Implicit velocity correction-based immersed boundary-lattice Boltzmann method and its applications

A version of immersed boundary-lattice Boltzmann method (IB-LBM) is proposed in this work. It is based on the lattice Boltzmann equation with external forcing term proposed by Guo et al. [Z. Guo, C. Zheng, B. Shi, Discrete lattice effects on the forcing term in the lattice Boltzmann method, Phys. Rev. E 65 (2002) 046308], which can well consider the effect of external force to the momentum and momentum flux as well as the discrete lattice effect. In this model, the velocity is contributed by two parts. One is from the density distribution function and can be termed as intermediate velocity, and the other is from the external force and can be considered as velocity correction. In the conventional IB-LBM, the force density (external force) is explicitly computed in advance. As a result, we cannot manipulate the velocity correction to enforce the non-slip boundary condition at the boundary point. In the present work, the velocity corrections (force density) at all boundary points are considered as unknowns which are computed in such a way that the non-slip boundary condition at the boundary points is enforced. The solution procedure of present IB-LBM is exactly the same as the conventional IB-LBM except that the non-slip boundary condition can be satisfied in the present model while it is only approximately satisfied in the conventional model. Numerical experiments for the flows around a circular cylinder and an airfoil show that there is no any penetration of streamlines to the solid body in the present results. This is not the case for the results obtained by the conventional IB-LBM. Another advantage of the present method is its simple calculation of force on the boundary. The force can be directly calculated from the relationship between the velocity correction and the force density.     

变像管相机中空间电荷效应的统计动力学分析

 从Boltzmann积分微分方程出发推出了保守势场中电子数密度按势能的分布规律,即Boltzmann统计分布。以此为基础,从统计动力学的角度详细分析了变像管相机中超短电子脉冲内部的空间电荷效应,通过求解Poisson方程得出了表征空间电荷效应的两个特征参量：空间电荷密度分布函数和速度分布函数,并对其按电位的动态变化规律进行了定性讨论。结果表明,限制变像管中的低电位区域和其中光电子脉冲从高电位向低电位传输的区域都将有助于优化整个变像管的性能。同时也重新讨论了光电阴极附近强加速场对光电子脉冲时间弥散的抑制作用,最终确定了其物理机制为不等位区间中电子脉冲空间分布的高度集中性。     

Boltzmann Limit for a Homogeneous Fermi Gas with Dynamical Hartree-Fock Interactions in a Random Medium

We study the dynamics of the thermal momentum distribution function for an interacting, homogeneous Fermi gas on ℤ³ in the presence of an external weak static random potential, where the pair interactions between the fermions are modeled in dynamical Hartree-Fock theory. We determine the Boltzmann limits associated to different scaling regimes defined by the size of the random potential, and the strength of the fermion interactions.     

One-Dimensional Steady Transport by Molecular Dynamics Simulation：Non-Boltzmann Position Distribution and Non-Arrhenius Dynamical Behavior

A non-equilibrium steady state can be characterized by a nonzero but stationary flux driven by a static external force. Under a weak external force, the drift velocity is difficult to detect because the drift motion is feeble and submerged in the intense thermal diffusion. In this article, we employ an accurate method in molecular dynamics simulation to determine the drift velocity of a particle driven by a weak external force in a one-dimensional periodic potential. With the calculated drift velocity, we found that the mobility and diffusion of the particle obey the Einstein relation, whereas their temperature dependences deviate from the Arrhenius law. A microscopic hopping mechanism was proposed to explain the non-Arrhenius behavior. Moreover, the position distribution of the particle in the potential well was found to deviate from the Boltzmann equation in a non-equilibrium steady state. The non-Boltzmann behavior may be attributed to the thermostat which introduces an effective "viscous" drag opposite to the drift direction of the particle.     

Screened electrostatic interactions between clay platelets

An effective pair potential for systems of uniformly charged lamellar colloids in the presence of an electrolytic solution of microscopic co- and counterions is derived. The charge distribution on the discs is expressed as a collection of multipole moments, and the tensors which determine the interactions between these multipoles are derived from a screened Coulomb potential. Unlike previous theoretical studies of such systems, the interaction energy may now be expressed for discs at arbitrary mutual orientation. The potential is shown to be exactly equivalent to the use of linearized Poisson–Boltzmann theory.     

