Cyanide Complexes Based on {Mo6I8}4+ and {W6I8}4+ Cluster Cores

Compounds based on new cyanide cluster anions [{Mo₆I₈}(CN)₆]^2–, trans-[{Mo₆I₈}(CN)₄(MeO)₂]^2– and trans-[{W₆I₈}(CN)₂(MeO)₄]²⁻ were synthesized using mechanochemical or solvothermal synthesis. The crystal and electronic structures as well as spectroscopic properties of the anions were investigated. It was found that the new compounds exhibit red luminescence upon excitation by UV light in the solid state and solutions, as other cluster complexes based on {Mo₆I₈}⁴⁺ and {W₆I₈}⁴⁺ cores do. The compounds can be recrystallized from aqueous methanol solutions; besides this, it was shown using NMR and UV-Vis spectroscopy that anions did not undergo hydrolysis in the solutions for a long time. These facts indicate that hydrolytic stabilization of {Mo₆I₈} and {W₆I₈} cluster cores can be achieved by coordination of cyanide ligands.     

Novel Highly Energetic Pyrazoles: N‐Trinitromethyl‐Substituted Nitropyrazoles

A new family of energetic compounds, nitropyrazoles bearing a trinitromethyl moiety at the nitrogen atom of the heterocycle, was designed. The desirable high‐energy dense oxidizers 3,4‐dinitro‐ and 3,5‐dinitro‐1‐(trinitromethyl)pyrazoles were synthesized in good yields by destructive nitration of the corresponding 1‐acetonylpyrazoles. All of the prepared compounds were fully characterized by multinuclear NMR and IR spectroscopy, as well as by elemental analysis. Single‐crystal X‐ray diffraction studies show remarkably high density. Impact sensitivity tests and thermal stability measurements were also performed. All of the pyrazoles possess positive calculated heats of formation and exhibit promising energetic performance that is the range of 1,3,5‐trinitroperhydro‐1,3,5‐triazine and pentaerythritol tetranitrate. The new pyrazoles exhibit positive oxygen balance and are promising candidates for new environmentally benign energetic materials.     

Synthesis and Structure of Tin(II) Hexafluorozirconate

The crystal structure of SnZrF₆ is determined. The compound is synthesized by slow crystallization from a melted mixture of SnF₂ and ZrF₄ (2 : 1). The crystals are monoclinic: a = 6.6119(5), b = 5.2503(5), c = 6.9929(6) Å, = 114.239(4)°, space group P2/n, Z = 2. The structure is layered. The layers are formed from the chains of edge-sharing, eight-vertex zirconium polyhedra and Sn²⁺ cations. The Zr–F and Sn–F bond lengths in the layer vary from 2.309(1) to 2.269(1) Å and from 2.186(1) to 2.361(1) Å, respectively. The layers are linked by intermolecular Sn–F bonds with lengths of 2.868(1) and 2.871(1) Å.     

Generalized nonlinear Schrödinger equation for dispersive susceptibility and permeability: application to negative index materials

A new generalized nonlinear Schr?dinger equation describing the propagation of ultrashort pulses in bulk media exhibiting frequency dependent dielectric susceptibility and magnetic permeability is derived and used to characterize wave propagation in a negative index material. The equation has new features that are distinct from ordinary materials (mu=1): the linear and nonlinear coefficients can be tailored through the linear properties of the medium to attain any combination of signs unachievable in ordinary matter, with significant potential to realize a wide class of solitary waves.     

Lévy Flights in a Steep Potential Well

Lévy flights in steeper than harmonic potentials have been shown to exhibit finite variance and a critical time at which a bifurcation from an initial monomodal to a terminal bimodal distribution occurs (Chechkin et al., Phys. Rev. E 67:010102(R) (2003)). In this paper, we present a detailed study of Lévy flights in potentials of the type U(x)∝|x| ^c with c>2. Apart from the bifurcation into bimodality, we find the interesting result that for c>4 a trimodal transient exists due to the temporal overlap between the decay of the central peak around the initial δ-condition and the building up of the two emerging side-peaks, which are characteristic for the stationary state. Thus, for certain system parameters there exists a transient trimodal distribution of the Lévy flight. These properties of Lévy flights in external potentials of the power-law type can be represented by certain phase diagrams. We also present details about the proof of multimodality and the numerical procedures to establish the probability distribution of the process.     

Experimental study of the reverse flow in the forward separation region in a pulsating flow around a spiked body

The flow with a free-stream Mach number M _∞ = 6 around a cylindrical body with a sharp spike is studied. The existence of a supersonic reverse flow for one of the phases of the pulsating flow regime is experimentally validated. A range of spike lengths is determined, which ensures a region of a supersonic reverse flow near the side surface of the spike. The time of existence of the supersonic reverse flow region is shown to be 0.15 of the period of pulsations if the spike length equals the model diameter. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 4, pp. 30–39, July–August, 2007.     

Slow light on a printed circuit board

Slow-light effects induced by stimulated Raman scattering in polymer waveguides on a printed circuit board are shown to enable a widely tunable delay of broadband optical signals, suggesting an advantageous platform for optical information processing and ultrafast optical waveform transformation.     

Ionization penalty in nonlinear Raman neuroimaging

Light-assisted ionization accompanying coherent anti-Stokes Raman scattering (CARS) of ultrashort laser pulses in brain tissue is shown to manifest itself in a detectable blueshift of the anti-Stokes signal. This blueshift can serve as an indicator of ionization processes in CARS-based neuroimaging.     

On the Gomory–Hu Inequality

It was proved by R. Gomory and T. Hu in 1961 that, for every finite nonempty ultrametric space (X, d), the inequaliy \( \left| {\mathrm{Sp}(X)} \right|\leq \left| X \right|-1 \), where Sp(X) = {d(x, y) : x, y ∈ X, x ≠ y} , holds. We characterize the spaces X for which the equality is attained by the structural properties of some graphs and show that the set of isometric types of such X is dense in the Gromov–Hausdorff space of the isometric types of compact ultrametric spaces.