Precipitate growth in concentrated binary alloys: a comparison between kinetic Monte Carlo simulations,cluster dynamics and the classical theory

The numerical modelling of concentrated alloy precipitation kinetics remains a challenge at all scales. At the microscopic scale, kinetic Monte Carlo (KMC) simulations can cope with nucleation and early growth whatever the solute concentration may be; it cannot, however, address coarsening. At the mesoscopic scale, the advantage of cluster dynamics (CD) is its ability to describe the whole kinetics of precipitation but lacks of reliability for nucleation in concentrated alloys. Finally, analytical models are preferred at the macroscopic scale for their simplicity, their flexibility and their ability to be incorporated within more general approaches, to predict mechanical properties, for instance. The present work aims at examining the ability of CD and classical analytical models to describe the growth of an isolated precipitate in a concentrated binary alloy, by comparison with KMC simulations taken as the reference.     

Experimental study of granular compaction dynamics at different scales: grain mobility, hexagonal domains, and packing fraction

We present an original experimental study of the compaction dynamics for two-dimensional granular systems. Compaction dynamics is measured at three different scales: the macroscopic scale through the normalized packing fraction rho, the mesoscopic scale through the normalized fraction phi of hexagonal domains in the system, and the microscopic scale through the grain mobility mu. Moreover, the hexagonal domains are found to obey a growth process dominated by the displacement of domain boundaries. A global picture of compaction dynamics relevant at each scale is proposed.     

Stochastic simulation of variations in the autoignition delay time of premixed methane and air

A mesoscopic stochastic particle model for homogeneous combustion is introduced. The model can be used to investigate the physical fluctuations in a system of coupled chemical reactions with energy (heat) release/consumption. In the mesoscopic model, the size of the homogeneous gas volume is an additional variable, which is eliminated in macroscopic continuum models by the thermodynamic limit N→∞. Thus, continuous homogeneous models are macroscopic models wherein fluctuations are excluded by definition. Fluctuations are known to be of particular importance for systems close to the autoignition limits. The new model is used to investigate the stochastic properties of the autoignition delay time in a homogeneous system with stoichiometric premixed methane and air. Temperature and species concentrations during autoignition of sub-macroscopic volumes, including physically meaningful fluctuations, are presented. It is found that different realizations mainly differ in the time when ignition occurs; besides this the development is similar. The mesoscopic range and the macroscopic limit are identified. Which range a specific system is assigned to is not only a question of the length scale or particle number, but also depends on the complete thermodynamic state. The stochastic algorithm yields the correct results for the macroscopic limit compared to the continuous balance equations. The sensitivity of the results to two different detailed reaction mechanisms (for the same system) is studied and found to be low. We show that when approaching the autoignition limit by decreasing the temperature, the fluctuations in the autoignition delay time increase and an increasing number of realizations will have exceedingly long ignition delay times, meaning they are in practice not autoignitable. With this result the mesoscopic simulations offer an explanation of the transition between autoignitable and non-autoignitable conditions. The calculated distributions were compared with ten repetitions of the same experiment. A mesoscopic distribution that matches the experimental results was found.     

Nonlinear quantum mechanics,the superposition principle,and the quantum measurement problem

There are four reasons why our present knowledge and understanding of quantum mechanics can be regarded as incomplete. (1) The principle of linear superposition has not been experimentally tested for position eigenstates of objects having more than about a thousand atoms. (2) There is no universally agreed upon explanation for the process of quantum measurement. (3) There is no universally agreed upon explanation for the observed fact that macroscopic objects are not found in superposition of position eigenstates. (4) Most importantly, the concept of time is classical and hence external to quantum mechanics: there should exist an equivalent reformulation of the theory which does not refer to an external classical time. In this paper we argue that such a reformulation is the limiting case of a nonlinear quantum theory, with the nonlinearity becoming important at the Planck mass scale. Such a nonlinearity can provide insights into the aforesaid problems. We use a physically motivated model for a nonlinear Schr?dinger equation to show that nonlinearity can help in understanding quantum measurement. We also show that while the principle of linear superposition holds to a very high accuracy for atomic systems, the lifetime of a quantum superposition becomes progressively smaller, as one goes from microscopic to macroscopic objects. This can explain the observed absence of position superpositions in macroscopic objects (lifetime is too small). It also suggests that ongoing laboratory experiments may be able to detect the finite superposition lifetime for mesoscopic objects in the near future.     

固体破坏的损伤演化诱致突变现象

固体破坏问题在理论上及实际上均极为重要，是涉及力学，物理学及非线性科学等学科的一个十分复杂基本问题，文章介绍了基于细观非线性动力学模型的研究所取得的进展，发现系统显示一种共性特征，称为演化诱致突变，即演化模式从整体稳定向灾变性模式转变，宏观破坏的样本个性行为，以及宏观性质对细观无序性的敏感性。     

A study on the inclusion of body forces in the lattice Boltzmann BGK equation to recover steady-state hydrodynamics

When the lattice Boltzmann (LB) method is used to solve hydrodynamic problems containing a body force term varying in space and/or time, its modelling at the mesoscopic scale must be verified in terms of consistency in order to avoid the appearance of non-hydrodynamic error terms at the macroscopic scale. In the present work it is shown that the modelling of spatially varying steady body force terms in the LB equation must be different from the time-dependent case, when a steady-state flow solution is sought. For that, the Chapman-Enskog analysis is used to derive the LB body force model for the LB BGK equations in a steady-state flow problem. The theoretical findings are supported by numerical tests performed on two different 2D steady-state laminar flows driven by spatially varying body forces with known analytical solutions.     

