High-resolution electron microscopy observations of continuous precipitates with Pitsch-Schrader orientation relationship in an Mg–Al based alloy and interpretation with the O-lattice theory

High-resolution electron microscopy was applied to analyze the continuous precipitated particles of the γ-Mg₁₇Al₁₂ phase with Pitsch-Schrader OR in the heat-treated AZ91 alloy at 473 K for 8 h. The existence of a continuous precipitated particle with the Pitsch-Schrader OR including the selection of the habit plane and the growth direction in Mg–Al system is rationalized by the constrained coincidence site lattice/constrained complete pattern shift lattice (CCSL/CDSCL) model and the O-lattice theory.     

相场法研究Fe-Cu-Mn-Al合金富Cu相析出机制

基于Ginzburg-Landau理论采用连续相场法模拟了Fe-15%Cu-3%Mn-x Al(质量分数x=1%, 3%, 5%)合金在873 K等温时效时纳米富Cu析出相沉淀机制及Al含量对富Cu相析出的阻碍效应.通过计算成分场变量和结构序参数,研究了富Cu析出相的形貌、颗粒密度、平均颗粒半径、生长和粗化动力学.研究结果表明:在时效早期阶段,纳米富Cu相通过失稳分解机制析出,由于原子扩散速率存在差异,从而形成以富Cu相为核心的核壳结构.随着时效时间延长,富Cu相析出物结构由体心立方转变为面心立方.其中Al和Mn原子在富Cu核外偏析形成Al/Mn簇,可以将其视为阻碍富Cu析出相形成的缓冲层;在沉淀过程中,随着Al含量的增大, Al/Mn金属间相促进了缓冲层的生长,阻碍富Cu析出相的生长和粗化.     

Microhardness studies on melt-grown single-phase mixed (NaK)Cl and solution-grown two-phase NaClKCl crystals

Microhardness studies were carried out on melt-grown (NaK)Cl crystals. The quenching strains and the difference in the ionic sizes of the cations constituting the mixed system introduced large numbers of defects, viz. dislocations, grain boundaries, etc. The etching experiments and supplementary X-ray studies clearly revealed that the Na⁺ or K⁺ ions are precipitated at the dislocation sites. These phase particles strongly interact with dislocations so as to obstruct the mobility of the latter contributing to the hardening mechanism. Results are compared with solution-grown two-phase mixed NaClKCl pure NaCl and pure KCl crystals.     

Spontaneous partitioning of particles into cellar structures in a membrane system

Membranes are often used for material partitioning in biological systems and industry. Here we report a novel physical mechanism of particle partitioning using topological transformation of bilayer membranes. Upon phase separation of a homogeneous sponge phase of a membrane system into a dense sponge and a water phase, we found quite unusual partitioning behavior of particles into the cellar structure of a water phase. The compartments next to one having particles always have no particles, and those next to a compartment having no particles always have particles. We confirm that this partitioning is purely geometrically induced, and thus it may be universal.     

LES-DSMC方法研究超细颗粒气固两相流动过程

采用考虑颗粒脉动流动对气相湍流流动影响的大涡模拟(LES)研究气相湍流,采用直接模拟蒙特卡罗方法(DSMC)模拟颗粒间的碰撞。单颗粒运动满足牛顿第二定律,颗粒相和气相相间作用的双向耦合由牛顿第三定律确定,考虑超细颗粒间的van der Waals作用力。数值模拟垂直管内超细颗粒气固两相流动,对颗粒相速度、浓度以及团聚物流动过程进行分析。     

Theory of diffusive decomposition of supersaturated multicomponent systems

A closed system of equations, which describes the evolution of supersaturated multicomponent solutions, is obtained. A general solution of these equations is determined in the late stage of decomposition, which is determined by nonlinear diffusive interaction of macrodefects.The algebraic equations, which determine the coexistent phases, are obtained.The size of distribution function for particles is determined for each phase. The boundaries of the coexistent phases are defined.     

Anomalous kinetic energy of a system of dust particles in a gas discharge plasma

The system of equations of motion of dust particles in a near-electrode layer of a gas discharge has been formulated taking into account fluctuations of the charge of a dust particle and the features of the nearelectrode layer of the discharge. The molecular dynamics simulation of the system of dust particles has been carried out. Performing a theoretical analysis of the simulation results, a mechanism of increasing the average kinetic energy of dust particles in the gas discharge plasma has been proposed. According to this mechanism, the heating of the vertical oscillations of dust particles is initiated by induced oscillations generated by fluctuations of the charge of dust particles, and the energy transfer from vertical to horizontal oscillations can be based on the parametric resonance phenomenon. The combination of the parametric and induced resonances makes it possible to explain an anomalously high kinetic energy of dust particles. The estimate of the frequency, amplitude, and kinetic energy of dust particles are close to the respective experimental values.     

