等离子体湍流理论研究的最新进展

评述和分析了磁约束核聚变理论研究、数值模拟和实验研究等方面最近几年共同关心的一个重要问题——寻找托卡马克等离子体湍流中的带状剪切流（zonal flows）。简要介绍了作者最近对电阻性-重力模湍流中的带状剪切流的研究结果。 Progress of the research on the zonal flows in tokamak plasma turbulence is surveyed, especially it is reviewed that the zonal flows observed in the experiments and numerical simulations on atmosphere turbulence and ocean turbulence and the discovery of H-mode in tokamak experiments how lead the researchers in magnetic confinement fusion community to find out the existence of the zonal flow in tokamak plasma turbulence and subsequently give the experimental verification of its existence. Finally, the results of our research on zonal flow generation and evolution in resistive-g mode turbulence are presented in brief.     

基于湍流球泡折射的空间量子密钥分发性能分析

为了研究大气湍流对自由空间量子密钥分发的性能影响,将大气湍流建模为空间中随机分布的空气球泡,利用几何光学原理分析单光子在湍流球泡中的传播,定量计算了经过两次折射后由于偏振态变化造成的光子透射率比值k和误码率Ep的起伏,利用蒙特卡洛方法模拟了湍流折射率随机变化时二者的趋势;最后推导了经过湍流折射后的诱骗态空间量子密钥分发成码率公式并通过分析误码来源得到满足成码率需要的k值上限,建立偏振误码率与入射角和湍流折射率的关系并得到Ep的安全阈值.仿真结果表明当入射角在44.8°~76.5°,湍流折射率在1~1.33范围内可以满足误码率的上限约束.该研究为湍流条件下进行空间量子通信实验提供了理论参考.     

Discussion of the Klimontovich Theory of Hydrodynamic Turbulence

The Klimontovich Theory which yields the effective turbulent viscosity as a linear function of the Reynolds number is compared with experimental data. The new theory seems to be able to describe the observed effective viscosity of hydrodynamic vortices and after introducing some modifications the flow in tubes up to very high Reynold numbers.     

Nonstandard Methods in Quantum Field Theory I: A Hyperfinite Formalism of Scalar Fields

A nonstandard approach to axiomatic quantum field theory is given. Nonstandard axioms for a Hermitian scalar field is proposed, where the field operators act on a hyperfinite-dimensional Hilbert space. The axioms are shown to be equivalent to the Gårding–Wightman axioms. An example of a model of the nonstandard axioms is examined.     

A Functional Formulation of the Statistical Theory of Turbulence

Doklady Physics - The Navier–Stokes equation in the presence of external regular and random forces is considered. The statistical solution is described in terms of the characteristic...     

Multi-Scale Analysis of Energy Transfer in Scalar Turbulence

The energy transfer of homogeneous scalar turbulence is studied numerically by triad interaction in spectral space. The different transfer properties between turbulent kinetic energy and turbulent scalar energy reveal that non-local energy transfer exists as important as the local energy transfer in scalar turbulence. The non-local energy transfer of scalar turbulence results from non-local triad interaction. As a result there will be longer inertiaconvective range in scalar turbulence than the inertial subrange in turbulent kinetic transfer at Reλ = Peλ. The non-local transfer of turbulent scalar energy generates more energy transfer into dissipation range. The discovery of non-local transfer of turbulent scalar energy indicates that this phenomenon should be concerned carefully in numerical scheme and subgrid modelling of direct numerical simulation or large eddy simulation scalar turbulence.     

A Theory of Hydrodynamic Turbulence Based on Non-equilibrium Statistical Mechanics

In earlier papers, we have studied the turbulent flow exponents \(\zeta _p\), where \(\langle |\Delta \mathbf{v}|^p\rangle \sim \ell ^{\zeta _p}\) and \(\Delta \mathbf{v}\) is the contribution to the fluid velocity at small scale \(\ell \). Using ideas of non-equilibrium statistical mechanics we have found

$$\begin{aligned} \zeta _p={p\over 3}-{1\over \ln \kappa }\ln \Gamma \left( {p\over 3}+1\right) \end{aligned}$$

where \(1/\ln \kappa \) is experimentally \(\approx \,0.32\,\pm \,0.01\). The purpose of the present note is to propose a somewhat more physical derivation of the formula for \(\zeta _p\). We also present an estimate \(\approx \,100\) for the Reynolds number at the onset of turbulence.

