Phase-space density in heavy-ion collisions revisited

We derive the phase space density of bosons from a general boson interferometry formula. We find that the phase space density is connected with the two-particle and the single-particle density distribution functions. If the boson density is large, the two-particle density distribution function cannot be expressed as a product of two single-particle density distributions. However, if the boson density is so small that the two-particle density distribution function can be expressed as a product of two single-particle density distributions, then Bertsch's formula is recovered. For a Gaussian model, the effects of multi-particles Bose-Einstein correlations on the mean phase space density are studied.Received: 10 July 2002, Revised: 18 June 2003, Published online: 5 September 2003     

The Explicit Density Functional and Its Connection with Entropy Maximization

The intrinsic Helmholtz free energy, commonly used as a basis for density functional theories, is here given explicitly as a cluster diagram expansion with density field points. Also given are explicit variational procedures for determining the chemical potential for a given density, the pair potential for a given pair correlation function, and the pair correlation function for a given pair potential. The physical meaning of the density functional is established within the context of a new derivation of statistical mechanics based on entropy that supplies a variational principle for equilibrium by generalizing the thermodynamic potential to nonequlibrium states. This shows that the conventional density functional determines not only the equilibrium density, but also the probability of fluctuations about that density.     

Dependence of resonance condition on pressure in an RF resonancemethod

The plasma density is shown as functions of pressure and magnetic flux density in an RF resonance method using the XPDP1 simulation code. The RF resonance method has the unique feature that a strong electric field in bulk controls the plasma density. Owing to the balance between the electric field decrease and the collision rate increase, the plasma density in the RF resonance method has a peak with respect to pressure. The plasma density with respect to the magnetic flux density depends on the condition of the RF resonance method, and the dependence is strong at low pressure because of the strong resonance. Sheath thickness is the most important parameter that determines the strength of the resonance induced. It is shown that the sheath thickness s is related to the plasma density n as a function of ns, obtained from a dispersion relation at constant external parameters. The magnetic flux density which induces the strong resonance is determined from sheath thickness. The plasma density in the RF resonance method can be predicted from discharge parameters using the relation between plasma density and sheath thickness     

Spatial structure of an incompressible quantum Hall strip

The incompressible quantum Hall strip is sensitive to charging of localized states in the cyclotron gap. We study the effect of localized states by a density functional approach and find electron density and the strip width as a function of the density of states in the gap. Another important effect is electron exchange. By using a model density functional which accounts for negative compressibility of the QH state, we find electron density around the strip. At large exchange, the density profile becomes nonmonotonic. Both effects, localized states and exchange, lead to a substantial increase of the strip width.     

Charge densities and charge noise in mesoscopic conductors

We introduce a hierarchy of density of states to characterize the charge distribution in a mesoscopic conductor. At the bottom of this hierarchy are the partial density of states which represent the contribution to the local density of states if both the incident and the out-going scattering channel is prescribed. The partial density of states play a prominent role in measurements with a scanning tunneling microscope on multiprobe conductors in the presence of current flow. The partial density of states determine the degree of dephasing generated by a weakly coupled voltage probe. In addition the partial density of states determine the frequency-dependent response of mesoscopic conductors in the presence of slowly oscillating voltages applied to the contacts of the sample. The partial density of states permit the formulation of a Friedel sum rule which can be applied locally. We introduce the off-diagonal elements of the partial density of states matrix to describe charge fluctuation processes. This generalization leads to a local Wigner-Smith life-time matrix.     

Density profiles and solvation force for a liquid in a slit

Computer simulations and density functional theory results are reported for a Lennard-Jones liquid in a slit or pore formed by two parallel hard walls. Both density profiles and solvation forces are computed. Two classes of calculation are performed. In the first class, a high bulk density is selected and, starting from a high temperature, the temperature is reduced until the temperature corresponding to bulk liquid—vapour coexistence is reached. For small slit widths or exceedingly large widths, the density in the slit decreases continuously until the slit is virtually empty or ‘dry’. When the slit width is somewhat larger than a molecular diameter, but still finite, the density in the slit decreases continuously as the temperature is decreased until there is an abrupt change in the density in the slit. Below this temperature, the density is smaller. Further decreases in the temperature, result in a continuous decrease in the slit density until the slit is virtually empty. In the second class, the density and temperature for bulk coexistence are chosen and the bulk density is increased. At the temperature and bulk density for bulk coexistence, the slit is virtually empty and remains so for all widths that we consider. As the bulk density is increased at constant temperature, the slit remains empty as the width is increased until some specific width is reached and then starts to fill abruptly. The agreement of the density functional and simulation results is qualitative but good.     

