Approach to field-induced stationary state in a gas of hard rods

The Boltzmann equation describing one-dimensional motion of a charged hard rod in a neutral hard rod gas at temperatureT = 0 is solved. Under the action of a constant and uniform field the charged particle attains a stationary state. In the long time limit the velocity autocorrelation function decays via damped oscillations. In the reference system moving with the mean particle velocity the decay of fluctuations in the position space is governed (in the hydrodynamic limit) by the diffusion equation. Both the stationary current and the diffusion coefficient are proportional to the square root of the field. It is conjectured that this result also holds forT > 0 in a strong field limit.On leave from the Institute of Theoretical Physics, University of Warsaw, Hoza 69, 00-081 Warsaw, Poland.     

Field induced motion of a test particle in a hard rod fluid

The motion of a charged test particle in a hard rod fluid is studied within Boltzmann's kinetic theory. The external field is supposed to be uniform and constant. In the case where the host fluid particles move isotropically with a fixed speed the problem can be exactly solved. The stationary velocity distribution is derived. It is shown that the drift velocity varies linearly with the field in the weak field limit and becomes proportional to the square root of the field for strong fields.     

The pressure of a hard sphere fluid on a curved surface

Utilizing the integral equation approach to the hard sphere fluid system developed in the preceding paper, the hard sphere-hard wall interaction is studied. For the case of a flat wall, perturbation solutions of the integral equation valid to second and third order in the packing fraction,y, are derived. For a surface of arbitrary curvature, an equation of state valid to second order in the packing fraction is also derived. When applied to very small cavities, it is found that the pressure at high densities is significantly higher than it would be for a flat wall.     

Monte Carlo simulation of a confined hard ellipse fluid

The structural and thermodynamic properties of a confined hard ellipse fluid are studied using Monte Carlo simulation. The angular, average number densities and order parameters of hard ellipses confined between hard parallel walls are obtained for various bulk densities, aspect ratios and wall separations. The results show that the effect of the existence of the wall on the molecular fluid structure, either on their directions or their locations, with respect to the bulk, especially close to the walls, is significant. For this system the pressure is also obtained and it is shown that the average density at the wall is proportional to the pressure, βP=〈ρ_w〉. Our simulation results show that the order parameters depend on the number of the particles in the box unless it exceeds thousand.     

Integral equation theory of a one dimensional hard-ellipse fluid between hard walls

Density functional theory is used to study the structure of a one dimensional fluid model of hard-ellipse molecules with their axes freely rotating in a plane, confined between hard walls. A simple Hypernetted chain (HNC) approximation is used for the density functional of the fluid and the integral equation for the density is obtained from the grand potential. The only required input is the direct correlation function of the one dimensional hard-ellipse fluid. For this model, the pressure, sum rule and the density at the walls are obtained. The Percus Yevick (PY), for lower density, and HNC, for higher density, integral equations are also solved to obtain the direct correlation function of hard-ellipse model introduced here. We obtain the average density at the wall as well as the radial density profile. We compare these with Monte Carlo simulations of the same model and find reasonable agreement.     

黏性流体中超细长弹性杆的动力学不稳定性

基于坐标基矢摄动的方法研究了黏性流体中超细长弹性杆动力学稳定性判据与失稳后的模态选择,推导出了黏性介质中超细长弹性杆Kirchoff动力学方程的一阶摄动表示,即线性的二阶偏微分方程组.以平面扭转DNA环为例,说明了以上结果的应用,得到了平面扭转DNA环的稳定性判据及其稳定的临界区域,讨论了其失稳后的模态选择及黏性阻力对其的影响.     

A new integral equation for the radial distribution function of a hard sphere fluid

Based on a proposal by Shinomoto, a new integral equation is derived for the radial distribution function of a hard-sphere fluid using mainly geometric arguments. This integral equation is solved by a perturbation expansion in the density of the fluid, and the results obtained are compared with those from molecular dynamics simulations and from the Born-Green-Yvon (BGY) and Percus-Yevick (PY) theories. The present theory provides results for the radial distribution function which are intermediate in accuracy between those obtained from the BGY and from the PY theories.     

The optical phonon effect of quantum rod qubits

The Hamiltonian of a quantum rod with an ellipsoidal boundary is given by using a coordinate transformation in which the ellipsoidal boundary is changed into a spherical one.Under the condition of strong electron-longitudinal optical phonon coupling in the rod,we obtain both the electron eigenfunctions and the eigenenergies of the ground and first-excited state by using the Pekar-type variational method.This quantum rod system may be used as a two-level qubit.When the electron is in the superposition state of the ground and first-excited states,the probability density of the electron oscillates in the rod with a certain period.It is found that the oscillation period is an increasing function of the ellipsoid aspect ratio and the transverse and longitudinal effective confinement lengths of the quantum rod,whereas it is a decreasing function of the electron-phonon coupling strength.     

Thermodynamic properties of molecular fluid mixtures of hard ellipsoids

Thermodynamic properties of molecular fluid mixtures of hard ellipsoids are calculated. Numerical results are given for equation of state and excess-free energy of the binary mixture of both additive and non-additive hard ellipsoids. It is found that the equation of state and free energy of mixtures increase with increase of anisotropy parameterx ₀.     