     

Analysis of Relative Diffusion in Homogeneous Isotropic Turbulence

The relative diffusion in homogeneous isotropic turbulence is studied in this letter. The mean square of the separation (Y²)∝t³ has been shown by the mean-field approximation as well as the analysis based upon the assumption that the particle displacement has the Gaussian distribution. The analytical results are in agreement with the conclusion of Richardson 4/3 law.     

The Decay of Z→3γ via Charged Higgs Boson Loops in Some Nonstandard Models

The fourth rank polarization tensor and the helicity amplitudes of Z→3γ via charged Higgs boson loops in some nonstandard models with more than one Higgs doublet are calculated by using a nonlinear Re gauge. The results are presented in terms of three transcendental functions of B(x), T(x) and I(x, y). We have checked the analytic results in Ref.[6] in comparison with ours.     

Plasma Maser Theory of Whistler Waves in the Presence of Ion Cyclotron Turbulence

In this paper we consider the plasma maser theory of whistler waves in the presence of ion cyclotron waves in a magnetized plasma. In a plasma with low frequency ion cyclotron turbulence and a high frequency test whistler wave, growth of the whistler wave takes place because of the turbulent bremsstrahlung interaction between the resonant electrons and the modulated electric fields. The growth rate of the whistler wave is calculated and the results discussed.     

反射式鬼成像在海洋湍流中的成像分析

基于惠更斯-菲涅尔原理和鬼成像理论,研究了反射式无透镜鬼成像在Kolmogorov海洋湍流中目标成像问题,得到了成像脉冲响应函数和可见度理论表达式。结果表明随着目标随机反射角的增大,关联重构的图像质量将会失真退化.为进一步分析海洋湍流对目标图像质量的影响,数值模拟了不同探测距离、不同海洋湍流情况下鬼成像的可见度,得到了海洋湍流作用下的鬼成像目标探测规律.该研究对远距离自适应水下鬼成像大规模应用具有重要的理论指导意义.     

Nonstandard Boundary Conditions in Quantum Mechanics

The class of boundary conditions for wave functions which follow from the quantum mechanical continuity equation for the probability density and the probability current is considered.     

Nonstandard mixing in a system of fermions

In this paper we continue to study the mixing of fermionic fields with different parities. Here we are interested in the manifestation of the latter in pion-nucleon scattering, which is analyzed for systems with particles having 3/2^± spins. Also, theoretical calculations are compared with experimental data from the partial analysis.     

Nonstandard roughness of terraced surfaces

We present a class of surfaces which are simultaneously flat and rough over the same range of lengths. They are self-affine, have well-defined roughness exponents, and consist of terraces of all sizes. The coexistence of flat and rough makes them respond to different external interactions with variable roughness. We demonstrate this for optical scattering (including x rays), two wetting situations, diffusion currents, and catalysis. A terraced Cu surface is a "self-assembled" experimental example, and designs for nano- and micromachined examples are presented.     

Elementary Concepts and Fundamental Laws of the Theory of Heat

The elementary concepts and fundamental laws concerning the science of heat are examined from the point of view of its development with special attention to its theoretical structure. The development is divided into four periods, each one characterized by the concept that was attributed to heat. The transition from one to the next period was marked by the emergence of new concepts and new laws, and by singular events. We point out that thermodynamics, as it emerged, is founded on the elementary concepts of temperature and adiabatic wall, and on the fundamental laws: Mayer-Joule principle, or law of conservation of energy; Carnot principle, which leads to the definition of entropy; and the Clausius principle, or law of increase in entropy.     

Kinetic Theory and Lax Equations for Shock Clustering and Burgers Turbulence

We study shock statistics in the scalar conservation law ? _t u+? _x f(u)=0, x∈?, t>0, with a convex flux f and spatially random initial data. We show that the Markov property (in x) is preserved for a large class of random initial data (Markov processes with downward jumps and derivatives of Lévy processes with downward jumps). The kinetics of shock clustering is then described completely by an evolution equation for the generator of the Markov process u(x,t), x∈?. We present four distinct derivations for this evolution equation, and show that it takes the form of a Lax pair. The Lax equation admits a spectral parameter as in Manakov (Funct. Anal. Appl. 10:328–329, 1976), and has remarkable exact solutions for Burgers equation (f(u)=u ²/2). This suggests the kinetic equations of shock clustering are completely integrable.     

研究天体运动要理清的几个概念

近几年的高考试卷，几乎都出现过与万有引力有关的物理问题．分析其原因，万有引力有关的物理问题涉及的知识面比较宽，可以考查学生的相关的空间想象能力，建立物理模型的能力，物理知识的迁移能力，学科综合能力等等．本文谈谈运用好万有引力定律研究天体运动必须要理清的几个概念．