A First Order Generalized Thomas-Fermi Approximation for the Electron Density in Inversion Layers

An operator evaluation of the one-particle density matrix of a degenerate system of independent particles in first order with respect to the gradient of the potential developed by Macke and Rennert yields an analytic expression for the particle density. This method is extended here to potentials with an infinite step and to finite temperatures – a situation which is characteristic for inversion electrons in MIS-systems. The resulting density can be expressed as the Airy transform of the zeroth order (local density approximation). The first order yields both the tunneling into the classically forbidden region and oscillations of the density near the step of the potential. The operator evaluation of the density matrix is shown to be equivalent to solving a Schrödinger like equation. The first order density yields results for the subband structure of (100)Si inversion and accumulation layers at OK in remarkable agreement to density functional calculations of Ando.     

Defect-induced transitions in synchronous asymmetric exclusion processes

The effects of a single local defect in synchronous asymmetric exclusion processes are investigated via theoretical analysis and Monte Carlo simulations. Our theoretical analysis shows that there are four possible stationary phases, i.e., the (low density, low density), (low density, high density), (high density, low density) and (high density, high density) in the system. In the (high density, low density) phase, the system can reach a maximal current which is determined by the local defect, but independent of boundary conditions. A phenomenological domain wall approach is developed to predict dynamic behavior at phase boundaries. The effects of defective hopping probability p on density profiles and currents are investigated. Our investigation shows that the value of p determines phase transitions when entrance rate α and exit rate β are fixed. Density profiles and currents obtained from theoretical calculations are in agreement with Monte Carlo simulations.     

Magnetic phase diagram in a quasi-two-dimensional electron gas

Using spin density functional theory within the framework of the local spin density approximation with Perdew-Zunger type exchange-correlation energy, ferromagnetism in a quasi-two-dimensional electron gas (Q-2DEG) is studied. The electronic and magnetic structures of a thin film are calculated as a function of film thickness and electron density. Ferromagnetism in the Q-2DEG is found to appear at a higher electron density than in the three-dimensional electron gas. Unless a film is very thin, with decreasing electron density, a magnetic phase transition occurs from a spin-unpolarized fluid to a Wigner film with surface magnetism, in which the spin polarization localizes only in the neighborhood of surfaces. Further decreasing density induces another transition to a fully spin-polarized ferromagnetic Wigner film.     

Neutrino oscillations with three flavors in matter of varying density

In this paper, we discuss the evolution operator and the transition probabilities expressed as functions of the vacuum mass squared differences, the vacuum mixing angles, and the matter density parameter for three flavor neutrino oscillations in matter of varying density in the plane wave approximation. The applications of this to neutrino oscillations in a model of the earth's matter density profile, step function matter density profiles, constant matter density profiles, linear matter density profiles, and finally in a model of the sun's matter density profile are discussed. We show that for matter density profiles which do not fluctuate too much, the total evolution operator consisting of n operators can be replaced by one single evolution operator in the semi-classical approximation. Received: 23 March 2001 / Published online: 8 June 2001     

A single current density component imaging by MRCDI without subject rotations

Magnetic resonance current density imaging (MRCDI) is a useful method for measuring electrical current density distribution inside a subject. Due to the requirement of subject rotations in MRCDI, MRCDI has not been widely applied to in vivo studies. In this paper, we propose a new current density image (CDI) reconstruction method by which a single component of the current density can be imaged by MRCDI without subject rotations. After measuring one of the two magnetic field components, produced by the current density component passing through the measurement plane, we have reconstructed the current density component images in the spatial frequency domain. Even though the proposed method has a limitation that the area of magnetic field measurement should be much larger than that of the current density, the proposed method is expected to expedite MRCDI applications to in vivo studies.     

On the stability of the Hartree-Fock homogeneous density solution for nuclear matter

The nuclear matter energy density used by Overhauser is shown not to be realistic. The consequence of a static density fluctuation thus seems doubtful. The application of the method of Baym, Bethe and Pethik, developed for neutron star matter problems, shows that for a more realistic nuclear energy density containing the Thomas-Fermi part plus gradient terms, both spatially periodic compression and decompression about the saturation density, augment the energy. In addition, positive gradient terms tend to prevent a rippled density.     

HL－1电子密度行为在各种条件下的实验研究

在ＨＬ－１装置电子密度测量中，进一步改进了密度相移信号的处理方法。在氘放电、氦补充送气条件下得到了ＨＬ－１最高电子密度１０．８×１０１３ｃｍ－３。总结了密度在各种实验条件下的行为，并对各种实验条件对密度的影响进行了分析。     

On synchronizability and heterogeneity in unweighted networks

Synchronization in classes of continuous-time dynamical unweighted networks with different topologies is investigated. A synchronization-optimal network model based on rewiring of links is proposed. Compared with other networks, it exhibits a stronger synchronizability. We presented link density and investigated the correlation of synchronizability, link density and heterogeneity in degree distribution. In this work, it will be shown that synchronizability of Type I networks is independent of heterogeneity in the degree distribution when the link density is smaller than 0.02. Synchronizability and link density are proportional. When the link density is larger than 0.025, heterogeneity decides the curve slope. The synchronizability of Type II networks is drastically enhanced by enhancing the link density when the link density is smaller than 0.025. However synchronizability increases weakly by enhancing the link density when the link density is larger than 0.025.     

