Anomalous, quasilinear, and percolative regimes for magnetic-field-line transport in axially symmetric turbulence

We studied a magnetic turbulence axisymmetric around the unperturbed magnetic field for cases having different ratios l( ||)/l( perpendicular). We find, in addition to the fact that a higher fluctuation level deltaB/B(0) makes the system more stochastic, that by increasing the ratio l( ||)/l( perpendicular) at fixed deltaB/B(0), the stochasticity increases. It appears that the different transport regimes can be organized in terms of the Kubo number R=(deltaB/B(0))(l( ||)/l( perpendicular)). The simulation results are compared with the two analytical limits, that is the percolative limit and the quasilinear limit. When R<1 weak chaos, closed magnetic surfaces, and anomalous transport regimes are found. When R approximately 1 the diffusion regime is Gaussian, and the quasilinear scaling of the diffusion coefficient D( perpendicular) approximately (deltaB/B(0))(2) is recovered. Finally, for R>1 the percolation scaling of the diffusion coefficient D( perpendicular) approximately (deltaB/B(0))(0.7) is obtained.     

Kinetic Description of Particle Interaction with a Gravitational Wave

The interaction of charged particles, moving in a uniform magnetic field, with a plane polarized gravitational wave is considered using the Fokker-Planck-Kolmogorov (FPK) approach. By using a stochasticity criterion, we determine the exact locations in phase space, where resonance overlapping occurs. We investigate the diffusion of orbits around each primary resonance of order m by deriving general analytical expressions for an effective diffusion coefficient. A solution of the corresponding diffusion equation (Fokker-Planck equation) for the static case is found. Numerical integration of the full equations of motion and subsequent calculation of the diffusion coefficient verifies the analytical results.     

Controlling global stochasticity of Hamiltonian systems by nonlinear perturbation

A method of controlling global stochasticity in Hamiltonian systems by applying nonlinear perturbation is proposed. With the well-known standard map we demonstrate that this control method can convert global stochasticity into regular motion in a wide chaotic region for arbitrary initial condition, in which the control signal remains very weak after a few kicks. The system in which chaos has been controlled approximates to the original Hamiltonian system, and this approach appears robust against small external noise. The mechanism underlying this high control efficiency is intuitively explained. Received 15 January 2002 Published online 6 June 2002     

核磁共振二维谱反演

核磁共振二维谱包含扩散系数 D 和横向弛豫时间 T₂ 的信息,利用核磁共振仪来测量多孔介质中物质的信息,根据其弛豫时间和扩散系数的差别来区分不同物质;利用全局反演方法,提出了核磁共振二维谱反演的物理模型和数学模型;介绍了传统的奇异值分解（SVD）和改进的奇异值分解反演算法;采用改进的奇异值分解法对核磁共振二维谱进行反演,其反演算法具有计算速度快和二维谱分布连续等优点. 它适合于信噪比较高的数据反演,当原始数据信噪比SNR≥100时,可以对二维谱图进行定量分析;当60≤SNR<100时,可以对二维谱图进行定性分析. 核磁共振二维谱可以一次性直接区分油和水,为核磁共振测井提供了新的科学技术.     

Diffusion and relaxation effects in general stray field NMR experiments

We analyze the evolution of magnetization following any series of radiofrequency pulses in strongly inhomogeneous fields, with particular attention to diffusion and relaxation effects. When the inhomogeneity of the static magnetic field approaches or exceeds the strength of the RF field, the magnetization has contributions from different coherence pathways. The diffusion or relaxation induced decay of the signal amplitude is in general nonexponential, even if the sample has single relaxation times T(1), T(2) and a single diffusion coefficient D. In addition, the shape of the echo depends on diffusion and relaxation. It is possible to separate contributions from different coherence pathways by phase cycling of the RF pulses. The general analysis is tested on stray field measurements using two different pulse sequences. We find excellent agreement between measurements and calculations. The inversion recovery sequence is used to study the relaxation effects. We demonstrate two different approaches of data analysis to extract the relaxation time T(1). Finite pulse width effects on the timing of the echo formation are also studied. Diffusion effects are analyzed using the Carr--Purcell--Meiboom--Gill sequence. In a stray field of a constant gradient g, we find that unrestricted diffusion leads to nonexponential signal decay versus echo number N, but within experimental error the diffusion attenuation is still only a function of g(2)Dt(3)(E)N, where t(E) is the echo spacing.     

