X-ray Raman spectroscopic study of benzene at high pressure

We have used X-ray Raman spectroscopy (XRS) to study benzene up to approximately 20 GPa in a diamond anvil cell at ambient temperature. The experiments were performed at the High-Pressure Collaborative Access Team's 16 ID-D undulator beamline at the Advanced Photon Source. Scanned monochromatic X-rays near 10 keV were used to probe the carbon X-ray edge near 284 eV via inelastic scattering. The diamond cell axis was oriented perpendicular to the X-ray beam axis to prevent carbon signal contamination from the diamonds. Beryllium gaskets confined the sample because of their high transmission throughput in this geometry. Spectral alterations with pressure indicate bonding changes that occur with pressure because of phase changes (liquid: phase I, II, III, and III') and possibly due to changes in the hybridization of the bonds. Changes in the XRS spectra were especially evident in the data taken when the sample was in phase III', which may be related to a rate process observed in earlier shock wave studies.     

Spectral resonances which become eigenvalues

The stationary Schrödinger equation is ? _x ² φ + λV(x)φ=zφ for φ∈?²(R ⁺,dx). If the potential is bounded below, singular only atx=0, negative on some compact interval and behaves likeV(x)～1/x ^μ asx→∞ with 2≧μ>0, then the system admits shape resonances which continuously become eigenvalues as λ increases. Here λ>0 and for μ=2 a sufficiently large λ is required. Exponential bounds are obtained on Im(z) as λ approaches a threshold. The group velocity near threshold is also estimated.     

Extraction of trivalent iron in the ionic and colloidal states with Di-n-butylphosphoric acid

The extraction of trivalent iron in the ionic and colloidal states from diluted nitric acid solutions with di-n-butylphosphoric acid in cyclohexane has been studied. Depending on the concentration of di-n-butylphosphoric and nitric acid, the ionic and colloidal trivalent iron can be distributed between the solvent, aqueous phase and solvent-aqueous interface.     

Self-similarity and non-Markovian behavior in traded stock volumes

The volume traded daily for 17 stocks is followed over a period of about half a century.We look at the volume of stocks traded in a certain time interval (day, week, month) andanalyze how long that traded volume keeps monotonically increasing or decreasing. On allthree times scales we find that the sequence of traded volumes behaves neither like asequence of independent and identically distributed variables, nor like a Markov sequence.A compressed exponential survival function with the same parameters at all timescales isfirmly established. A day with an increase (decrease) of traded volume is most likelyfollowed by a day with a decrease (increase) of traded volume. We show how the apparentself-similarity results because the small day-to-day anticorrelation carries over whenlarger time intervals are considered. The observed small anticorrelation can be explainedas a consequence of market forces and trader reactions.     

Organic cyclic difluoramino‐nitramines: infrared and Raman spectroscopy of 3,3,7,7‐tetrakis(difluoramino)octahydro 1,5‐dinitro‐1,5‐diazocine (HNFX)

We present the first vibrational structure investigation of 3,3,7,7‐tetrakis(difluoramino)octahydro‐1,5‐dinitro‐ 1,5‐diazocine (HNFX)—and, more generally, of a member of the new class of gem‐bis(difluoramino)‐substituted heterocyclic nitramine energetic materials—using combined theoretical and experimental approaches. Optimized molecular structure and vibrational spectra of the Ci… symmetry conformer constituting the HNFX crystal were computed using density functional theory methods. Fourier transform infrared and Raman spectra of HNFX crystalline samples were also collected at ambient temperature and pressure. The average deviation of calculated structural parameters from X‐ray diffraction data is ∼1% at the B3LYP/6‐311 + + G(d,p) level of theory, suggesting the absence of significant molecular distortion induced by the crystal field. Very good agreement was found between simulated and measured spectra, allowing reliable assignment of the fundamental normal modes of vibration of the HNFX crystal. Detailed analysis of the normal modes of the C–(NF₂)₂ and N–NO₂ moieties was performed due to their critical importance in the initial steps of the molecular homolytic fragmentation process. Copyright © 2009 John Wiley & Sons, Ltd.     