Equations of state for the hard disk fluids

By using the published accurate new virial coefficients B₁₁～B₁₄ for the hard disk fluids [C. Zhang and B.M. Pettitt, Mol. Phys., 2014, 112, 1427], we here propose a new updated version of Tian-Gui-Mulero equation of state [J.X. Tian, Y.X. Gui and A. Mulero, Phys. Chem. Chem. Phys., 2010, 12, 13597]. Compared with other proposals, the new version stands strongly to be the only which can reproduce the known virial coefficients B₂～B₁₃ at the same time that can describe the relation of the compressibility factor versus the packing fraction for the hard disk fluids with high accuracy.     

与质点连结的弹性杆的振动

用Laplace变换法求解了一端固定、一端与质点连结的弹性杆的振动问题,并详细讨论了几种极限情况下的运动图像,Laplace变换法对于同类问题普遍有效,而且不需要用到关于本征函数的完备性或(广义)正交性的定理。     

Dynamics of a charged particle in a progressive plane wave

The dynamics of a charged particle in a relativistic strong electromagnetic plane wave propagating in a medium is studied. The problem is shown to be integrable when the wave propagates in vacuum. When it propagates in plasma, and when the full plasma response is considered, an exhaustive numerical work allows us to conclude that the problem is not integrable.     

Dynamics of a charged particle bunch in a penning trap

The Lagrangean equations for gas dynamics of a spherical bunch of charged particles in a Penning trap are solved. The solution describes the pulsation of an inhomogeneous particle bunch whose center behaves as a spatial oscillator in a coordinate system rotating with the Larmor frequency.     

与质点连接的杆横振动的频率特性

推导了一端固定、一端与质点连接的弹性杆横振动的频率特性方程,并详细讨论了几种质量比情形下的特征频率。     

Dynamics of a charged particle in a linearly polarized traveling wave

The basic physical processes in laser-matter interaction, up to (for a neodymium laser) are now well understood, on the other hand, new phenomena evidenced in PIC code simulations have to be investigated above . Thus, the relativistic motion of a charged particle in a linearly polarized homogeneous electromagnetic wave is studied, here, using the Hamiltonian formalism. First, the motion of a single particle in a linearly polarized traveling wave propagating in a non-magnetized space is explored. The problem is shown to be integrable. The results obtained are compared to those derived considering a cold electron plasma model. When the phase velocity is close to c, it is shown that the two approaches are in good agreement during a finite time. After this short time, when the plasma response is taken into account no chaos take place at least when considering low densities and/or high wave intensities. The case of a charged particle in a traveling wave propagating along a constant homogeneous magnetic field is then considered. The problem is shown to be integrable when the wave propagates in vacuum. The existence of a synchronous solution is shown very simply. In the case when the wave propagates in a low density plasma, using a simplifying Lorentz transformation, it is shown that the system can be reduced to a time-dependent system with two degrees of freedom. The system is shown to be nonintegrable, chaos appears when a secondary resonance and a primary resonance overlap. Finally, stochastic instabilities are studied by considering the motion of one particle in a very high intensity wave perturbed by one or two low intensity traveling waves. Resonances are identified and conditions for resonance overlap are studied.     

On the non-radiating motion of a charged particle

The most general class of the electric and magnetic fields such that a charged particle moving in this field will not radiate is obtained. Apart from suitably orientated constant fields, it includes some special varying (but steady) fields.     

Force on a charged test particle in a collisional flowing plasma

The force on a charged test particle embedded in a flowing (electron-ion) plasma is calculated using the linear dielectric response formalism. This approach allows us to take into account ion-neutral collisions self-consistently. The effect of collisions on the ion drag force is analyzed. It is shown that collisions can play a major role and can enhance the force substantially.     

Density functional theory for molecular orientation of hard rod fluids in hard slits

A density functional theory (DFT) is used to investigate molecular orientation of hard rod fluids in a hard slit. The DFT approach combines a modified fundamental measure theory (MFMT) for excluded-volume effect with the first order thermodynamics perturbation theory for chain connectivity. In the DFT approach, the intra-molecular bonding orientation function is introduced. We consider the effects of molecular length (i.e. aspect ratio of rod) and packing fraction on the orientations of hard rod fluids and flexible chains. For the flexible chains, the chain length has no significant effect while the packing fraction shows slight effect on the molecular orientation distribution. In contrast, for the hard rod fluids, the chain length determines the molecular orientation distribution, while the packing fraction has no significant effect on the molecular orientation distribution. By making a comparison between molecular orientations of the flexible chain and the hard rod fluid, we find that the molecular stiffness distinctly affects the molecular orientation. In addition, partitioning coefficient indicates that the longer rodlike molecule is more difficult to enter the confined phase, especially at low bulk packing fractions.     

电解液中带电平板与带电胶体球之间的有效相互作用

用Poisson-Boltzmann方程，计算了在具有单价离子的电解质溶液中均匀地带同号电荷的两无限大平行平板间的有效相互作用，以及用Derjaguin近似研究了边界对带电胶体球的影响.不考虑微离子相互作用时，两带电平板只有排斥作用，而且边界条件(面电荷密度)的改变对它们之间的有效相互作用影响不大.带电平板与带电胶体球之间的相互作用也有类似规律. 关键词： Poisson-Boltzmann方程 Derjaguin近似 双电层 渗透压