Quantum Spectrum of Some Anharmonic Central Potentials: Wave Functions Ansatz

Based on the ansatz to the wave functions, the quasi-exact solutions of the 2D Schrödinger equation with some anharmonic potentials are reviewed and analyzed if admitting restrictions on the parameters of the potential and the angular momentum m. These potentials are taken as the screened Coulomb potential V(r)=a/r+b/(r+), the singular one-fraction power one V(r)=ar ^–1/2+br ^–3/2 and the singular two-fraction one V(r)=ar ^2/3+br ^–2/3+cr ^–4/3. The latter one is found that the hidden symmetry exists if substituting r–ir. It will reverse the signs of E and c of quantum system, leaving the remaining parameters invariant.     

Collision of a Solid with an Incompressible Fluid

We give a predictive theory of the collisions of a viscous incompressible fluid with solids. The theory is based on interior percussions which account for the very large stresses and contact forces resulting from the kinematic incompatibilities responsible for the collision. New equation of motion and constitutive laws result from the theory. Examples dealing with a fluid colliding with its container and with a diver impacting the water of a swimming pool are studied.     

Quantum Monodromy and Bohr–Sommerfeld Rules

This article is based on a talk given in Dijon for the 2000 summer school Topological and Geometrical Methods: Applications to Dynamical Systems. The standard definitions of the monodromy invariant for completely integrable classical systems are reviewed, and the link to the quantum monodromy observed in the joint spectrum of commuting operators is explained. The mathematical treatment relies on a modern and attractive version of the Bohr–Sommerfeld quantisation rules.     

Order parameter description of walk-off effect on pattern selection in degenerate optical parametric oscillators

Degenerate optical parametric oscillators can exhibit both uniformly translating fronts and nonuniformly translating envelope fronts under the walk-off effect. The nonlinear dynamics near threshold is shown to be described by a real convective Swift-Hohenberg equation, which provides the main characteristics of the walk-off effect on pattern selection. The predictions of the selected wave vector and the absolute instability threshold are in very good quantitative agreement with numerical solutions found from the equations describing the optical parametric oscillator.     

Dependence of pulser driving responses on electrical and motional characteristics of NDE ultrasonic probes

Acoustic performance in ultrasonic transmitters can be improved by means of a suitable electrical driving response and matching/tuning networks. It is important to predict this electrical response, but doing so is not easy because it departs notably from the nominal pattern with the loading probes. In practice, the analysis of HV pulser spikes in NDE applications requires fairly complex models in the transient regime and, in addition, non-linear problems could arise, especially in the case of tuned transmitters. In this paper, the most relevant influences of loading characteristics of NDT ultrasonic probes on the pulser electrical driving responses are evaluated in time and frequency domains. Conventional pulse generators and typical NDE pulsers are considered. Driving responses are analysed across commercial ultrasonic probes and, alternatively, across similar purely electrical loads. Distinct influences on pulser responses from electrical and motional sections of the probes are identified. All these aspects are studied on the basis of experimental and computer results.     

Magnetic and noise properties of as-deposited and annealed soft underlayer

We studied the magnetic and noise properties with various soft underlayer (SUL) types. For an as-deposited SUL, the results of spectrum, oscilloscope waveform and MFM indicated that the SUL types with IrMn pinning layer have more noise level than that of SUL types without IrMn pinning layer. And, after magnetic filed annealing along radial direction of disk, the exchange bias field increased and the noise level of type B (exchange bias type) decreased. These results reveal that incomplete or partial coupling may be generated at the interface between IrMn and ferromagnetic layer in as-deposited SUL. This incomplete coupling may result in complex or multidomain patterns in ferromagnetic layer.     

A direct‐forcing pressure‐based lattice Boltzmann method for solving fluid–particle interaction problems

A direct‐forcing immersed boundary‐lattice Boltzmann method (IB–LBM) is developed to simulate fluid–particle interaction problems. This method uses the pressure‐based LBM to solve the incompressible flow field and the immersed boundary method to handle the fluid–particle interactions. The pressure‐based LBM uses the pressure distribution functions instead of the density distribution functions as the independent dynamic variables. The main idea is to explicitly eliminate the compressible effect due to the density fluctuation. In the IB method, a direct‐forcing method is introduced to capture the particle motion. It directly computes an IB force density at each lattice grid from the differences between the pressure distribution functions obtained by the LBM and the equilibrium pressure distribution functions computed from the particle velocity. By applying this direct‐forcing method, the IB–LBM becomes a purely LBM version. Also, by applying the Gauss theorem, the formulas for computing the force and the torque acting on the particle from the flows are derived from the volume integrals over the particle volume instead of from the surface integrals over the particle surface. The order of accuracy of the IB–LBM is demonstrated on the errors of velocity field, wall stress, and gradients of velocity and pressure. As a demonstration of the efficiency and capabilities of the new method, sedimentation of a large number of spherical particles in an enclosure is simulated. Copyright © 2010 John Wiley & Sons, Ltd.     

Associative and segregative phase separations of poly(N-tert-butylacrylamide)/poly(acrylic acid) mixtures. Effect of solvent

Poly(N-tert-butylacrylamide) (PNtBAm) and poly(acrylic acid) (PAA) form interpolymer complexes in 1- and 2-propanol, blend in ethanol, whereas a segregative phase separation is observed when using methanol as solvent as shown by Fourier transform infrared (FTIR) spectrometry and elemental analysis studies. The composition of PNtBAm/PAA complexes has been determined. Thermal studies demonstrated that all complexes show unique glass transition temperatures, higher than those of the polymer components. Complexation of PAA with PNtBAm results in an improvement of its thermal stability. Solvent effects and specific interactions in the system PNtBAm/PAA have been studied by FTIR, revealing that differences in the polymer–solvent interactions are a decisive factor governing complex formation in solution.     

Isothermal martensitic transformation in a 12Cr–9Ni–4Mo–2Cu stainless steel in applied magnetic fields

This work concerns an in situ study of the isothermal formation of martensite in a stainless steel under the influence of magnetic fields up to 9 T at three different temperatures (213, 233 and 253 K). It is shown that the presence of a constant applied magnetic field promotes the formation of martensite significantly. The activation energy for the nucleation of martensite has been derived using a semi-empirical kinetic model. The experimental results have been analyzed using the Ghosh and Olson model. While this model describes the time and field dependences of the experimental data well, the thermal frictional energy and the defect size values are much lower than those expected from earlier work.