Suppression of plasma turbulence during optimized shear configurations in JET

Correlation of density turbulence suppression and reduced plasma transport is observed in the internal transport barrier (ITB) region of JET tokamak discharges with optimized magnetic shear. The suppression occurs in two stages. First, low frequency turbulence and ion transport are reduced across the plasma core by a toroidal velocity shear generated by intense auxiliary heating. Then with the ITB formation, high frequency turbulence and electron transport are reduced locally within the steep pressure gradient region of the ITB.     

High-pressure studies of cyclohexane to 40 GPa

We present data from two room temperature synchrotron X-ray powder diffraction studies of cyclohexane up to approximately 40 and approximately 20 GPa. In the first experiment, pressure cycling was employed wherein pressure was varied up to approximately 16 GPa, reduced to 3.5 GPa, and then raised again to 40 GPa. Initially, the sample was found to be in the monoclinic phase (P12(1)/n1) at approximately 8.4 GPa. Beyond this pressure, the sample adopted triclinic unit cell symmetry (P1) which remained so even when the pressure was reduced to 3.5 GPa, indicating significant hysteresis and metastability. In the second experiment, pressure was more slowly varied, and the monoclinic unit cell structure (P12(1)/n1) was observed at lower pressures up to approximately 7 GPa, above which a phase transformation into the P1 triclinic unit cell symmetry occurred. Thus, the pressure onset of the triclinic phase may be dependent upon the pressurizing conditions. High-pressure Raman data that further emphasize a phase transition (probably into phase VI) around 10 GPa are also presented. We also have further evidence for a phase VII, which is probably triclinic.     

Spectral analysis for optical fibres and stratifled fluids II: Absence of Eigenvalues ∗

The operator ? appears in the study of the propagation of acoustical waves in stratified fluids , as well as of electromagnetic waves in layered dielectric media , and in optical fibres . The density and signal speed are (possibly long range) perturbations of a density and speed , . Positive commutator methods along with Virial techniques are used to show that in many cases of physical interest the point spectrum of ? is empty. More generally, eigenfunctions of ? if they exist, must decay faster than .     

Solutions of a class of multiplicatively advanced differential equations

The multiplicatively advanced differential equations (MADEs) of form $f^{(n)}(t)=\alpha f(\beta t)$ with $\alpha \ne 0$, $\beta >1$ are studied along with a class of their solutions of type $f_{\mu ,\lambda }(t)$ defined on $[0,\infty )$. For $\lambda \in {\mathbb{Q}}^{+},\mu \in \mathbb{R}$, the solutions $f_{\mu ,\lambda }(t)$ are extended to $(?\infty ,\infty )$ in a non-unique manner to obtain Schwartz wavelet solutions $F_{\mu ,\lambda }(t)$ of the original MADE, with all moments of $F_{\mu ,\lambda }(t)$ vanishing. Examples are studied in detail. The Fourier transform of each $F_{\mu ,\lambda }(t)$ is computed and, in a number of examples, is related to the Jacobi theta function. Additional conditions sufficient for the uniqueness of certain MADE initial value problems are given. Conditions for decay and non-decay at ?∞ are obtained. Decay rates at ±∞ in terms of familiar functions are established.     

High-pressure studies of 1,3,5,7-cyclooctatetraene: experiment and theory

High-pressure studies of 1,3,5,7-cyclooctatetraene have been performed by using Raman spectroscopy up to 16 GPa and compared with complementary density functional calculations. Angular-dispersive X-ray diffraction studies were also performed in the solid state at elevated pressure. The lattice constants of solid 1,3,5,7-cyclooctatetraene obtained from the X-ray diffraction pattern taken at 3.8 GPa and room temperature are in good agreement with theoretical results. At least two phase transitions were observed during pressure increase followed by the loss of long-range crystallographic order, which was also associated with a strong pressure-induced luminescence that allowed estimation of band gap alterations with pressure.