Magnetostatic relations including fluctuation fields - the local expansion

Using the approach of local expansion, we analyze the magnetostatic relations in the case of conventional turbulence. The turbulent relations are obtained consisten tly for themomentum equation and induction equation of both the average and fluctuation relations.In comparison with the magnetostatic relations as discussed usually, turbulent fluctuationfields produce forces, one of which 1/(4π)(α1×B0)×B0 may have parallel and perpendicular components in the direction of magnetic field, the other of which 1/(4π)K×B0 is introduced by the boundary value of turbulence and is perpendicular to the magnetic field. In the case of 2-dimensional configuration of magnetic field, the basic equation will be reduced into a second-order elliptic equation, which includes some linear and nonlinear terms introduced by turbulent fluctuation fields. Turbulent fields may change the configuration of magnetic field and even shear it non-uniformly. The study on the influence of turbulent fields is significant since they are observed in many astrophysical environments.

Representation of microscale ocean wavenumber spectrum correct to the second order

In this paper, the analytical representations of four wave source functions in high-frequency spectrum range are given on the basis of ocean wave theory and dimensional analysis, and the perturbation method is used to solve the governing equations of ocean wave high-frequency spectrum on the basis of the temporally stationary and locally homogeneous scale relations of microscale wave. The microscale ocean wavenumber spectrum correct to the second order has an explicit structure, its first order part represents the equilibrium between different source functions, and its second order part represents the contribution of microscale wave propagation.

Stress Wave Propagation in a Gradient Elastic Medium

The gradient elastic constitutive equation incorporating the second gradient of the strains is used to determine the monochromatic elastic plane wave propagation in a gradient infinite medium and thin rod. The equation of motion, together with the internal material length, has been derived. Various dispersion relations have been determined. We present explicit expressions for the relationship between various wave speeds, wavenumber and internal material length.

A second-order dynamic subgrid-scale stress model

A second-order dynamic model based on the general relation between the subgrid-scale stress and the velocity gradient tensors was proposed. A priori test of the second-order model was made using moderate resolution direct numerical simulation date at high Reynolds number ( Taylor microscale Reynolds number R-lambda = 102 similar to 216) for homogeneous, isotropic forced flow, decaying flow, and homogeneous rotating flow. Numerical testing shows that the second-order dynamic model significantly improves the correlation coefficient when compared to the first-order dynamic models.

Shock slip-relations for thermal and chemical nonequilibrium flows

This paper appears to be the first where the multi-temperature shock slip-relations for the thermal and chemical nonequilibrium flows are derived. The derivation is based on analysis of the influences of thermal nonequilibrium and viscous effects on the mass, momentum and energy flux balance relations at the shock wave. When the relaxation times for all internal energy modes tend to sere, the multi-temperature shock slip-relations are converted into single-temperature ones for thermal equilibrium hows. The present results can be applied to flows over vehicles of different geometries with or without angles of attack. In addition, the present single-temperature shock slip-relations are compared with those in the literature, and Some defects and limitations in the latter are clarified.

Parameter-transformation relations for traveling-wave solutions of kdv-burgers equation

 Burgers suggested that the main properties of free-turbulence in the boundless area without basic flow might be understood with the aid of the following equation, which was much simpler than those of fluid dynamics, 更多还原

The magnetostatic relations including fluctuation fields

The influences of the fluctuation fields are important in many astrophysical environments as shown by the observations, and can not be neglected. On the basis of the first-order smoothing approximation, in the present paper, we demonstrate the magnetostatic equations for both the cases of the conventional turbulence aud the random waves, and discuss the consistent conditions of the equations. In the static problem, the fluctuation Lorentz force(▽×δB)×δB influences the large-scale configurations of magnetic field. To study this influence in detail is quite necessary for the explanations of the observation features, especially for the astrophysical environments where the magnetic fields, including the fluctuation fields, are the dominant factors in the equilibrium of momentum and energy.

Simulation of Vibration Caused by Blasting for a Layered Slope

Recent studies showed that vibration caused by blasting mainly reflects the property of geological structure itself neighboring the blasting center. Different vibration signals can be collected for different geological structures under blasting. Hence, vibration signal can be used to identify geological structure, especial for a slope with a weak layer. As the geological structure for a practical slope is usually complicated, the simulation of vibration caused by blasting should be carried out first. Generally, the material in a certain zone near the blasting center will undergo damage, so the physical model to simulate this region is the most concerned. In this paper, the damaged zone near blasting center is neglected, and the blasting load can be considered being applied on the interface between the damaged zone and undamaged zone. Regarding the relations between the weight of explosive, the size of damaged zone, and the dynamic loading to propagate out away, the vibration caused by blasting for a practical layered slope is simulated. Compared with the measured signal in site, it can be seen that the simulating result is in well agreement with that of practical testing. The results also indicate that the farther the testing point apart from the blasting center, the more accurate the simulation is.

The effect of the group delay ripple of chirped fiber grating on composite second-order in optical fiber CATV system

The effect of group delay ripple of chirped fiber gratings on composite second-order (CSO) performance in optical fiber CATV system is investigated. We analyze the system CSO performances for different ripple amplitudes, periods and residual dispersion amounts in detail. It is found that the large ripple amplitude and small ripple period will deteriorate the system CSO performance seriously. Additionally, the residual dispersion amount has considerable effect on CSO performance in the case of small ripple amplitude and large ripple period. (c) 2004 Elsevier B.V. All rights reserved.

Composite second-order performance improvement in optical fibre CATV transmission system using chirped fibre grating

Theoretically, we analyse the dispersion compensation characteristics of the chirped fibre grating (CFG) in an optical fibre cable television (CATV) system and obtain the analytic expression of the composite second-order (CSO) distortion using the time-domain form of the field envelope wave equation. The obtained result is in good agreement with the numerical simulation result. Experimentally, we verify the result by making use of the tunable characteristics of CFG to change the dispersion compensation amount and obtain an optimal CSO performance in a 125km fibre transmission link. Both the theoretical and experimental results show that the CSO performance can be improved by properly choosing the dispersion compensation amount for a certain fibre transmission link.

Analysis of a second-order polarization-independent filter made of a single ring resonator and a Sagnac interferometer

A novel second-order polarization-independent filter made of a single ring resonator and a Sagnac interferometer (SRRSI) is proposed, and its filtering characteristics are investigated. By using birefringence in waveguide, a single ring resonator can be used to synthesize a filter with second-order response. Analytical formulas are derived for characteristics of the SRRSI varied with waveguide parameters.. such as the coupling coefficient; and the critical condition of a second-order Butterworth filter is given. The influence of loss in the ring resonator is also analyzed. (c) 2005 Elsevier B.V. All rights reserved.

Measuring ultrashort optical pulses using multi-shot second harmonic generation frequency resolved optical gating

Frequency resolved optical gating (FROG), is an effective technique for characterizing the ultrafast laser pulses. The multi-shot second harmonic generation (SHG) FROG is the most sensitive one in different FROGs. In this paper we use this technique to measure the femtosecond optical pulses generated by a conventional Ti:sapphire oscillator.