BEC from a time-dependent variational point of view

We use the time-dependent variational principle of Balian and Vénéroni to derive a set of equations governing the dynamics of a trapped Bose gas at finite temperature. We show that this dynamics generalizes the Gross-Pitaevskii equations in that it introduces a consistent dynamical coupling between the evolution of the condensate density, the thermal cloud, and the “anomalous” density.     

On the Propagation of a Perturbation in an Anharmonic System

We give a not trivial upper bound on the velocity of disturbances in an infinitely extended anharmonic system at thermal equilibrium. The proof is achieved by combining a control on the non equilibrium dynamics with an explicit use of the state invariance with respect to the time evolution.     

Dynamical deformations of the electron density in an H2 molecule under strong,oscillating magnetic fields: an application of time-dependent quantum fluid density functional theory

Following the time-dependent quantum fluid density functional theory developed in our laboratory, the present quantum-mechanical, dynamical study of the H₂ molecule under strong, oscillating magnetic fields reveals a coexistence of both slow and fast dynamics, as seen earlier in the cases of hydrogen and helium atoms. Using the Deb–Chattaraj equation of motion we find that, contrary to the situation with static magnetic fields, the electron density now transiently expands. Consequently, the fate of the H–H bond under such strong TD magnetic fields has been addressed through detailed and accurate TD density profiles computed by direct numerical solution of the real-time evolution equation. A detailed interpretation of the slow dynamics has been made.     

Ultrasoft colloids in cavities of oscillating size or sharpness

We employ dynamical density functional theory (DDFT) and Brownian Dynamics (BD) simulations to examine the fully developed dynamics of ultrasoft colloids interacting via a Gaussian pair potential in time-dependent external fields. The DDFT formalism employed is that of Marconi and Tarazona [J. Chem. Phys., 110, 8032 (1999)], which allows for determination of the time-dependent density profile based on knowledge of the static, equilibrium density functional. Three different dynamical situations are examined: firstly, the behaviour of Gaussian particles in a spherical cavity of oscillating size, including both sudden and continuous changes in the size of the cavity. Secondly, a spherical cavity with a fixed size but varying sharpness. Finally, to investigate a strong inhomogeneity in the density profile we study the diffusion of one layer of particles which is initially strongly confined and separated from the remaining system via an external potential. In all cases, DDFT is in excellent agreement with BD results, demonstrating the applicability of the theory to dynamical problems involving overdamped interacting particles in a solvent.     

固体炸药爆轰的一种考虑热学非平衡的反应流动模型

基于固体炸药爆轰过程中化学反应混合区内的固相反应物与气相生成物处于力学平衡状态及热学非平衡状态的事实,提出一种考虑热学非平衡效应的反应流动模型来描述固体炸药的爆轰流动现象.该爆轰流动模型的主要特点是,在反应混合物Euler方程和固相反应物质量守恒方程的基础上,通过附加一套关于固相反应物的组分物理量的流动控制方程来表达固相反应物与气相生成物之间的热学非平衡效应.根据反应混合区内固相反应物与气相生成物这两种化学组分保持各自内能守恒的混合规则,并借助它们具有压力相等的性质以及满足体积分数总和为1的条件,推导获得的附加方程有：固相反应物的内能演化方程、体积分数演化方程及反应混合物的压力演化方程.这样,建立的爆轰模型包括：反应混合物的质量守恒方程、动量守恒方程、总能量守恒方程、压力演化方程,以及固相反应物的质量守恒方程、内能演化方程、体积分数演化方程.对所获得的爆轰模型方程组采用一个时空二阶精度的有限体积法进行数值求解,典型爆轰问题算例结果表明本文提出的固体炸药爆轰模型是合理的.     

Mesoscopic approach to inviscid gas dynamics with thermal lag

A phenomenological model for thermal relaxation and wave propagation in ideal polyatomic gases is developed by introducing a dynamical non‐equilibrium temperature. The system of equations governing the evolution of the gas is derived and the speeds of propagation of thermo‐mechanical disturbances together with the Rankine‐Hugoniot jump conditions for shock waves are calculated. The hyperbolic theories of heat propagation in incompressible fluids and rigid solids are recovered as particular cases. For rigid solids, the well posedness of the Cauchy problem is proved by a classical method.     

