Integral relations for the heat and mass transfer resistivities of the liquid–vapor interface

We derived integral relations for the heat and mass transfer resistivities of the liquid–vapor interface in a one-component system. These relations were obtained assuming the validity of the standard expression for the local entropy production rate as the product of the measurable heat flux times the gradient of the inverse temperature through the surface. The integral relations will be useful to interpret results from nonequilibrium molecular dynamics simulations. We verified in this paper that earlier results obtained using the nonequilibrium van der Waals square gradient model are reproduced. For this case, we calculated the Kapitza length along the coexistence curve.     

Viscosity of Lennard-Jones fluid: Integral equation method

One of the most useful models to study the real systems is the Lennard-Jones (LJ) potential which has an attractive and repulsive part. In this work we use this potential model and examine the viscosity of one-component LJ fluids and LJ binary fluid mixtures. For this purpose, we apply the integral equation method and solve numerically the Ornstein-Zernike (OZ) integral equation by using the mean spherical approximation (MSA). Thus, we obtain the pair correlation functions to calculate the viscosity of these fluids. Finally, we compare our results with computer simulation results and the available experimental data and illustrate the ability of the LJ model to predict the results.     

Stable quasiperiodic icosahedral states

The discovery of icosahedral quasicrystals five years ago, has challenged the validity of the well-known conjecture that the ground state of a system of particles interacting via short-range forces is always crystalline at absolute zero. We have calculated the classical cohesive energies and pair distribution functions of a large class of monatomic icosahedral structures, interacting via the Lennard-Jones (LJ) and the Square-Well (SW) potentials. For the SW potential, we have found an icosahedral phase, with lower enthalpy than the BCC, FCC and HCP phases. The phase is robust with respect to small changes in the potential, pressure and even structure, and transforms to the BCC phase above a critical pressure. Our results suggest that icosahedral ground states may indeed be possible for a class of potentials with Friedel-like oscillations, whose extremal positions satisfy geometric constraints favoring icosahedral order.     

Luminescence quenching kinetics upon diffusion-accelerated dipole-dipole energy transfer for a realistic condensed-matter model

The hard-sphere model is considered as a more realistic condensed-matter model. In this model, the radial distribution function of molecules in a medium, used for calculations of luminescence decay kinetics, takes into account the short-range order in fluids and has the shape of damped oscillations. It is assumed that the motion of donor and acceptor molecules in a solution for the lifetime of the excited state of the donor is described by the diffusion equation, while the luminescence quenching occurs due to the long-range dipole-dipole energy transfer. It is shown that, if diffusion coefficients are small, the kinetics determined in this study hardly differs at all from the traditional kinetics. At intermediate and large diffusion coefficients, this difference becomes significant and should be taken into account in estimating the Förster energy transfer radius and diffusion coefficients from experimental luminescence decay curves.     

Vortex mass in a superfluid at low frequencies

An inertial mass of a vortex can be calculated by driving it around in a circle with a steadily revolving pinning potential. We show that in the low-frequency limit this gives precisely the same formula that was used by Baym and Chandler, but find that the result is not unique and depends on the force field used to cause the acceleration. We apply this method to the Gross-Pitaevskii model, and derive a simple formula for the vortex mass. We study both the long-range and short-range properties of the solution. We agree with earlier results that the nonzero compressibility leads to a divergent mass. From the short-range behavior of the solution we find that the mass is sensitive to the form of the pinning potential, and diverges logarithmically when the radius of this potential tends to zero.     

Determination of the steady state response of a Timoshenko beam of varying cross-section by use of the spline interpolation technique

The steady state response of an internally damped Timoshenko beam of varying cross-section to a sinusoidally varying point force is determined by use of the spline interpolation technique. For this purpose, with the beam divided into small elements, the response of each element is expressed by a quintic spline function with unknown coefficients. The response is obtained by determining these coefficients so that the spline function satisfies the equation of motion of the beam at each dividing point and also satisfies the boundary conditions at both ends. In this case, the slope due to pure bending of the beam is conveniently adopted as the function essentially expressing the response, from which the transverse deflection, driving point impedance, transfer impedance and force transmissibility of the beam are derived. The method is applied to cantilever beams with linearly, parabolically and exponentially varying rectangular cross-sections; these responses of the beams are calculated numerically and the effects of the varying cross-section on them are studied.     