Complex fields in heterogeneous materials under shock: modeling,simulation and analysis

In this mini-review we summarize the progress of modeling, simulation and analysis of shock responses of heterogeneous materials in our group in recent years. The basic methodology is as below. We first decompose the problem into different scales. Construct/Choose a model according to the scale and main mechanisms working at that scale. Perform numerical simulations using the relatively mature schemes. The physical information is transferred between neighboring scales in such a way: The statistical information of results in smaller scale contributes to establishing the constitutive equation in larger one. Except for the microscopic Molecular Dynamics(MD) model, both the mesoscopic and macroscopic models can be further classified into two categories,solidic and fluidic models, respectively. The basic ideas and key techniques of the MD, material point method and discrete Boltzmann method are briefly reviewed. Among various schemes used in analyzing the complex fields and structures, the morphological analysis and the home-built software, GISO, are briefly introduced. New observations are summarized for scales from the larger to the smaller.     

Nonlinear and stochastic dynamics in the heart

In a normal human life span, the heart beats about 2–3 billion times. Under diseased conditions, a heart may lose its normal rhythm and degenerate suddenly into much faster and irregular rhythms, called arrhythmias, which may lead to sudden death. The transition from a normal rhythm to an arrhythmia is a transition from regular electrical wave conduction to irregular or turbulent wave conduction in the heart, and thus this medical problem is also a problem of physics and mathematics. In the last century, clinical, experimental, and theoretical studies have shown that dynamical theories play fundamental roles in understanding the mechanisms of the genesis of the normal heart rhythm as well as lethal arrhythmias. In this article, we summarize in detail the nonlinear and stochastic dynamics occurring in the heart and their links to normal cardiac functions and arrhythmias, providing a holistic view through integrating dynamics from the molecular (microscopic) scale, to the organelle (mesoscopic) scale, to the cellular, tissue, and organ (macroscopic) scales. We discuss what existing problems and challenges are waiting to be solved and how multi-scale mathematical modeling and nonlinear dynamics may be helpful for solving these problems.     

Entangling Mesoscopic Squeezed Vacuum States and Mesoscopic Coherent States in Dissipative Cavity QED System

A scheme has been proposed for generating the macroscopic entanglement between the mesoscopic squeezed vacuum states and mesoscopic coherent states by considering both the two-photon interaction and the single photon interaction of N two-level atoms in cavities with high quality factor assisted by a strong driving field. Moreover, we derive the dissipative interaction models for single photon interaction and two-photon interaction, respectively. The corresponding analytical expressions of the fidelities can be given. Our scheme can be realized in the current techniques on the cavity QED.     

A multi-scale numerical simulation of the crystallisation and temperature field of glass

There is a big difference in the spatial scale between temperature field simulation and crystallisation simulation of the glass cooling process. The temperature field belongs to the macroscopic scale, while crystallisation is on the mesoscopic scale. In this paper, a coupled algorithm for the temperature field and crystallisation calculation is established in which the macroscopic temperature simulation is based on the finite element method while the mesoscopic crystallisation simulation is based on the Monte Carlo method using the Uhlmann model. In calculations, the temperature value is regarded as the input condition of the crystallisation calculation while the results of crystallisation in the form of latent heat are used as the input conditions for the temperature calculation. The pixel method is employed to deal with the collision process of crystal grain interfaces. A corresponding numerical simulation scheme has been developed and a multi-scale simulation of glass crystallisation and the cooling temperature field has been carried out. Finally, the presented model and developed simulation scheme have been shown to be very reasonable in comparison to both numerical predictions and with previous results from the literature.     

Effect of grain boundary on the mechanical behaviors of irradiated metals: a review

The design of high irradiation-resistant materials is very important for the development of next-generation nuclear reactors. Grain boundaries acting as effective defect sinks are thought to be able to moderate the deterioration of mechanical behaviors of irradiated materials, and have drawn increasing attention in recent years. The study of the effect of grain boundaries on the mechanical behaviors of irradiated materials is a multi-scale problem. At the atomic level, grain boundaries can effectively affect the production and formation of irradiation-induced point defects in grain interiors, which leads to the change of density, size distribution and evolution of defect clusters at grain level. The change of microstructure would influence the macroscopic mechanical properties of the irradiated polycrystal. Here we give a brief review about the effect of grain boundaries on the mechanical behaviors of irradiated metals from three scales: microscopic scale, mesoscopic scale and macroscopic scale.     