Optimal Decay Estimates on the Linearized Boltzmann Equation with Time Dependent Force and their Applications

Although the decay in time estimates of the semi-group generated by the linearized Boltzmann operator without forcing have been well established, there is no corresponding result for the case with general external force. This paper is mainly concerned with the optimal decay estimates on the solution operator in some weighted Sobolev spaces for the linearized Boltzmann equation with a time dependent external force. No time decay assumption is made on the force. The proof is based on both the energy method through the macro-micro decomposition and the L ^p -L ^q estimates from the spectral analysis. The decay estimates thus obtained are applied to the study on the global existence of the Cauchy problem to the nonlinear Boltzmann equation with time dependent external force and source. Precisely, for space dimension n ≥ 3, the global existence and decay rates of solutions to the Cauchy problem are obtained under the condition that the force and source decay in time with some rates. This time decay restriction can be removed for space dimension n ≥ 5. Moreover, the existence and asymptotic stability of the time periodic solution are given for space dimension n ≥ 5 when the force and source are time periodic with the same period.     

用格子Boltzmann模型模拟非等温流场

根据微观和宏观之间的质量、动量、能量守恒准则和在原格子Boltzmann模型基础上,建立了几个新的格子Boltzmann模型,使得在外力场中的格子Boltzmann模型得到进一步完善.通过还原宏观流体力学方程,捕捉到了浮力强迫系数与Grashof数之间的关系.所得动量方程和Navier Stokes方程相比,在黏性输运项上有明显的改进,说明黏性应力不但与流体的速度梯度和流体的压缩性有关,而且还与非定常的内能梯度和动量通量有关.该模型对非等温流场的数值结果证明了其具有很好的数值稳定性和适用性. 关键词： Boltzmann模型 平衡分布函数 流体力学方程     

Generation of VUV radiation in Lyman and Werner bands of pulsed space discharge in hydrogen mixtures with helium

A self-consistent numerical model for the self-sustained high-current pulsed discharge is constructed based on the solution of the equations of the population of H₂ electronic and vibrational states. The model accounts for electronic, ion-molecular, and vibrational kinetics, electron attachment to and detachment from the H₂ molecule, Lyman and Werner band emission, and their radiation trapping. The equations of electron-vibrational kinetics are solved simultaneously with the Boltzmann equation for the electron energy distribution function and the external electrical circuit equations.     

Analysis of energy distribution in a loaded quantum anharmonic oscillator in a wide temperature range

Analysis of the energy distribution in an ensemble of quantum anharmonic oscillators loaded by an external force in a wide temperature range (from T = 0) is carried out using a general approach based on the virial theorem. At T = 0, anharmonic effects are observed: a linear variation of zero-point energy of an oscillator under loading (energy decrease during extension and increase under compression) and a linear variation of the average kinetic and potential energy components. At high temperatures, at which the dynamics of the oscillators becomes classical, the anharmonic effects are manifested in a linear variation in the vibrational energy and a linear variation in the average kinetic and potential energy components upon an increase in force. Mutually compensating variation in the average kinetic and potential energy components of the internal dynamic energy of an oscillator (energy redistribution upon loading) takes place both at low and high temperatures.     

梯度磁场下磁流体三维结构的格子-Boltzmann方法模拟

考虑磁性颗粒受到的各种内力与外力包括重力、布朗力、van der、Waaks力、磁偶极-偶极作用力以及外磁场作用力,建立了描述磁流体结构的两相格子-Boltzmann三维模型,对外加梯度磁场条件下磁流体的介观结构进行了模拟.模拟结果表明:外加梯度磁场时磁流体粒子沿梯度方向聚集并出现分层现象,且随时间推移和外加磁场增大,分层现象越来越明显.     

磁流体结构的Lattice-Boltzmann方法模拟

本文运用Lattice-Boltzmann(LB)方法建立了宏观静止磁流体模型,提出磁性聚集体概念,充分考虑了磁性颗粒受到的各种内力与外力包括重力、布朗力、vanderWaals相互作用及静磁相互作用,对无外加磁场及外加竖直均匀磁场时磁流体的结构进行了模拟,并分析了磁能与热能之比对磁流体系统中粒子分布形态的影响。模拟结果表明:无外加磁场时磁流体结构易失去稳定性,外加均匀磁场时磁流体粒子沿外磁场方向排列,随着磁热能比例的增大,外磁场对粒子分布的影响逐渐明显。     

Global Existence of Classical Solutions to the Vlasov-Poisson-Boltzmann System

The time evolution of the distribution function for the charged particles in a dilute gas is governed by the Vlasov–Poisson–Boltzmann system when the force is self-induced and its potential function satisfies the Poisson equation. In this paper, we give a satisfactory global existence theory of classical solutions to this system when the initial data is a small perturbation of a global Maxwellian. Moreover, the convergence rate in time to the global Maxwellian is also obtained through the energy method. The proof is based on the theory of compressible Navier–Stokes equations with forcing and the decomposition of the solutions to the Boltzmann equation with respect to the local Maxwellian introduced in [23] and elaborated in [31].     