Equilibration,Generalized Equipartition,and Diffusion in Dynamical Lorentz Gases

We demonstrate approach to thermal equilibrium in the fully Hamiltonian evolution of a dynamical Lorentz gas, by which we mean an ensemble of particles moving through a d-dimensional array of fixed soft scatterers that each possess an internal harmonic or anharmonic degree of freedom to which moving particles locally couple. We analytically predict, and numerically confirm, that the momentum distribution of the moving particles approaches a Maxwell-Boltzmann distribution at a certain temperature T, provided that they are initially fast and the scatterers are in a sufficiently energetic but otherwise arbitrary stationary state of their free dynamics—they need not be in a state of thermal equilibrium. The temperature T to which the particles equilibrate obeys a generalized equipartition relation, in which the associated thermal energy k _B T is equal to an appropriately defined average of the scatterers’ kinetic energy. In the equilibrated state, particle motion is diffusive.     

Phenomenology and theory of horizontally oscillated granular mixtures

We overview the physics of a granular mixture subject to horizontal oscillations, recently investigated via experiments and molecular dynamics simulations. First we discuss the rich phenomenology exhibited by this system, which encompasses both segregation and dynamical instabilities. Then we show that the phenomenology can be explained via an effective interaction approach, by which the driven, non-thermal, granular mixture in mapped into a monodispersed thermal system of particles interacting via an effective potential. After determining the effective interaction we discuss its microscopic origin and investigate how it induces the observed phenomenology. Finally, as much as in thermal fluids, from the effective interaction we derive a Cahn-Hilliard dynamics equation, which appears to capture the essential characteristics of the dynamics of the granular mixture.     

Dynamical density functional theory for colloidal dispersions including hydrodynamic interactions

A dynamical density functional theory (DDFT) for translational Brownian dynamics is derived which includes hydrodynamic interactions. The theory reduces to the simple Brownian DDFT proposed by Marconi and Tarazona (U. Marini Bettolo Marconi and P. Tarazona, J. Chem. Phys. 110, 8032 (1999); J. Phys.: Condens. Matter 12, A413 (2000)) when hydrodynamic interactions are neglected. The derivation is based on Smoluchowski’s equation for the time evolution of the probability density with pairwise hydrodynamic interactions. The theory is applied to hard-sphere colloids in an oscillating spherical optical trap which switches periodically in time from a stable confining to an unstable potential. Rosenfeld’s fundamental measure theory for the equilibrium density functional is used and hydrodynamics are incorporated on the Rotne-Prager level. The results for the time-dependent density profiles are compared to extensive Brownian dynamics simulations which are performed on the same Rotne-Prager level and excellent agreement is obtained. It is further found that hydrodynamic interactions damp and slow the dynamics of the confined colloid cluster in comparison to the same situation with neglected hydrodynamic interactions.     

TiO2/ZnO纳米薄膜界面热导率的分子动力学模拟

采用平衡分子动力学方法及Buckingham势研究了金红石型TiO₂薄膜与闪锌矿型ZnO薄膜构筑的纳米薄膜界面沿晶面[0001](z轴方向)的热导率.通过优化分子模拟初始条件中的截断半径r_c和时间步后,计算并分析了平衡温度、薄膜厚度、薄膜截面大小对热导率的影响.研究表明,薄膜热导率受薄膜温度和厚度的影响很大,当温度由300 K升高600 K时,薄膜的热导率逐渐减小;当薄膜厚度由1.8 nm增大到5 nm时,热导率会逐渐增大;并在此基础 关键词： 热导率 分子动力学 2/ZnO纳米薄膜界面')" href="#">TiO₂/ZnO纳米薄膜界面 数值模拟     