Scales and kinetics of granular flows

When a granular material experiences strong forcing, as may be the case, e.g., for coal or gravel flowing down a chute or snow (or rocks) avalanching down a mountain slope, the individual grains interact by nearly instantaneous collisions, much like in the classical model of a gas. The dissipative nature of the particle collisions renders this analogy incomplete and is the source of a number of phenomena which are peculiar to "granular gases," such as clustering and collapse. In addition, the inelasticity of the collisions is the reason that granular gases, unlike atomic ones, lack temporal and spatial scale separation, a fact manifested by macroscopic mean free paths, scale dependent stresses, "macroscopic measurability" of "microscopic fluctuations" and observability of the effects of the Burnett and super-Burnett "corrections." The latter features may also exist in atomic fluids but they are observable there only under extreme conditions. Clustering, collapse and a kinetic theory for rapid flows of dilute granular systems, including a derivation of boundary conditions, are described alongside the mesoscopic properties of these systems with emphasis on the effects, theoretical conclusions and restrictions imposed by the lack of scale separation. (c) 1999 American Institute of Physics.     

剪切应变下刃型位错的滑移机理的晶体相场模拟

针对刃型位错的滑移运动, 构建包含外力场与晶格原子密度耦合作用的体系自由能密度函数, 建立剪切应变作用体系的晶体相场模型. 模拟了双相双晶体系的位错攀移和滑移运动, 计算了位错滑移的Peierls势垒和滑移速度. 结果表明: 施加较大的剪切应变率作用, 体系能量变化为单调光滑曲线, 位错以恒定速度做连续运动, 具有刚性运动特征; 剪切应变率较小时, 体系能量变化出现周期波动特征, 位错运动是处于低速不连续运动状态, 运动出现周期“颠簸”式滑移运动, 具有黏滞运动特征; 位错启动运动, 存在临界的势垒. 位错启动攀移运动的Peierls势垒要比启动滑移Peierls势垒大几倍. 位错攀移和滑移运动特征与实验结果相符合.     

Heterogeneous anisotropic complex structure gradual model and constitutive relation

Four new gradually delaminate models of the three-dimensional macro-/mesoscopic structure and delamination of the heterogeneous anisotropic composite (HAC) are set up by conducting research into its structure and performance. A general theory, which demonstrates the three-dimensional constitutive relation of the macro-/mesoscopic performance of this structure is further developed. The macroscopic expression of HAC is presented in terms of a Tanigawa delaminate homogeneous equivalent approach, the mesoscopic problems are analysed utilizing Eshelby－Mori－Tanaka theory, with the introduction of the representative volume elements of monolayer single unit cell and interlaminar double unit cells. According to the gradual continuity of the structure as a whole, great attention is given to the modelling and research of the interlaminar macroscopic and mesoscopic problems of HAC structure. Comparison with the existing solutions is made through calculation of typical cases.     

Free energy self-averaging in protein-sized random heteropolymers

Current theories of heteropolymers are inherently macroscopic, but are applied to mesoscopic proteins. To compute the free energy over sequences, one assumes self-averaging--a property established only in the macroscopic limit. By enumerating the states and energies of compact 18, 27, and 36mers on a lattice with an ensemble of random sequences, we test the self-averaging approximation. We find that fluctuations in the free energy between sequences are weak, and that self-averaging is valid at the scale of real proteins. The results validate sequence design methods which exponentially speed up computational design and simplify experimental realizations.     

Wetting of He on rough cesium substrates

We discuss the behaviour of ⁴He meniscus on various disordered Cs substrates. We have first studied the dynamics of the contact line on Cs substrates evaporated at low temperature. The activated motion of the line is consistent with a substrate disorder of mesoscopic length scale. We have performed further studies of the contact line behaviour on substrates with roughness of macroscopic length scale. Close to the wetting transition, we find that a film invades the substrate leading to marked changes in the value of the contact angle.     

Quantum point contacts as heat engines

The efficiency of macroscopic heat engines is restricted by the second law of thermodynamics. They can reach at most the efficiency of a Carnot engine. In contrast, heat currents in mesoscopic heat engines show fluctuations. Thus, there is a small probability that a mesoscopic heat engine exceeds Carnot's maximum value during a short measurement time. We illustrate this effect using a quantum point contact as a heat engine. When a temperature difference is applied to a quantum point contact, the system may be utilized as a source of electrical power under steady state conditions. We first discuss the optimal working point of such a heat engine that maximizes the generated electrical power and subsequently calculate the statistics for deviations of the efficiency from its most likely value. We find that deviations surpassing the Carnot limit are possible, but unlikely.     

Demonstrating mesoscopic superpositions in double-well Bose-Einstein condensates

The availability of Bose-Einstein condensates as mesoscopic or macroscopic quantum objects has aroused new interest in the possibility of making and detecting coherent superpositions involving many atoms. We consider the important problem of distinguishing whether a coherent superposition or a statistical mixture is generated by a given experimental procedure, using the specific example of a double-well condensate. In this system, such a superposition state can be generated by using a Feshbach resonance to tune the inter-atomic interactions. We find that unambiguously distinguishing even a perfect ‘NOON’ state from a statistical mixture using standard detection methods will present experimental difficulties.