利用激光光梯度力消除气溶胶雾霾粒子的机理研究

针对气溶胶雾霾粒子在大气流中所受力的平衡体系(旋转升力平衡重力, 粒子与粒子之间依靠斥力形成稳定的网状的力平衡体系)的问题, 提出了用激光光梯度力破坏力平衡进而消除雾霾的新机理. 首先, 根据牛顿第二定理, 得到了粒子所受力的非线性方程组, 应用Runge-Kutta 法积分求解了雾霾颗粒在大气流中所受的主要力(空气曳引阻力、范德瓦耳斯斥力、旋转升力)的数值, 成功验证了西安市2013年12月17-25日、2014年2月20-26日两次雾霾检测试验结论: 在雾霾过程中, 粒径在0.5-0.835 μm径段的粒子数浓度增加最明显. 其次, 在雾霾粒子形成的均匀介质中, 计算了激光光梯度力的大小. 研究发现, 激光光梯度力的数量级恒大于雾霾颗粒所受主要力的数量级, 激光光梯度力完全可以破坏雾霾颗粒所受力的平衡体系. 因此, 用激光光梯度力消除雾霾是可行的, 这种新的解决雾霾的方法对人们的实际生活、环保及创建美丽的蓝天具有非常重要的意义.     

On the motion of a three-body system on hypersurface of proper energy

Based on the fact that for hamiltonian system there exists equivalence between phase trajectories and geodesic trajectories on the Riemannian manifold, the classical three-body problem is formulated in the framework of six ordinary differential equations (ODEs) of the second order on the energy hypersurface of body system. It is shown that in the case when the total interaction potential of the body system depends on the relative distances between particles, the three of six geodesic equations describing rotations of formed by three bodies triangle are solved exactly. Using this fact, it is shown that the three-body problem can be described in the limits of three nonlinear ODEs of canonical form, which in phase space is equivalent to the autonomous sixth-order system. The equations of geodesic deviations on the manifold (the space of relative distances between particles) are derived in an explicit form. A system of algebraic equations for finding the homographic solutions of restricted three-body problem is obtained. The initial and asymptotic conditions for solution of the classical scattering problem are found.     

Spontaneous Breaking of Translational Invariance and Spatial Condensation in Stationary States on a Ring. II. The Charged System and the Two-Component Burgers Equations

We further study the stochastic model discussed in ref. 2 in which positive and negative particles diffuse in an asymmetric, CP invariant way on a ring. The positive particles hop clockwise, the negative counter-clockwise and oppositely-charged adjacent particles may swap positions. We extend the analysis of this model to the case when the densities of the charged particles are not the same. The mean-field equations describing the model are coupled nonlinear differential equations that we call the two-component Burgers equations. We find roundabout weak solutions of these equations. These solutions are used to describe the properties of the stationary states of the stochastic model. The values of the currents and of various two-point correlation functions obtained from Monte-Carlo simulations are compared with the mean-field results. Like in the case of equal densities, one finds a pure phase, a mixed phase and a disordered phase.     

Anharmonic interactions of elastic and orientational waves in one-dimensional crystals

Planar oscillations of a chain of dumbbell-shaped particles possessing three degrees of freedom are studied. This system models the dynamics of quasi-one-dimensional crystals consisting of elongated anisotropic molecules. A system of nonlinear differential equations describing the anharmonic interaction of the elastic and orientational waves in the lattice, corresponding to different degrees of freedom of the particles, is constructed assuming a cubic interparticle interaction potential. It is shown that in the low-frequency approximation the system obtained is equivalent to the equations of the moment theory of elasticity, widely employed for describing nonlinear and dispersion properties of layered crystals and phase transformations in alloys. Some types of three-wave collinear interactions are investigated, suggesting the possibility of exciting orientational waves in organic crystals because of their nonlinear interaction with acoustic waves. Fiz. Tverd. Tela (St. Petersburg) 39, 137–144 (January 1997)     

Phase transitions for a continuous system of classical particles in a box

A continuous classical system involving an infinite number of distinguishable particles is analyzed along the same lines as its quantum analogue, considered in [1]. A commutativeC*-algebra is set up on the phase space of the system, and a representation-dependent definition of equilibrium involving the static KMS condition is given. For a special class of interactions the set of equilibrium states is realized as a convex Borel set whose extremal states are characterized by solutions to a system of integral equations. By analyzing these integral equations, we prove the absence of phase transitions for high temperature and construct a phase transition for low temperature. The construction also provides an example of a translation-invariant state whose decomposition at infinity yields states that are not translation-invariant. Thus we have an example in the classical situation of continuous symmetry breaking.This article is a part of the author's doctoral thesis, which was submitted to the mathematics department at Duke University     

Collisionless Boltzmann equations and integrable moment equations

A collisionless Boltzmann equation, describing long waves in a dense gas of particles interacting via short-range forces, is shown to be equivalent to the Benney equations, which describe long waves in a perfect two-dimensional fluid with a free surface. These equations also describe, in a random phase approximation, the evolution, on long space and time scales, of multiply periodic solutions of the nonlinear Schrödinger equation. The derivative nonlinear Schrödinger equation is likewise shown to be related to an integrable system of moment equations.     

