Collective Grain Interactions II. Non‐linear Collective Drag Force

It is found that the collective effects operating at large distances from the grain surface can produce substantial scattering of the ion flux and create an additional collective drag force dominant for large grain densities. The consideration is restricted to large grain charges β = Z_de ²a /T_iλ_Di ? 1 and T_i /T_e ? 1 (–eZ_d being the grain charge in units of electron charge, a being the grain size, λ_Di being the ion Debye radius and T_e,i being electron and ion temperatures, respectively). For present dusty plasma experiments β ≈ 10–50, the large charges of grains are screened non‐linearly and the ion scattering creates non‐linear drag force. The present investigation considers effects of scattering by collective grain fields at large distances from the grains. It is found that the physical reason of the importance of collective drag force, calculated in this paper, is related to presence of weakly screened collective field of grains outside the non‐linear screening distance depending on grain densities. The amplitude of this collective fields of the grains is determined by non‐linear screening at non‐linear screening radius. It is shown that for dust densities of present experiments the collective drag force related to this scattering can be of the order of the non‐linear drag force caused by scattering inside the non‐linear screening radius or even larger. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

非线性振子的矩阵元及其经典近似

对于势能为V(x)=1/2 mω2x2+λx4的非线性谐振子,不能用微扰论对经典方程进行求解.这里利用海森伯对应原理,由量子力学的矩阵元得到了非线性振子的经典解,从而对于非线性振子的性质有了进一步的理解.     

Perturbation Theory for Open Two-Level Nonlinear Quantum Systems

Perturbation theory is an important tool in quantum mechanics. In this paper, we extend the traditional perturbation theory to open nonlinear two-level systems, treating decoherence parameterγ as a perturbation. By this virtue, we give a perturbative solution to the master equation, which describes a nonlinear open quantum system. The results show that for small decoherence rateγ, the ratio of the nonlinear rate C to the tunneling coefficient V (i.e., r=C/V) determines the validity of the perturbation theory. For small ratio r, the perturbation theory is valid, otherwise it yields wrong results.     

Dust-free regions around Langmuir probes in complex plasmas under microgravity

Dust-free regions around a Langmuir probe are studied in a complex plasma under microgravity. The dust particles settle in the presheath of the probe, where an equilibrium of the electric field force and the ion-drag force is established. The size and shape of the dust cloud are discussed with simple models. A more sophisticated presheath model is solved numerically to analyze the acting forces and the equilibrium position of the dust. The formation of distinct particle layers in the dust shell can be explained by the force gradients of the effective potential well.     

Spherical Kadomtsev–Petviashvili equation for dust acoustic waves with dust size distribution and two-charges-ions

The nonlinear dust acoustic waves in dusty plasmas with negative as well as positive ions and the combined effects of bounded spherical geometry and the transverse perturbation and the size distribution of dust grains are studied. Using the perturbation method, a spherical Kadomtsev–Petviashvili (SKP) equation that describes the dust acoustic waves is deduced.     

Note on Mechanism for Formation of Bulbs (Structures) in Complex Plasmas with Grains of Different Size

In this note the phenomena of formation of grain bulbs (compact grain structure) in presence of grains with different size is discussed from point of view of grain force balance. The requirement is found showing where in the equilibrium conditions the larger size grains are expelled from the regions of smaller size grains forming dust bulbs containing only the smallest size grains. The experiments where this phenomenon was observed are discussed. It is possible to conclude that these experiments can serve as direct evidence for existence of the non‐linear screening of individual grains and for excitation of collective large scale electric fields that balances the drag forces in domain of structures. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Strain-Induced Surface Roughening in Polycrystalline VT1-0 Titanium Specimens under Uniaxial Tension

Surface roughening in uniaxially tensile specimens of commercially pure titanium VT1-0 has been investigated using electron backscatter diffraction, optical and atomic force microscopy, and numerical simulation. It is shown that intragranular slip leads to the rotation of surface grains, due to which the grain surface is inclined and a terrace is formed at the interface with neighboring grains. The effect of the crystallographic grain orientation on the grain shape change and the degree of grain rotation occurring under constrained plastic deformation is demonstrated.     

The KP and ZK equations for electrostatic waves with grain charge fluctuation

The propagation of three-dimensional nonlinear dust-acoustic and dust-Coulomb waves in unmagnetized/magnetized dusty plasmas consisting of electrons, ions, and charged dust particles is investigated. The grain charge fluctuation effect is also incorporated through the current balance equation. By using the perturbation method, a Kadomtsev－Petviashvili equation and a Zakharov－Kuznetsov equation governing the nonlinear waves in the unmagnetized and magnetized systems are obtained respectively. It has been shown that with the combined effects of grain charge fluctuation, the transverse perturbation, and the external magnetic field would modify the wave structures. Waves in those systems are unstable to the high-order long-wave perturbations.     