宽气压范围空气中微波击穿电场的计算公式

为了简便快捷地计算微波击穿电场,依据电子扩散模型的基本理论,结合气体放电的基本参量,应用特征扩散长度的概念,给出了适合于规则结构微波部件的击穿电场的计算方法。为避免各种气体参数的不确定性对计算准确度的影响,对等效直流电场与特征扩散长度之间的实验关系进行了拟合,并根据等效直流电场的定义,得出了一个适用于较高气压范围的击穿电场计算表达式。为了将该计算表达式扩展到更低的气压范围,综合考虑了电子扩散模型和基于二次电子发射现象的真空微放电机理,引入了一个合理形式的等效扩散长度,进一步给出了适合于更广气压范围的微波击穿电场的计算表达式,计算结果更符合A.D.Macdonald的实验结果。     

Effect of noise on the standard mapping

The effect of a small amount of noise on the standard mapping is considered. Whenever the standard mapping possesses accelerator modes (where the action increases approximately linearly with time), the diffusion coefficient contains a term proportional to the reciprocal of the variance of the noise term. At large values of the stochasticity parameter, the accelerator modes exhibit a universal behavior. As a result the dependence of the diffusion coefficient on the stochasticity parameter also shows some universal behavior.     

Fractal structures of normal and anomalous diffusion in nonlinear nonhyperbolic dynamical systems

A paradigmatic nonhyperbolic dynamical system exhibiting deterministic diffusion is the smooth nonlinear climbing sine map. We find that this map generates fractal hierarchies of normal and anomalous diffusive regions as functions of the control parameter. The measure of these self-similar sets is positive, parameter dependent, and in case of normal diffusion it shows a fractal diffusion coefficient. By using a Green-Kubo formula we link these fractal structures to the nonlinear microscopic dynamics in terms of fractal Takagi-like functions.     

Spatial and temporal coarse graining for dispersion in randomly packed spheres

The propagator for molecular displacements P(zeta, t) and its first three cumulants were measured for Stokes flow in monodisperse bead packs with different sphere sizes d and molecular diffusion coefficients D(m). We systematically varied the normalized mean displacement /d and diffusion length L(D)=sqrt[2D(m)t]/d. The experimental results map onto each other with this scaling. For L(D)/d<0.2 the propagator remains non-Gaussian, and thus an advection diffusion equation is not obeyed, for mean displacements measured up to 10d. A Gaussian shape is approached for large mean displacements when L(D)>0.3d.     

Magnetic stochasticity in gyrokinetic simulations of plasma microturbulence

Analysis of the magnetic field structure from electromagnetic simulations of tokamak ion temperature gradient turbulence demonstrates that the magnetic field can be stochastic even at very low plasma pressure. The degree of magnetic stochasticity is quantified by evaluating the magnetic diffusion coefficient. We find that the magnetic stochasticity fails to produce a dramatic increase in the electron heat conductivity because the magnetic diffusion coefficient remains small.     

Stability of operator splitting methods for systems with indefinite operators: Advection–diffusion–reaction systems

This brief paper presents an A-stability result for operator splitting type time integration methods applied to advection–diffusion–reaction equations with possibly indefinite source terms. These results extend our earlier work on diffusion–reaction systems [D.L. Ropp, J.N. Shadid, Stability of operator splitting methods for systems with indefinite operators: reaction–diffusion systems, J. Comput. Phys. 203 (2) (2005) 449–466]. The A-stability result presents sufficient conditions that control both low and high wave number instabilities. A corollary shows that if L-stable methods are used for the diffusion term the high wave number instability will be controlled more easily. Numerical results are presented that verify second-order convergence for the operator splitting methods and demonstrate control of instabilities on a chemotaxis problem by use of an L-stable diffusion integrator.     

The dynamical temperature and the standard map

Numerical experiments with the standard map at high values of the stochasticity parameter reveal the existence of simple analytical relations connecting the volume and the dynamical temperature of the chaotic component of the phase space.     

On the security of 3D Cat map based symmetric image encryption scheme

A 3D Cat map based symmetric image encryption algorithm, which significantly increases the resistance against statistical and differential attacks, has been proposed recently. It employs a 3D Cat map to shuffle the positions of image pixels and uses the Logistic map to diffuse the relationship between the cipher-image and the plain-image. Based on the factor that it is sufficient to break this cryptosystem only with the equivalent control parameters, some fundamental weaknesses of the cryptosystem are pointed out. With the knowledge of symbolic dynamics and some specially designed plain-images, we can calculate the equivalent initial condition of diffusion process and rebuild a valid equivalent 3D Cat matrix. In this Letter, we will propose a successful chosen-plain-text cryptanalytic attack, which is composed of two mutually independent procedures: the cryptanalysis of the diffusion process and the cryptanalysis of the spatial permutation process. Both theoretical and experimental results show that the lack of security discourages the use of these cryptosystems for practical applications.     