A classical density functional approach to depletion interaction of Lennard-Jones binary mixtures

In this article, we apply classical density functional theory to investigate the characteristics of depletion interaction in Lennard-Jones (LJ) binary fluid mixtures. First, to confirm the validity of our adopted density functional formalism, we calculate the radial distribution functions using a theoretical approach and compare them with results obtained by molecular dynamics simulation. Then, this approach is applied to two colloids immersed in LJ solvent systems. We investigate the variation of depletion interaction with respect to the distance of two colloids in LJ binary systems. We find that depletion interaction may be attractive or repulsive, mostly depending on the bulk density of the solvent and the temperature of the binary system. For high bulk densities, the repulsive barrier of depletion force is remarkable when the total excluded volume of colloids touches each other and reaches a maximum. The height of the repulsive barrier is related to the parameters of the LJ potential and bulk density. Moreover, the depletion force may exhibit attractive wells if the bulk density of the solvent is low. The attractive well tends to appear when the surface–surface distance of colloids is half of the size of the polymer and deepens with temperature lowering in a fixed bulk density. In contrast with the hard-sphere system, no oscillation of depletion potential around zero is observed.     

Further property of Lennard-Jones fluid: Thermal conductivity

In this paper, we calculate the thermal conductivity of noble gases, methane, and three noble gas mixtures including He+Kr, He+Xe, and Kr+Xe assuming they obey Lennard-Jones (LJ) (12-6) model potential. One of the required quantities to calculate the thermal conductivity of these systems is the pair correlation function. Therefore, we solve numerically the Ornstein-Zernike (OZ) integral equation using the mean spherical approximation (MSA) to obtain the pair correlation functions. We use these functions to obtain the thermal conductivity, then compare our results with the available data. According to the results obtained from the present work for pure and mixtures of LJ fluids reveals that the integral equations method is suitable for predicting the thermal conductivity of this class of fluid.     

Pressures for a One-Component Plasma on a Pseudosphere

The classical (i.e., non-quantum) equilibrium statistical mechanics of a two-dimensional one-component plasma (a system of charged point-particles embedded in a neutralizing background) living on a pseudosphere (an infinite surface of constant negative curvature) is considered. In the case of a flat space, it is known that, for a one-component plasma, there are several reasonable definitions of the pressure, and that some of them are not equivalent to each other. In the present paper, this problem is revisited in the case of a pseudosphere. General relations between the different pressures are given. At one special temperature, the model is exactly solvable in the grand canonical ensemble. The grand potential and the one-body density are calculated in a disk, and the thermodynamic limit is investigated. The general relations between the different pressures are checked on the solvable model.     

Short-range spin correlations and pseudogap in underdoped cuprates

In this paper we show that local spin-singlet amplitude with d-wave symmetry can be induced by short-range spin correlations even in the absence of pairing interactions. In the present scenario for the pseudogap, the normal state pseudogap is caused by the induced local spin-singlet amplitude due to short-range spin correlations, which compete in the low energy sector with superconducting correlations to make T_c go to zero near half-filling.     

Corrections to the classical continuity boundary conditions at the interface of a composite medium

Using the multiple-scales homogenization method, we derive generalized sheet transition conditions (GSTCs) for electromagnetic fields at the interface between two media, one of which is free-space and the other a certain type of composite material. The parameters in these new boundary conditions are interpreted as effective electric and magnetic surface susceptibilities, which themselves are related to the geometry of the scatterers that constitute the composite. We show that the effective tangential E and H fields are not continuous across the interface except in the limit when the lattice constant (the spacing between the scatterers—atoms, molecules or inclusions in the case of a composite material) of the composite medium is very small compared to a wavelength. We derive first-order corrections to the classical continuity conditions. For naturally occurring materials whose lattice constants are on an atomic scale, these effects are shown to be negligible for waves at optical frequencies or lower. However, once the lattice constant becomes a significant fraction of a wavelength (which is the case for many artificial dielectrics and metamaterials), the corrections can be important. In previous work we have alluded to the fact that such a GSTC is needed to correctly account for the surface effects when extracting the effective material properties of a metamaterial. The results of this current paper justify the assumptions made in that previous work. In general, these GSTCs will result in corrections to the classical Fresnel reflection and transmission coefficients (which are themselves merely zeroth-order approximations to the actual reflection and transmission coefficients), and in a separate publication we will use these GSTCs to address this issue.     