Inertial microfluidics with multi-particle collision dynamics

Using the method of multi-particle collision dynamics (MPCD), we investigate inertial focussing in microfluidic channels that gives rise to the Segré-Silberberg effect. At intermediate Reynolds numbers, we model the motion of a spherical colloid in a circular microchannel under pressure-driven flow. We determine the radial distribution function and show how its width and the location of its maximum are strongly influenced by the colloid size and the Reynolds number of the Poiseuille flow. We demonstrate that MPCD is well suited for calculating mean values for the lift force acting on the colloid in the cross-sectional plane and for its mean axial velocity. We introduce a Langevin equation for the cross-sectional motion whose steady state is the Boltzmann distribution that contains the integrated lift force as potential energy. It perfectly coincides with the simulated radial distribution function.     

FFT-LB Modeling of Thermal Liquid-Vapor System

We present an improved lattice Boltzmann(LB) model for thermal liquid-vapor system.In the new model,the Windowed Fast Fourier Transform(WFFT) and its inverse are used to calculate both the convection term and the external force term of the LB equation.By adopting the WFFT scheme,Gibbs oscillations can be damped effectively in unsmooth regions while high resolution feature of the spectral method can be retained in smooth regions.As a result,spatial discretization errors are dramatically decreased,conservation of the total energy is much better preserved,and the spurious velocities near the liquid-vapor interface are significantly reduced.The high resolution,together with the low complexity of the WFFT approach,endows the proposed method with considerable potential for studying a wide class of problems in the field of multiphase flows.     

Potential energy,force distribution and oscillatory motion of chloride ion inside electrically charged carbon nanotubes

In this research, a continuum-based model is presented to explore potential energy, force distribution and oscillatory motion of ions, and in particular chloride ion, inside carbon nanotubes (CNTs) decorated by functional groups at two ends. To perform this, van der Waals (vdW) interactions between ion and nanotube are modeled by the 6-12 Lennard-Jones (LJ) potential, whereas the electrostatic interactions between ion and functional groups are modeled by the Coulomb potential and the total interactions are analytically derived by summing the vdW and electrostatic interactions. Making the assumption that carbon atoms and charge of functional groups are all uniformly distributed over the nanotube surface and the two ends of nanotube, respectively, a continuum approach is utilized to evaluate the related interactions. Based on the actual force distribution, the equation of motion is also solved numerically to arrive at the time history of displacement and velocity of inner core. With respect to the proposed formulations, comprehensive studies on the variations of potential energy and force distribution are carried out by varying functional group charge and nanotube length. Moreover, the effects of these parameters together with initial conditions on the oscillatory behavior of system are studied and discussed in detail. It is found out that chloride ion escapes more easily from negatively charged CNTs which is followed by uncharged and positively charged ones. It is further shown that the presence of functional groups leads to enhancing the operating frequency of such oscillatory systems especially when the electric charges of ion and functional groups have different signs.     

Surface-tension-confined droplet microfluidics

This article is a concise overview about the developing microfluidic systems named surface-tension-confined droplet microfluidics(STORMs). Different from traditional complexed droplet microfluidics which generated and confined the droplets by three-dimensional(3D) poly(dimethylsiloxane)-based microchannels, STORM systems provide twodimensional(2D) platforms for control of droplets. STORM devices utilize surface energy, with methods such as surface chemical modification and mechanical processing, to control the movement of fluid droplets. Various STORM devices have been readily prepared, with distinct advantages over conventional droplet microfluidics, which generated and confined the droplets by 3D poly(dimethylsiloxane)-based microchannels, such as significant reduction of energy consumption necessary for device operation, facile or even direct introduction of droplets onto patterned surface without external driving force such as a micropump, thus increased frequency or efficiency of droplets generation of specific STORM device, among others. Thus, STORM devices can be excellent alternatives for majority areas in droplet microfluidics and irreplaceable choices in certain fields by contrast. In this review, fabrication methods or strategies, manipulation methods or mechanisms,and main applications of STORM devices are introduced.     

Conservative force fields in non-Gaussian statistics

In this Letter, we determine the κ-distribution function for a gas in the presence of an external field of force described by a potential U(r). In the case of a dilute gas, we show that the κ-power law distribution including the potential energy factor term can rigorously be deduced in the framework of kinetic theory with basis on the Vlasov equation. Such a result is significant as a preliminary to the discussion on the role of long range interactions in the Kaniadakis thermostatistics and the underlying kinetic theory.