Renormalized Kinetic Theory of Classical Fluids in and out of Equilibrium

We present a theory for the construction of renormalized kinetic equations to describe the dynamics of classical systems of particles in or out of equilibrium. A closed, self-consistent set of evolution equations is derived for the single-particle phase-space distribution function f, the correlation function C=〈δfδf〉, the retarded and advanced density response functions χ ^R,A =δf/δφ to an external potential φ, and the associated memory functions Σ ^R,A,C . The basis of the theory is an effective action functional Ω of external potentials φ that contains all information about the dynamical properties of the system. In particular, its functional derivatives generate successively the single-particle phase-space density f and all the correlation and density response functions, which are coupled through an infinite hierarchy of evolution equations. Traditional renormalization techniques (involving Legendre transform and vertex functions) are then used to perform the closure of the hierarchy through memory functions. The latter satisfy functional equations that can be used to devise systematic approximations that automatically imply the conservation laws of mass, momentum and energy. The present formulation can be equally regarded as (i) a generalization to dynamical problems of the density functional theory of fluids in equilibrium and (ii) as the classical mechanical counterpart of the theory of non-equilibrium Green’s functions in quantum field theory. It unifies and encompasses previous results for classical Hamiltonian systems with any initial conditions. For equilibrium states, the theory reduces to the equilibrium memory function approach used in the kinetic theory of fluids in thermal equilibrium. For non-equilibrium fluids, popular closures of the BBGKY hierarchy (e.g. Landau, Boltzmann, Lenard-Balescu-Guernsey) are simply recovered and we discuss the correspondence with the seminal approaches of Martin-Siggia-Rose and of Rose and we discuss the correspondence with the seminal approaches of Martin-Siggia-Rose and of Rose.     

不同初始温度下H2/O2混合物等离子体的演化

本文对不同初始温度下,H₂/O₂混合物等离子体中主要粒子随时间发展的演化规律进行了数值模拟,得到了放电后等离子体中主要带电粒子和中性粒子密度随时间的变化规律.计算结果表明,H₂/O₂混合物等离子体中主要活性粒子密度随时间的增加减小,化学反应达到平衡所需的时间随初始温度升高逐渐减少. 关键词： 等离子体 化学过程 数值模拟 演化     

不同初始温度下H2/O2混合物等离子体的演化

本文对不同初始温度下,H₂/O₂混合物等离子体中主要粒子随时间发展的演化规律进行了数值模拟,得到了放电后等离子体中主要带电粒子和中性粒子密度随时间的变化规律.计算结果表明,H₂/O₂混合物等离子体中主要活性粒子密度随时间的增加减小,化学反应达到平衡所需的时间随初始温度升高逐渐减少.     

Evaporating droplets in turbulent reacting flows

Three-dimensional direct numerical simulations are carried out to determine the effects of turbulence on the preferential segregation of an evaporating spray and then to study the evolution of the resulting mixture fraction topology and propagating flame. First, the mixing between an initially randomly dispersed phase and the turbulent gaseous carrier phase is studied with non-evaporating particles. According to their inertia and the turbulence properties, the formation of clusters of particles is analyzed (formation delay, cluster characteristic size and density). Once the particles are in dynamical equilibrium with the surrounding turbulent flow, evaporation is considered through the analysis of the mixture fraction evolution. Finally, to mimic ignition, a kernel of burnt gases is generated at the center of the domain and the turbulent flame evolution is described.     

三角波加载下金属铝动态破坏现象的微观模拟

采用嵌入原子势模型和分子动力学方法, 模拟研究了三角波加载下金属铝动态破坏的微观过程和动力学性质. 根据原子中心对称参数变化给出了样品微结构演化过程, 解读了熔化前后破坏过程的形态差异; 基于Virial定理统计了样品中压力和温度等力学量波形, 分析了熔化前后材料的强度变化. 通过不同碰撞速度的模拟, 讨论了破碎区内物质形态和密度分布的变化, 给出了材料破坏深度的变化规律. 研究还发现, 熔化后材料的动态拉伸强度已显著降低, 而此时由声学近似推算的材料拉伸强度已明显高于内部应力直接计算结果. 关键词： 破坏 分子动力学 冲击     