低密度聚环己基乙烯泡沫的制备

低密度CH聚合物多孔材料是惯性约束聚变(ICF)的重要靶材料,利用热致相分离原理对低密度聚环己基乙烯泡沫的制备进行了研究。首先通过聚苯乙烯(PS)氢化反应制备了聚环己基乙烯(PVCH),经过溶剂选择,确定以环己烷/1,4-二氧六环为溶剂体系,经热致相分离和冷冻干燥技术制备出低密度PVCH泡沫。通过分析溶液浓度对泡沫密度的影响,确定了泡沫密度与聚合物溶液质量浓度之间的关系,在0.04~0.15 g/cm3范围之内可实现对泡沫密度的有效控制。泡沫孔结构测试结果表明随着密度的增加,平均孔径有升高的趋势,孔径分布趋于单一化,孔径范围为23.63~0.83μm。     

Influence of electrode separation on ion density in the vacuum arc

The density of singly ionized chromium shortly before and after forced extinction of vacuum arcs between chromium-copper electrodes was measured by laser-induced fluorescence for 2- and 10-mm contact gaps and currents between 200 A and 1 kA. In all cases studied, the ion density was constant before ramping down to the current and decayed exponentially after current zero. The ion density at current zero was found to be lower and to decay faster for a short gap than for a longer one, clearly indicating the effect of the contact separation on the charge carrier density. The variation of the time constant for the ion density decay with contact separation is closely analogous to the influence of contact separation on the recovery time of a switch gap. Furthermore, the recovery of dielectric strength of a chromium-copper gap proceeds on the same timescale as the decay of the density of singly ionized chromium. Both of these findings confirm that the ion density has a strong impact on the recovery of a vacuum gap     

尘埃颗粒与等离子体鞘层相互作用的数值模拟

通过求解一维稳态的尘埃等离子体鞘层模型,得到了等离子体鞘层势、正离子密度、电子密度和尘埃颗粒密度随一维横向的分布,Bohm判据及鞘层边界无量纲Bohm速度随尘埃密度的变化曲线,尘埃颗粒的带电量和尘埃密度的关系,尘埃颗粒的温度对尘埃颗粒自身在鞘层中分布的影响。结果表明,随着尘埃密度的增加,鞘层的厚度在减小,鞘层内的电子密度在下降,而且尘埃颗粒的带电量也在逐渐减少;随着尘埃温度的增加,鞘层的厚度减小,电子密度下降,而且鞘层附近的尘埃颗粒在逐渐增多。     

Free energies of supercritical solvation from molecular dynamics simulation and integral equation studies

We present here molecular dynamics (MD) simulation and integral equation (IE) studies on free energies of solvation of a non-polar solute in a dilute supercritical solvent to estimate the contribution of inhomogeneities in solvent density to the free energy of solvation. The solvation of a Xe-like solute in an Ne-like solvent as well as that of naphthalene in CO₂ have been investigated. At state points in the compressible region in the neighborhood of the solvent critical point, we have utilized the IE estimates of free energies to model the ideal situation where local density inhomogeneities would be absent. The difference between the free energies in the presence (as derived from MD simulation) and in the absence (from IE) of local density inhomogeneities was studied as a function of density along an isotherm close to the critical point. Although for low density supercritical solvents, a marked difference is observed, a study of the density dependence of this difference across the critical density does not directly reveal any signature of local density enhancement on the thermodynamics of solvation.     

On the slow dynamics of density fluctuations near the colloidal glass transition

Slow dynamics of density fluctuations near the colloidal glass transition is discussed from a new viewpoint by numerically solving a nonlinear stochastic diffusion equation for the density fluctuations recently proposed by one of the present authors (MT). The effects of spatial heterogeneities on the dynamics of density fluctuations are then investigated in an equilibrium system. The spatial heterogeneities are generated by the nonlinear density fluctuations, while in a nonequilibrium system they are described by a nonlinear deterministic equation for the average number density. The dynamics of equilibrium density fluctuations is thus shown to be quite different from that of nonequilibrium ones, leading to a logarithmic decay followed by less distinct α- and β-relaxation processes. Received 9 March 2002 and Received in final form 19 September 2002