Pinning effect of different shape second-phase particles on grain growth in polycrystalline: numerical and analytical investigations

The pinning effect of different shape second-phase particles on the grain growth in polycrystalline structures is numerical simulated by the phase-field method. Simulation results indicate that the average grain size is highly dependent on the shape and distribution of the second-phase particles, and the shape effect of particles on grain growth restraining is enhanced with increasing numbers of particles. In order to discuss the relation between the constraint grain growth and the second-phase particles, pinning forces induced by different shape particles are theoretically calculated via the Zener pinning theory. The calculated pining forces indicate that the maximum pinning force is highly dependent on the contact mode between grains and particles, and the distance between particles has a significantly influence on the pinning forces. Therefore, controlling the shape and distributions of second-phase particles in polycrystalline metals or ceramics might be an efficient way to achieve materials with specified microstructures.     

Radiation force exerted on nanometer size non-resonant Kerr particle by a tightly focused Gaussian beam

We calculate the radiation force that is exerted by a focused continuous-wave Gaussian beam of wavelength λ on a non-absorbing nonlinear particle of radius a ? 50λ/π. The refractive index of the mechanically-rigid particle is proportional to the incident intensity according to the electro-optic Kerr effect. The force consists of two components representing the contributions of the electromagnetic field gradient and the light scattered by the Kerr particle. The focused intensity distribution is determined using expressions for the six electromagnetic components that are corrected to the fifth order in the numerical aperture (NA) of the focusing objective lens. We found that for particles with a < λ/21.28, the trapping force is dominated by the gradient force and the axial trapping force is symmetric about the geometrical focus. The two contributions are comparable with larger particles and the axial trapping force becomes asymmetric with its zero location displaced away from the focus and towards the beam propagation direction. We study the trapping force behavior versus incident beam power, NA, λ, and relative refractive index between the surrounding liquid and the particle. We also examine the confinement of a Kerr particle that exhibits Brownian motion in a focused beam. Numerical results show that the Kerr effect increases the trapping force strength and significantly improves the confinement of Brownian particles.     

Effects of grain size on dislocation organization and internal stresses developed under tensile loading in fcc metals

The relationship between deformation and dislocation properties has been studied for pure polycrystalline nickel and austenitic stainless steel AISI 316L in stage III. Special care was taken to study statistically the effects of the grain size and grain orientation on dislocation densities and distribution. It is shown that the nature of dislocation cells depends on grain size and crystallographic orientation. The dimensional parameters, which depend on grain size, i.e. the inter-boundary spacing (λ) and boundary thickness (e), define three domains of crystallographic orientation and depend on the grain size. Scaling hypotheses reveal two physical mechanisms which, at this level of plastic strain, are correlated to a specific value of the noise, associated with distribution functions. Similarities between structural parameters and dislocation densities in each phase (walls and inter-walls spacing) are identified and discussed in terms of kinetic equations describing dislocation density evolution and fluctuations of certain physical parameters. This similarity provides physical signification of the scaling distribution obtained on λ and e in terms of a stochastic approach to dislocation distribution. The origin of Hall–Petch behaviour observed at large strain is interpreted in terms of an interaction between inter- and intra-granular long-range internal stresses, which depends on grain size. We conclude that, at high strain, the Hall–Petch phenomenological relationship is a consequence of plastic strain history and strain gradient in grains. From this last point, a length scale arises naturally, which depends on stacking fault energy.     

Long-time evolution of charged grains in plasma under harmonic external force and after being withdrawn

Evolution of the charged grains in a two-dimensional dusty plasma under a spatially harmonic external force,in particular,their long-time behaviors after the force has been withdrawn,is studied by using molecular dynamics simulation.Under an external force and a grain–grain interaction force,initially homogeneously distributed grains can reach a quasistationary state in the form of a disk crystal.After the external force is withdrawn,the disk moves initially with its size and shape nearly unchanged until it rapidly stops moving,and eventually the disk grain rotates like a vortex.The time needed to reach the final state increases with the strength of the initial external force increasing.     