Effects of the Space Charge Forces and the Beam Halo in an AVF Cyclotron with Intense Beam Currents

The equations of motion of particles in an AVF cyclotron in a curvilinear coordinate system are derived for the cases with and without space charge forces. Assuming a set of the parameter values in the equations, numerical calculations are carried out by using Lunge-Kutta methods in the case with space charge forces. The results show that the formation of the beam halo is also a main reason of the beam losses, but the mechanism here is different from that in a linear accelerator. It is not given rise by resonance and chaos but the outward repellent motion and the vortex motion of the particles in the bunch.     

强流AVF型迴旋加速器中的空间电荷效应和束晕

详细推导了AVF型迴旋加速器中束团粒子在曲线坐标系中的动力学方程(考虑和不考虑空间电荷相互作用力两种情况).在假定动力学方程中各参数值的前提条件下,用Lunge-Kutta方法对考虑空间电荷时的动力学方程进行了数值计算.结果表明,束晕的形成和发展同样也是强流迴旋加速器中束流损失的一个主要原因.但束晕形成的机制不同于直线加速器的情况,它不是由共振和混沌引起,而是由于粒子的排斥运动和束团内粒子的涡流运动引起的.     

Faddeev equations and the method of hyperspherical harmonics in the problem of three-nucleon continuum

A method for solving the Faddeev equations in configuration space is developed for a three-nucleon system in the continuum by using the decomposition over a hyperspherical basis. The wave functions of Nd-system, phase shifts, and cross sections of Nd-scattering at subthreshold energies are calculated. Also, within the framework of this method, one-dimensional integral equations are formulated for the problem of infinite motion of all three strongly interacting particles, and the Faddeev equations for a system of three hadrons with Coulomb interaction in the continuum are modified. Similar methods of investigation of three-particle systems are reviewed.     

Dynamic features of stimulated raman atomic-molecular conversion in a mixture of two bose gases with the formation of bose condensates of heteronuclear molecules

Based on the mean-field approximation, a system of nonlinear differential equations is obtained which describes the dynamics of atomic-molecular conversion induced by two resonance Raman laser pulses. The obtained integrals of motion allow one to reduce the problem to one evolution equation for the density of molecules. The solutions of this equation show that different time evolution regimes of the system are possible, depending on the initial conditions: the periodic and aperiodic regimes and the rest. The dependences of the period and amplitude on the initial density of particles and the initial phase difference are studied in detail. The possibility of the phase control of the system dynamics is proved.     

Phase transitions of the many-particle Weinberg-Salam system at finite temperature

A method is proposed for calculating high-temperature asymptotic behaviour of an effective potential, which is intended to deal with the situation when the spectra of particles cannot be found explicitly. This method is applied to calculating the high-temperature effective potential of a gas of particles described by the Weinberg-Salam model in presence of leptonic charge density, as well as of all the nonzero average fields (W-condensate, Higgs scalar, electric and weak-neutral chemical potentials) that appear as solutions of the equilibrium equations of this system at zero temperature, with the overall electric and weak neutrality preserved. There are three possible phases of the system: the symmetrical phase, the phase with the Higgs condensate, and the one with the Higgs and W-condensate. Equations for the boundary curves separating these phases are obtained and solved.     

Features of dynamics of stimulated atomic-molecular Raman conversion in a Bose-Einstein condensate

A set of nonlinear evolution equations describing the dynamics of atoms, molecules, and photons in the course of stimulated atomic—molecular conversion in a Bose—Einstein condensate is derived and studied in the mean-field approximation. It is shown that conversion can be periodic or aperiodic in time, the rate of the process being determined to a considerable extent by the initial density of particles and by the initial phase difference. Depending on the initial conditions, various conversion modes can be realized. The possibility of stabilization of a special state (of rest) of the system for nonzero initial number densities of particles is predicted. It is pointed out that coherence of a Bose condensate of atoms, molecules, and photons predetermines the possibility of phase control of the conversion process.     

Small-angle x-ray scattering study of the formation and growth of δ' in binary Al－7.87at% Li alloy

The formation and growth of δ' particles in an alloy of Al－7.87at% Li have been investigated using the small angle x-ray scattering technique. It has been shown that a transition zone, which exists between the δ' phase and the matrix after ageing for 16 h, disappears after ageing for 32 h. The existence of a transition zone indicates that the δ' phase is precipitated in the process of spinodal decomposition. This result also indicates that the growth of δ' particles should be divided into two stages. During the first stage, the δ' phase increases eating up the transition zone before ageing for 32 h, and in the second stage it grows by swallowing up each other after ageing for 32 h. In the latter stage, the larger and smaller δ' particles can coexist in the alloy.