Kinetics of Active Surface-Mediated Diffusion in Spherically Symmetric Domains

We present an exact calculation of the mean first-passage time to a target on the surface of a 2D or 3D spherical domain, for a molecule alternating phases of surface diffusion on the domain boundary and phases of bulk diffusion. We generalize the results of Bénichou et al. in (J. Stat. Phys. 142:657, 2011) and consider a biased diffusion in a general annulus with an arbitrary number of regularly spaced targets on a partially reflecting surface. The presented approach is based on an integral equation which can be solved analytically. Numerically validated approximation schemes, which provide more tractable expressions of the mean first-passage time are also proposed. In the framework of this minimal model of surface-mediated reactions, we show analytically that the mean reaction time can be minimized as a function of the desorption rate from the surface.     

Kinetic Theory of Area-Preserving Maps. Application to the Standard Map in the Diffusive Regime

The evolution of the distribution function of a dynamical system governed by a general two-dimensional area-preserving iterative map is studied by the methods of nonequilibrium statistical mechanics. A closed, non-Markovian master equation determines the angle-averaged distribution function (the density profile). The complementary, angle-dependent part (the fluctuations) is expressed as a non-Markovian functional of the density profile. Whenever there exist two widely separated intrinsic time scales, the master equation can be markovianized, yielding an asymptotic kinetic equation. The general theory is applied to the standard map in the diffusive regime, i.e., for large stochasticity parameter and large scale length. The non-Markovian master equation can be written and solved analytically in this approximation. The two characteristic time scales are exhibited. This permits the thorough study of the evolution of the density profile, its tendency toward the Markovian approximation, and eventually toward a diffusive Gaussian packet. The evolution of the fluctuations is also described in detail. The various relaxation processes are governed asymptotically by a single diffusion coefficient, which is calculated analytically. This model appears as a testing bench for the study of kinetic equations. The various previous approaches to this problem are reviewed and critically discussed.     

Fractality of deterministic diffusion in the nonhyperbolic climbing sine map

The nonlinear climbing sine map is a nonhyperbolic dynamical system exhibiting both normal and anomalous diffusion under variation of a control parameter. We show that on a suitable coarse scale this map generates an oscillating parameter-dependent diffusion coefficient, similarly to hyperbolic maps, whose asymptotic functional form can be understood in terms of simple random walk approximations. On finer scales we find fractal hierarchies of normal and anomalous diffusive regions as functions of the control parameter. By using a Green–Kubo formula for diffusion the origin of these different regions is systematically traced back to strong dynamical correlations. Starting from the equations of motion of the map these correlations are formulated in terms of fractal generalized Takagi functions obeying generalized de Rham-type functional recursion relations. We finally analyze the measure of the normal and anomalous diffusive regions in the parameter space showing that in both cases it is positive, and that for normal diffusion it increases by increasing the parameter value.     

Fractal diffusion in smooth dynamical systems with virtual invariant curves

Preliminary results of extensive numerical experiments with a family of simple models specified by the smooth canonical strongly chaotic 2D map with global virtual invariant curves are presented. We focus on the statistics of the diffusion rate D of individual trajectories for various fixed values of the model perturbation parameters K and d. Our previous conjecture on the fractal statistics determined by the critical structure of both the phase space and the motion is confirmed and studied in some detail. In particular, we find additional characteristics of what we earlier termed the virtual invariant curve diffusion suppression, which is related to a new very specific type of critical structure. A surprising example of ergodic motion with a “hidden” critical structure strongly affecting the diffusion rate was also encountered. At a weak perturbation (K ? 1), we discovered a very peculiar diffusion regime with the diffusion rate D=K ²/3 as in the opposite limit of a strong (K ? 1) uncorrelated perturbation, but in contrast to the latter, the new regime involves strong correlations and exists for a very short time only. We have no definite explanation of such a controversial behavior.     

ZnP2在GaP表面的定压箱法扩散

理论计算给出了带盖砂磨石英箱内扩散源蒸汽的泄漏率和箱子容积、缝隙宽度,蒸汽分子在缝隙中运动的相互关系。实验证实了ZnP2作为GaP LED高表面浓度扩散源的定压箱法扩散是可采用的。用设计加工的石英箱,对样片进行了多次定压箱法扩散,其结果与闭管扩散一致,且具有良好的重复性。     

Diagrammatic structure of the general coupled cluster equations

The general formula for the number of diagrammatic terms occurring in the T_n equation within a particular coupled cluster model is derived. Both the antisymmetrized and Goldstone diagrams are considered. In addition to the full coupled cluster equation approximate approaches are discussed, and for each the general formula for the number of terms is given. Analogous expressions are presented for the number of diagrammatic terms contributing to the elements of the transformed Hamiltonian [Hbar] = e^?T He^T .