Cylindrical Three-Dimensional Dust-Ion Acoustic Propagation in Plasmas

Wave properties of solitons in an unmagnetized four-component dusty plasma system contains isothermal distributed electrons, mobile ions, and negative-positive dusty grains have been examined. To study DIA wave properties, a reductive perturbation (RP) analysis is used. By a reductive perturbation (RP) analysis under convenient coordinate transformation, the three dimension Kadomtsev-Petviashvili equation in cylindrical coordinates is obtained. The effects of dust grain charge on soliton pulse structures are studied. More specifically, solitary profile depending on the axial, radial, and polar angle coordinates with time is discussed. This investigation may be viable in plasmas of the Earth's mesosphere.     

掺杂对CH样品Rayleigh-Taylor不稳定性增长的影响

在神光II激光装置上进行了辐射驱动不同掺杂样品的单模Rayleigh-Taylor(RT)不稳定性实验.结果显示:与纯碳氢(CH)样品相比,掺Br的CH样品的扰动更早、更快地进入非线性区,产生二次谐波,并且掺Br比例越高,CH样品扰动进入非线性区的时间越早,相同时刻扰动的二次谐波的幅度越高.这是因为密度梯度效应抑制了二次谐波的产生,掺Br比例越高,密度梯度标长越小;同时密度梯度效应还抑制三次谐波对基模增长的负反馈,造成基模具有更大的线性增长,导致线性饱和幅值大于经典值0.1λ.     

Localized ferromagnetic resonance in inhomogeneous thin films

The effect of sample inhomogeneity on the ferromagnetic resonance linewidth is determined by diagonalization of a spin wave Hamiltonian for ferromagnetic thin films with inhomogeneities spanning a wide range of characteristic length scales. A model inhomogeneity is used that consists of size D grains and an anisotropy field H(p) that varies randomly from grain to grain in a film with thickness d and magnetization M(s). The resulting linewidth agrees well with the two-magnon model for small inhomogeneity, H(p)DpiM(s)d, the precession becomes localized and the spectrum approaches that of local precession on independent grains.     

非均匀磁场尘埃等离子体中颗粒的复杂运动

本文研究了在非均匀磁场尘埃等离子体中不规则尘埃颗粒的复杂运动, 包括圆滚运动、尖头圆滚运动、圆周运动以及波浪运动等. 放置在电极上的圆柱形磁铁的主要作用是改变鞘层的径向分布, 进而对颗粒产生径向约束, 使尘埃颗粒悬浮于圆柱形磁铁周围, 其磁场并不足以磁化颗粒使其做圆滚运动. 通过与球形尘埃颗粒的对比实验发现, 圆滚运动是不规则尘埃颗粒在等离子体中特有的一种运动. 我们提出了一种新的机理: 由于不规则颗粒的自旋而引起的横向反Magnus力对颗粒的圆滚运动起了重要的作用. 文中通过受力分析定性地对实验中观察到的非球形颗粒的各种运动给出了合理的解释.     

Destabilization of a Saffman-Taylor fingerlike pattern in a granular suspension

We study the Saffman-Taylor instability in a granular suspension formed by micrometric beads immersed in a viscous liquid. When using an effective viscosity for the flow of the suspension in the Hele-Shaw cell to define the control parameter of the system, the results for the finger width of stable fingers are found to be close to the classical results of Saffman-Taylor. One observes, however, an early destabilization of the fingers that can be attributed to the discrete nature of the individual grains. Classically, the threshold of destabilization is linked to the noise in the cell and is thus difficult to quantify. We show that the grains represent a "controlled noise" and produce an initial perturbation of the interface with an amplitude proportional to the grain size. The finite amplitude instability mechanism proposed by Bensimon et al. allows us to link this perturbation to the value of the threshold observed.     

A simple example of a singular perturbation expansion

For the Hamiltonian?=?? _x ² -αδ(x)+λx ² the bound-(λ>0) and resonance(λ<0) states are discussed. The perturbation expansion of the ground-state? ₀(λ) in powers ofλ is divergent for allλ. The nature of the singularity atλ=0 is investigated and it turns out, that the perturbation series is asymptotic and therefore useful even forλ<0.     

Suppressing chaos by parametric perturbation at doubled frequency of periodic perturbation

An analysis of the chaos suppression of a nonlinear elastic beam(NLEB)is presented.In terms of modal transformation the equation of NLEB is reduced to the Duffing equation.It is shown that the chaotic behaviour of the NLEB is sensitively dependent on the parameters of perturbations and initial conditions.By adjusting the frequency of parametric perturbation to twice that of the periodic one and the amplitude of parametric pertubation to the same as the periodic one,the chaotic region of the nonlinear elastic beam driven by periodic force can be greatly suppressed.