Quasi-wavelet calculations of sound scattering behind barriers

Quasi-wavelets (QWs) are a representation of turbulence consisting of self-similar, eddy-like structures with random orientations and positions in space. They are used in this paper to calculate the scattering, due to turbulent velocity fluctuations, of sound behind noise barriers as a function of the size and spatial location of the eddies. The sound scattering cross-section for QWs of an individual size class (eddy size) is derived and shown to reproduce results for the von Kármán spectrum when the scattered energies from a continuous distribution of QW sizes are combined. A Bragg resonance condition is derived for the eddy size that scatters most strongly for a given acoustic wavenumber and scattering angle. Results for scattering over barriers show that, for typical barrier conditions, most of the scattered energy originates from eddies in the size range of approximately one-half to twice the size of the eddies responsible for maximum scattering. The results also suggest that scattering over the barrier due to eddies with a line of sight to both the source and receiver is generally significant only for frequencies above several kilohertz, for sources and receivers no more than a few meters below the top of the barrier, and for very turbulent atmospheric conditions.     

High-Pressure Phase Transition in CTAB-Micellar Solutions： A Raman Spectroscopic Study

We use a diamond anvil cell for the first time to investigate the Raman spectra of an aqueous micellar solution of hexadecyltrimethylammonium bromide （CTAB） at pressures up to 3.85 GPa. The pressure-induced phase transition between the micellar and coagel phases is found to occur at 0.64 GPa and 60℃. This phase transition has a pressure hysteresis, and thus exhibits the first-order phase transition properties. Further experimental results show that although the structure of the coagel phase is similar to that of the CTAB crystal, the interchain distance is slightly larger in the coagel phase than that in the CTAB crystal.     

Thermodynamic properties of cubic boron nitride under high pressure from ab initio calculations

The equations of state (EOS) and other thermodynamic properties of cubic boron nitride (C-BN) have been studied by the first-principles method under high pressure. Under ambient conditions, our results are consistent with the available experimental data and those calculated by others. At the same time, the dependences of Young’s modulus and the shear modulus of C-BN on pressure P are successfully obtained. Moreover, the variation of the Poisson ratio, Debye temperature, specific heat, and thermal expansion coefficient with pressure P up to 200 GPa at 300 K have been investigated for the first time by means of a quasi-harmonic Debye model, in which phononic effects are considered.     

Structural Stability of CaCuMn6O12 under High Pressure and Low Temperature

In situ high pressure energy-dispersive x-ray synchrotron radiation diffraction and resistance experiments are carried out on CaCuMn6O12. Its crystal structure is stable in the measured pressure range. The equation of state of CaCuMn6O12 is obtained from the V/Vo - P relationship （V and Vo are the volumes at pressure P and at atmosphere）. The bulk modulus Bo is calculated based on the Birch-Murnaghan equation. Low temperature x-ray diffraction shows no phase transition occurring down to 160K.     

Measuring Grüneisen Parameter of Lead by High Pressure-Jump Method

Using the technology of pressure jump, variations of temperature associated with pressure from 2.4 GPa to 4.6 GPa are measured for lead. The Grfuneisen parameter is calculated from the thermodynamic relation γ =（Ks/T）（aT/aP）s, in which substitution of △T/△P for aT/aP at median pressure is strictly justified. The correction of temperature change is carried out by analysing the experimental data, which makes the process more approaching to an adiabatic condition. The calculated values of △T/ △ P and γ gradually decrease with the increasing pressure. The decrease trend is consistent with the previous work. The γ values in the range of 2-3 GPa are averagely higher than the results of Ramakrishnan et al., indicating the effect of temperature correction. The improved method is promising for measurements of Grfineisen parameter to higher pressure range.     

Fluid membranes in hydrodynamic flow fields: Formalism and an application to fluctuating quasispherical vesicles in shear flow

The dynamics of a single fluid bilayer membrane in an external hydrodynamic flow field is considered. The deterministic equation of motion for the configuration is derived taking into account both viscous dissipation in the surrounding liquid and local incompressibility of the membrane. For quasi-spherical vesicles in shear flow, thermal fluctuations can be incorporated in a Langevin-type equation of motion for the deformation amplitudes. The solution to this equation shows an overdamped oscillatory approach to a stationary tanktreading shape. Inclination angle and ellipticity of the contour are determined as a function of excess area and shear rate. Comparisons to numerical results and experiments are discussed. Received 20 August 1998     

Formation of amorphous sapphire by a femtosecond laser pulse induced micro-explosion

We report on structural characterization of void-structures created by a micro-explosion at the locus of a tightly focused femtosecond laser pulse inside the crystalline phase of Al₂O₃ (R3c space group). The transmission electron microscopy (TEM), micro-X-ray diffraction (XRD) analysis, and Raman scattering revealed a presence of strongly structurally modified amorphous regions around the void-structures. We discuss issues of achieving the required resolution for structural characterization and assignment of newly formed phases of nano-crystallites by TEM, XRD, and Raman scattering from micro-volumes of modified materials enclosed inside the bulk of the host phase.     

Beyond Black-Scholes: semimartingales and Lévy processes for option pricing

We consider the problem of option pricing when the underlying asset follows a general semimartingale process. After reviewing the foundations of arbitrage pricing theory for semimartingales and the link with Lévy processes, we introduce a general method to price options in this framework based on Fourier and Wavelet analysis. Received 4 September 2000     

Magnetic collapse and electronic phase transitions at high pressure in transition metal oxides

A review of electronic and magnetic phase transition in metal oxides with strong electron correlations (SEC) is given. The bandwidth control of the insulator gap is expected in the Hubbard model when the decreasing of the interatomic distance results in the bandwidth W(P) increase and at some critical value P_c, W(P_c)∼U and the Mott–Hubbard gap disappears. The other situation takes place in transition metal boroxides FeBO₃ and GdFe₃(BO₃)₄, where the increase of crystal field parameter Δ(P) results in the high spin–low spin crossover.     

First-principles study of the pressure-induced phase transition in CaTiO3

An investigation into the phase stabilities of CaTiO₃ under high pressure was conducted using first-principles calculations based on density functional theory. We have identified three candidate structures of CaTiO₃, Pbnm, Pm3m and Cmcm, respectively. Our results demonstrate that a phase transition from orthorhombic (Pbnm) to cubic (Pm3m) is impossible for CaTiO₃ under high pressure at ambient temperature, and further predict that Pbnm-CaTiO₃ will transform to post-perovskite phase (Cmcm) at enough temperature and pressure.