Spectral Properties of the Linearization at the Burgers Vortex in the High Rotation Limit

We study a linearized operator of the equation for the axisymmetric Burgers vortex which gives a stationary solution to the three dimensional Navier–Stokes equations with an axisymmetric background straining flow. It is numerically known that the Burgers vortex obtains better stabilities as the circulation number (or the vortex Reynolds number) is increasing. Although the global stability of the axisymmetric Burgers vortex is already proved rigorously, mathematical understanding of this numerical observation has been lacking. In this paper we study a linearized operator that includes the circulation number as a parameter, and prove that if the operator is restricted on a suitable invariant subspace, then its spectrum moves to the left as the circulation number goes to infinity. As an application, we show that the axisymmetric Burgers vortex with a high rotation has a better stability, in the sense that the non-radially symmetric part of solutions to the associated evolution equation decays faster in time if the circulation number is sufficiently large.     

Prediction error criterion for selecting variables in a linear regression model

Several criteria, such as CV, C _p , AIC, CAIC, and MAIC, are used for selecting variables in linear regression models. It might be noted that C _p has been proposed as an estimator of the expected standardized prediction error, although the target risk function of CV might be regarded as the expected prediction error R _PE. On the other hand, the target risk function of AIC, CAIC, and MAIC is the expected log-predictive likelihood. In this paper, we propose a prediction error criterion, PE, which is an estimator of the expected prediction error R _PE. Consequently, it is also a competitor of CV. Results of this study show that PE is an unbiased estimator when the true model is contained in the full model. The property is shown without the assumption of normality. In fact, PE is demonstrated as more faithful for its risk function than CV. The prediction error criterion PE is extended to the multivariate case. Furthermore, using simulations, we examine some peculiarities of all these criteria.     

Velocity field after wave breaking

The velocity field in breaking water waves is considered in this paper. A numerical simulation describes in detail the transition from a primary overturning and consequent rebounding jets into a bore front, where the vorticity in the coherent large‐scale eddy structures devolves into turbulence. Spatial changes in the frequency spectra of the kinetic energy and the enstrophy are associated with the production, transport and dissipation of the Reynolds stress and the various wave and turbulent mixing length scales. Mean velocity fields and the wave and kinetic energy in a surf zone are evaluated. Fourier and wavelet spectral analysis is applied to study both the surface elevation and energy changes, and the distinction that must be made between spilling and plunging breakers is clarified in this paper. Copyright © 2002 John Wiley & Sons, Ltd.     

Determination of average ion energy in turbulently heated plasmas by secondary emission detector

An average energy of a high temperature part of ions in turbulently heated plasmas was measured by use of a secondary emission detector, and availability of this simple method for a determination of an average ion energy was discussed.     

Scattering time in GaAs/AlGaAs narrow wires in the presence of magnetic field

Magnetoresistance measurements have been performed in narrow GaAs/AlGaAs wires in order to study the scattering process in mesoscopic wires. Amplitude analysis of the Shubnikov -de Haas oscillations shows that electrons have two scattering times, depending upon the magnetic field range. The critical field which separates these scattering times seems to be determined by the relation between the wire width and the electron cyclotron radius. This effect is discussed in terms of the electron trajectories in a wire under the magnetic field.     

Temporal variation of electron density in a laser-perturbed discharge plasma and its relationship to the optogalvanic signal

By the method of microwave cavity resonance the authors have measured the temporal variation of the lctron density following the laser excitation of neon glow-discharge plasma, and the result is compared with the optogalvanic signal. It is found that the optogalvanic signal does not represent the change in the electron density; i.e., the time resolution is poor and the absolute magnitude is smaller by an order.     

Color confining parton model for heavy quarkonium decay

We present a gluon jet model for the heavy quarkonium decay incorporating the color neutralization mechanism. Postulating that final hadrons are produced from the color singlet quark-antiquark pair originated each from different gluons, we formulate the production mechanism of hadrons from gluons explicitly. The fragmentation function thus obtained can describe the hadron production not only in the fragmentation region but also in the central one owing to the usage of the Sudakov variables. The result of the average charged multiplicity from Υ(9.46) is in reasonable agreement with the data, in contrast to the naive estimates. Furthermore, the inclusive momentum and multiplicity distributions are discussed.     

Diquarks in nucleons

Under the assumption that a scalar diquark coexists in part of the time with a single quark within a nucleon, which is favored to describe the higher twist effects of both γ and ν induced nucleon structure functions consistently, we consider how its presence affects nucleon properties. It is shown that the sum rule and the magnetic moment constrain its contribution strongly and the asymmetry is quite sensitive to it. In particular, theR=σ _L /σ _T ratio can be explained in terms of the large transverse momentum of the diquark which arises from the consideration on the neutron charge radius value.