The local stress tensor is defined as the field thermodynamically conjugate to the local strain tensor. Any free-energy change resulting from a strain can then be expressed either in terms of the stresses or in terms of the equivalent single-particle external force field. Using this equivalence, one obtains a well-defined expression for the local stress tensor in terms of this force field. On this basis we obtain unambiguous expressions for the surface tension and for the location of the surface of tension of a planar interface.

An underlying connection between the structure of a uniform fluid and that of its nonuniform counterpart provides a means of testing various approximations used in density-functional theories of nonuniform fluids. This paper proposes a density-functional approach to the structure of classical uniform fluids that is based on a simple version of the weighted-density approximation for the one-particle direct correlation function of the corresponding nonuniform fluid. In the context of the integral-equation method, this approach provides a closure to the Ornstein-Zernike relation that implicitly includes correlations to all orders. To demonstrate and test the accuracy of the approach, it is applied, at the first level of iteration, to the hard-sphere fluid. Results for three important structure-related functions, namely the radial distribution function, the cavity function, and the bridge function, are all shown to be in generally good agreement with simulation. In contrast, corresponding results from an alternative approach, based on a truncated-expansion approximation for the one-particle direct correlation function, are in significantly poorer agreement with simulation at higher densities.

In order to cope with numerical simulations of charged periodic systems bounded by an infinite wall, the planewise summation method is discussed. The equations needed to evaluate, in this quasi-two-dimensional geometry, the lattice sums of arbitrary derivatives of 1/r at any field point of a general lattice, are given. The relationship with the Ewald method is discussed and it is found that, roughly speaking, the computational time required is comparable for both methods.

We present a density-functional theory for the phase diagram of charge-stabilized colloids with bcc, fcc, and liquid phases. The theory requires inclusion of terms involving the three-body direct correlation function of the liquid, but even a simple parametrization of these terms reproduces the features of the experimental phase diagram. We make additional directly testable predictions from our theory.

A stochastic model is proposed and kinetic equations are derived to describe the boiling process on a solid surface. The model considers bubble growth at discrete nucleation sites and accounts for interactions between adjacent sites. The model is valid for initial stages of nucleate boiling when vigorous surface boiling has not yet commenced. The interactions considered are the seeding with vapor of inactive sites by bubbles at neighboring active sites, and the deactivation of active sites by thermal interference from neighboring sites. The stochastic model is applied in Monte Carlo simulation, employing parameters obtained from experimental results, to predict bubble emission rates and heat fluxes from the surface. The numerical results predict the presence of many permanently inactive sites, the formation of active-site clusters, and the rise in the density of active sites with increase in overall heat flux. The description of the homogeneous nucleate boiling process in terms of dynamic percolation theory is presented.

The Dharma-wardana and Perrot (DP) theory for a dense plasma is rewritten in another equivalent form in order to clarify its structure and approximations involved in it in comparison with the exact expression of structure factors in terms of the direct correlation functions (DCF) for a plasma as an ion-electron mixture. Thus it is shown that the DP theory breaks down when it treats a dense plasma with large bound-electron contribution, that is, with a significant number of bound electrons, as an ion. Also, this situation is numerically examined by using liquid metallic lithium as a test case, to which the quantal hypernetted-chain (QHNC) formulation is successfully applied. The breakdown in the DP theory is attributed to neglect of the electron-ion correlation given by the non-Coulomb part of the electron-ion DCF, ${\mathit{C}}_{\mathit{e}\mathit{I}}^{\mathrm{NC}}$(r), which is taken into account in the QHNC formulation. The non-Coulomb part ${\mathit{C}}_{\mathit{e}\mathit{I}}^{\mathrm{NC}}$(r) plays an important role in the reduction of a bare-electron–ion interaction ${\mathit{v}}_{\mathit{e}\mathit{I}}^{\mathit{C}}$(r) to a weak pseudopotential, when a nucleus in a plasma begins to have core electrons forming an ion, since the DCF ${\mathit{C}}_{\mathit{e}\mathit{I}}$(r)==-β${\mathit{v}}_{\mathit{e}\mathit{I}}^{\mathit{C}}$(r)+${\mathit{C}}_{\mathit{e}\mathit{I}}^{\mathrm{NC}}$(r) becomes a ‘‘weak’’ nonlinear pseudopotential ${\mathit{w}}_{\mathit{b}}^{\mathrm{NL}}$(r).

Nevertheless, it turned out that one of the equations in the DP theory is useful to determine the nonlinear pseudopotential ${\mathit{w}}_{\mathit{b}}^{\mathrm{NL}}$(r) with use of the step-function approximation for the radial distribution ${\mathit{g}}_{\mathit{I}\mathit{I}}$(r) between ions. Recently Perrot, Furutani, and Dharma-wardana [Phys. Rev. A 41, 1096 (1990)] tried to take account of the electron-ion correlation by using the QHNC approximation. However, it is shown that their improvement is not adequate to treat a plasma with core electrons in ions because of improper handling of the bound-electron density distribution in the definition of the electron-ion and electron-electron DCF’s. From the comparison between the DP and QHNC approaches, a simplified method for treating a dense plasma is proposed to calculate a pseudopotential ${\mathit{w}}_{\mathit{b}}^{\mathrm{NL}}$(r), an effective interionic potential, and the electron-ion radial distribution function ${\mathit{g}}_{\mathit{e}\mathit{I}}$(r), in addition to ${\mathit{g}}_{\mathit{I}\mathit{I}}$(r), with the use of the jellium-vacancy model.