Slow relaxation in microcanonical warming of a Ising lattice

We study the warming process of a semi-infinite cylindrical Ising lattice initially ordered and coupled at the boundary to a heat reservoir. The adoption of a proper microcanonical dynamics allows a detailed study of the time evolution of the system. As expected, thermal propagation displays a diffusive character and the spatial correlations decay exponentially in the direction orthogonal to the heat flow. However, we show that the approach to equilibrium presents an unexpected slow behavior. In particular, when the thermostat is at infinite temperature, correlations decay to their asymptotic values by a power law. This can be rephrased in terms of a correlation length vanishing logarithmically with time. At finite temperature, the approach to equilibrium is also a power law, but the exponents depend on the temperature in a non-trivial way. This complex behavior could be explained in terms of two dynamical regimes characterizing finite and infinite temperatures, respectively. When finite sizes are considered, we evidence the emergence of a much more rapid equilibration, and this confirms that the microcanonical dynamics can be successfully applied on finite structures. Indeed, the slowness exhibited by correlations in approaching the asymptotic values are expected to be related to the presence of an unsteady heat flow in an infinite system.     

Thermalization in Harmonic Particle Chains with Velocity Flips

We propose a new mathematical tool for the study of transport properties of models for lattice vibrations in crystalline solids. By replication of dynamical degrees of freedom, we aim at a new dynamical system where the “local” dynamics can be isolated and solved independently from the “global” evolution. The replication procedure is very generic but not unique as it depends on how the original dynamics are split between the local and global dynamics. As an explicit example, we apply the scheme to study thermalization of the pinned harmonic chain with velocity flips. We improve on the previous results about this system by showing that after a relatively short time period the average kinetic temperature profile satisfies the dynamic Fourier’s law in a local microscopic sense without assuming that the initial data is close to a local equilibrium state. The bounds derived here prove that the above thermalization period is at most of the order $L^{2/3}$ , where $L$ denotes the number of particles in the chain. In particular, even before the diffusive time scale Fourier’s law becomes a valid approximation of the evolution of the kinetic temperature profile. As a second application of the dynamic replica method, we also briefly consider replacing the velocity flips by an anharmonic onsite potential.     

汽液界面动力学行为与热力学性质的分子动力学研究

本文采用分子动力学方法研究了热平衡条件下的汽液界面的动力学行为和热力学性质。统计获得了界面区的密度、压力张量及温度的分布,并且从分子层次观察分析了界面结构和动力学特性。研究表明汽液界面是一个随时间起伏涨落的曲面,界面层的分子并不是处于液相和蒸汽相之间的一种过渡状态,从汽相到液相密度的连续变化是长时间的统计结果,汽渡过渡区的厚度与汽液界面区的密度涨落的范围是一致的。对于平衡条件下的汽液界面,由于汽液相变的影响,在紧贴界面处存在一个分子平均动能非平衡分布的区域。此非平衡区域的存在与汽液两相的宏观热平衡并不矛盾,但可能对蒸发／凝结流率的估计有不可忽略的影响。     

The sphericalp-spin interaction spin-glass model

The relaxational dynamics for local spin autocorrelations of the sphericalp-spin interaction spin-glass model is studied in the mean field limit. In the high temperature and high external field regime, the dynamics is ergodic and similar to the behaviour in known liquid-glass transition models. In the static limit, we recover the replica symmetric solution for the long time correlation. This phase becomes unstable on a critical line in the (T, h) plane, where critical slowing down is observed with a cross-over to power law decay of the correlation function ∝t ^?ν, with an exponent ν varying along the critical line. For low temperatures and low fields, ergodicity in phase space is broken. For small fields the transition is discontinuous, and approaching this transition from above, two long time scales are seen to emerge. This dynamical transition lies at a somewhat higher temperature than the one obtained within replica theory. For larger fields the transition becomes continuous at some tricritical point. The low temperature phase with broken ergodicity is studied within a modified equilibrium theory and alternatively for adiabatic cooling across the transition line. This latter scheme yields rather detailed insight into the formation and structure of the ergodic components.