半干旱草原下垫面动量和感热总体输送系数参数化关系研究

本文利用锡林郭勒草原2008年春季近地层涡旋相关系统和铁塔的风、 温平均梯度观测资料, 分析了总体输送系数随梯度Richardson数的变化特征, 建立了动量总体输送系数随大气稳定度、近地层风速以及感热总体输送系数随大气稳定度和近地层气温的关系. 中性条件下, 半干旱草原植被下垫面动量总体输送系数与近地层大气动力状态之间存在明显的相互作用, 总体输送系数与近地面层风速之间满足二次曲线拟合关系; 风速较小时, 大气动力特征对地表粗糙度长度的改变不是很明显, 动量总体输送系数随气流增强而增大; 而当风速较大时, 强风速会使植被高度发生改变, 动量总体输送系数随气流增强而减小. 另外, 感热总体输送系数与近地层气温之间也存在二次曲线关系. 动量总体输送系数与近地层风速之间的关系、感热总体输送系数与近地层气温之间关系的建立为总体输送系数参数化提供了重要途径, 同时该方案避免了对动力学粗糙度长度和热力学粗糙度长度的求解. 关键词： 总体输送系数 参数化 湍流通量 相似性函数     

Quantum confinements in highly asymmetric sub-micrometer device structures

With the ongoing miniaturization of MOSFET structures into the nanometer domain, experimental results suggest there are physical limits up to which one can reduce the gate lengths. Furthermore, it becomes progressively more difficult to overcome the short channel effects at small gate lengths. This has led the researchers in the industry to look for alternative device technologies. One solution to the problem are the asymmetric device structures. In this work, we have simulated a 50 nm asymmetric MOS device structure using a two-dimensional Monte Carlo Poisson particle-based solver, in which quantum effects have been taken into account via the effective potential scheme. The quantum effects in these small device structures lead to strong quantum confinement of the carriers at the semiconductor/oxide interface, thus affecting the device drive current and the threshold voltage. We also show that the Silvaco Atlas simulations performed on the same device structure using the energy balance model were strongly affected by the choice of the energy relaxation times.     

Counting rule of Nambu–Goldstone modes for internal and spacetime symmetries: Bogoliubov theory approach

When continuous symmetry is spontaneously broken, there appear Nambu–Goldstone modes (NGMs) with linear or quadratic dispersion relation, which is called type-I or type-II, respectively. We propose a framework to count these modes including the coefficients of the dispersion relations by applying the standard Gross–Pitaevskii–Bogoliubov theory. Our method is mainly based on (i) zero-mode solutions of the Bogoliubov equation originated from spontaneous symmetry breaking and (ii) their generalized orthogonal relations, which naturally arise from well-known Bogoliubov transformations and are referred to as “σ$\sigma$-orthogonality” in this paper. Unlike previous works, our framework is applicable without any modification to the cases where there are additional zero modes, which do not have a symmetry origin, such as quasi-NGMs, and/or where spacetime symmetry is spontaneously broken in the presence of a topological soliton or a vortex. As a by-product of the formulation, we also give a compact summary for mathematics of bosonic Bogoliubov equations and Bogoliubov transformations, which becomes a foundation for any problem of Bogoliubov quasiparticles. The general results are illustrated by various examples in spinor Bose–Einstein condensates (BECs). In particular, the result on the spin-3 BECs includes new findings such as a type-I–type-II transition and an increase of the type-II dispersion coefficient caused by the presence of a linearly-independent pair of zero modes.     

Fresnel boundary and interface conditions for polarized radiative transfer in a multilayer medium

In many applications of the theory of radiative transfer, it is important to consider the changes in the index of refraction that occur when the physical domain being studied consists of material regions with distinct optical properties. When polarization effects are taken into account, the radiation field is described by a vector of four components known as the Stokes vector. At an interface between two different material regions, the reflected and transmitted Stokes vectors are related to the incident Stokes vector by means of reflection and transmission matrices, which are derived from the Fresnel formulas for the amplitude coefficients of reflection and transmission. Having seen that many works on polarized radiative transfer that allow for changes in the index of refraction exhibit discrepancies in their expressions for the transmission matrix, we present in this work a careful derivation of the relations between the reflected and transmitted Stokes vectors and the Stokes vector incident on an interface. We obtain a general form of a transmission factor that is required to ensure conservation of energy and we show that most of the discrepancies encountered in existing works are associated with the use of improper forms of this factor. In addition, we derive explicit and compact expressions for the Fresnel boundary and interface conditions appropriate to the study of polarized radiative transfer in a multilayer medium.     

