral highly ordered interlocked molecules in good yields. In particular, the incorporation of stopper units, for example, diethyl phosphoramidate, lead to the isolation of the interlocked molecule 10 with an interesting ship's wheel-like structure, which was structurally studied with the help of detailed NMR experiments. Compared with 1, it was further found that the Cotton effect of (R)-1,1'-binaphthyl chromophore at 241 nm was greatly reduced in 5H(3)[PF(6)](3) and its derivatives. Moreover, a new positive Cotton effect at 248 nm appeared in the interlocked molecules; this observation could be attributed to the chirality transfer from the binaphthyl units to the macrocycles lying in the cavities of 1.

A highly efficient approach to [4]pseudocatenanes by threefold metathesis reactions of a triptycene-based tris[2]pseudorotaxane.

A triptycene-based homotritopic host was designed and synthesized. Assembly of the host with a bisbenzylammonium salt containing terminal double bonds resulted in a tris[2]pseudorotaxane, which further performed the threefold metathesis reaction and then hydrogenation to give a [4]pseudocatenane in high yield. The [4]pseudocatenane exhibited a novel topological structure with high symmetry, which was confirmed by the spectral data and X-ray analysis.

Iptycene quinones: synthesis and structure.

A practical and efficient method to synthesize iptycene quinones has been developed. As a result, a series of pentiptycene quinones 8-16 were conveniently synthesized by one-pot reaction of triptycene quinone 4 or 5 with anthracene 1 or its derivatives 2-3 in refluxing acetic acid in the presence of p-chloranil, followed by CAN oxidative demethylation. Similarly, a series of heptiptycene quinones 17-23 with U-shaped cavities were achieved with pentiptycene quinone 10 and triptycene diquinone 6 as precursors. Non-iptycene triquinones 24 with one tweezer-shaped cavity and 25 with two U-shaped cavities were synthesized by one-pot reactions of anthracene with pentiptycene triquinones 16a and 16b, respectively. Non-iptycene triquinone 26 with a dendritic structure was conveniently obtained by the reaction of anthracene with either pentiptycene diquinone 12 or triptycene triquinone 7. The structures of regioisomers 16a and 16b were determined by the single-crystal structure analysis of 16b. The structures of other regioisomers, including heptiptycene tetraquinones 19a/19b/19c and heptiptycene triquinones 23a/23b, were identified by comparative reactions.