Microscopic transport theory of heavy-ion collisions

Analytical expressions for the diffusion coefficients for the transfer of neutrons and protons in a heavy-ion collision are derived. The mass diffusion coefficient implied by these two coefficients is compared with previous theoretical calculations and the values extracted from experiment for a variety of systems. Drift coefficients are related to the diffusion coefficients and the driving potential by the usual Einstein relations. On approximating the driving potential by a second-order form, the Fokker-Planck equation is solved analytically by the moment expansion method. A comparison of the predictions of this theory with a variety of recent experimental data gives generally good agreement. Thus we conclude that the experimental data currently available can be interpreted in purely statistical terms. Some deviations between theory and experiment indicate a possible influence of shell effects and/or direct transfer processes in the early stages of the reaction.     

Extension of the uncertainty relations to the mixed states

In this paper we have extended the uncertainty relations to mixed states for some special cases of quantum oscillators, relations which are calculated for this kind of states by means of the earlier established virial and Hellmann-Feynman theorems. The lower bound of these uncertainty relations is estimated for a few exactly solvable potentials, too.     

Statistical mechanics of inhomogeneous model colloid—polymer mixtures

We describe two strategies for tackling the equilibrium statistical mechanics of inhomogeneous colloid—polymer mixtures treated in terms of the simple Asakura—Oosawa—Vrij (AO) model, in which colloid—colloid and colloid—polymer interactions are hard-sphere like, whereas the polymer—polymer interaction is zero (perfectly interpenetrating polymer spheres). The first strategy is based upon integrating out the degrees of freedom of the polymer spheres to obtain an effective one-component Hamiltonian for the colloids. This is particularly effective for small size ratios q = σ_p/σ_c < 0.1547, where σ_p and σ_c are the diameters of colloid and polymer spheres, respectively, since in this regime three and higher body contributions to the effective Hamiltonian vanish. In the second strategy we employ a geometry based density functional theory (DFT), specifically designed for the AO model but based on Rosenfeld's fundamental measure DFT for additive mixtures of hard-spheres, that treats colloid and polymer on an equal footing and which accounts for the fluid-fluid phase separation occurring for larger values of q. Using the DFT we investigate the properties of the ‘free’ interface between colloid-rich (liquid) and colloid-poor (gas) fluid phases and adsorption phenomena at the interface between the AO mixture and a hard-wall, for a wide range of size ratios. In particular, for q = 0.6 to 1.0, we find rich interfacial phenomena, including oscillatory density profiles at the free interface and novel wetting and layering phase transitions at the hard-wall-colloid gas interface. Where appropriate we compare our DFT results with those from computer simulations and experiment. We outline several very recent extensions of the basic AO model for which geometry based DFTs have also been developed. These include a model in which the effective polymer sphere—polymer sphere interaction is treated as a repulsive step function rather than ideal and one in which the depletant is a fluid of infinitely thin rods (needles) with orientational degrees of freedom rather than (non-interacting) polymer spheres. We comment on the differences between results obtained from these extensions and those of the basic AO model. Whilst the interfacial properties of the AO model share features in common with the those of simple (atomic) fluids, with the polymer reservoir density replacing the inverse temperature, we emphasize that there are important differences which are related to the many-body character of the effective one-component Hamiltonian.     

Generalized van der Waals theory VIII. An improved analysis of the liquid/gas interface

We extend a preceding application of the GvdW theory to the prediction of interface profiles and surface tension in simple fluids by incorporating a variational determination of the effective hard-sphere diameter. This has previously been found to improve the predicted equation of state. Here we find that it also improves the prediction of interface profiles and surface tension in LJ(12-6) fluids. The agreement with experiment and simulation when these quantities are considered as functions ofT/T _c is to within about 5%. As in our earlier calculations the nonlocal entropie effects are found to reduce the surface tension by 5%–10%. In the present conceptually more accurate theory this significantly improves the agreement with experiment and simulation.     

Plasma response functions,fluctuation-dissipation relations and the velocity-average-approximation

We derive and list relationships for quadratic and cubic static response functions and connect them with three- and four-point functions through generalized fluctuation-dissipation relations. We also introduce the useful concept of “response function of the second kind.” to describe the reponse of a system through the perturbation of its two-point functions. Next, we point out that the VAA (velocity-average-approximation) introduced earlier as a part of a dynamical approximation scheme for strongly coupled one-component plasmas is exact in the static limit. This observation, combined with the fluctuation-dissipation relations, allows one to derive a hierarchy of equations for response functions of increasing nonlinearity, which is equivalent to the BGY hierarchy for particle distribution functions.