The perturbative solution of the integral form of the kinetic equation for electrons in weakly ionized plasmas is extended to nonuniform and time-dependent situations, allowing the possibility of large energy, time, and space gradients of particle distributions. The small expansion parameter in the theory is δ=min(Δɛ/scrE,λ/L,1/νT), where Δɛ=eEλ is the electron-energy gain in the electric field E on a mean free path λ, ν is the total collision frequency, and scrE, L, and T are the characteristic electron energy, distance, and time, respectively, for which the distribution function is required. Unlike the conventional two-term spherical-harmonic expansion method, the theory is not limited to a weakly anisotropic case and thus allows applications to situations where the inelastic-collision cross sections are relatively large. The problem of relaxation of the electron-energy distribution function to a new steady state, after a drop in the electric field, is considered as an example. The analytic solution of this kinetic problem is similar to that encountered in the theory of shock waves. The predictions of the theory are tested via Monte Carlo computer simulations.

Two different types of counterpropagation neural networks are applied to the problem of classifying unknown Cm ii and Pu i energy levels according to their electronic configurations. Four features—energy level, angular momentum, g factor, and isotope shift—are used to describe each level. Both types of networks are trained at the 100% level for even-parity levels of Cm ii, while for odd-parity levels one type is trained at 100% and the other at 97.5%. Performance on test sets is not as good, ranging from 80.0% to 93.3%. The two network types are trained at 98.6% and 90.5%, respectively, for even-parity levels of Pu i, and at 98.6% and 91.6% for odd-parity levels. Test-set performances range from 64.0% to 77.7%. Classifications for 159 previously unclassified Cm ii levels and 485 previously unclassified Pu i levels are also obtained. Qualitative analysis of network-training results reveals several characteristics of those levels whose configurations the networks fail to learn, the most prevalent of which is an isotope-shift value that is consistent with two or more configurations. Rationalizations are also given for some of the other levels the networks misclassify. These qualitative observations should form a basis for understanding and precisely interpreting the performance of counterpropagation neural networks when applied to atomic systems.

The line-intensity ratio of the 3d→2p and 3d→3p transitions in the singlet system of C iii has been measured in a well-diagnosed gas-liner pinch in the density range 7×${10}^{17}$ to 2.6×${10}^{18}$ ${\mathrm{cm}}^{\mathrm{-}3}$, where large changes with density have been reported in the literature. No change with density was found, with a standard deviation of ±12% from a constant line-intensity ratio.

A two-center model is used to study the influence of the cylindrical symmetry, imposed by the nearest neighbor, on the ionic levels and emission spectra of a Li-like krypton ion immersed in hot and dense plasma. The symmetry breaking of the spherical symmetry of the local microfield in the peripheries of the ion due to the effect of its nearest neighbor is accounted for by expanding the total electric microfield into its multipole components. The resulting cylindrically symmetric Hamiltonian is diagonalized to obtain the energy levels in this distorted microfield. It is shown that the cylindrical symmetry mixes states with different l’s (l is the orbital quantum number), particularly for highly excited states, and thereby gives rise to forbidden transitions in the emission spectrum. Results are obtained for (i) the variation of the ionic level shifts and mixing coefficients with the distance to the nearest neighbor and (ii) representative computed spectra to show the density effects on the spectral line profiles, shifts, and widths, and the forbidden components in the spectrum. It is found that by an ion density of 3×${10}^{22}$ ${\mathrm{cm}}^{\mathrm{-}3}$ forbidden lines can be of the same magnitude as the original allowed lines. Linewidths resulting from the distribution of nearest-neighbor distances are narrower than the result from the mechanism of Woltz and Hooper [Phys. Rev. A 38, 4766 (1988)]. Mixing is not important for the dominant ground-state configuration species of the plasma but rather enters through its major effects on excited-state properties.

Theoretical spectral-line profiles have been obtained for dielectronic satellite transitions in heliumlike and lithiumlike argon ions. Particular emphasis has been given to the systematic and self-consistent incorporation of the non-local-thermodynamic-equilibrium autoionizing-level populations, together with the line-broadening effects, which are due to autoionization processes, radiative transitions, electron collisions, and the action of the plasma ion-produced electric microfields. An investigation has been carried out of the effects of the plasma electric microfields on predicted dielectronic satellite line-intensity ratios, and a discussion is presented on the consequences of the electric-microfield effects for the spectroscopic determination of basic physical properties in laser-produced plasmas.

The complex conductivity and dielectric-permeability tensors of strongly coupled plasmas are studied and constructed on the basis of exact relations and sum rules. Both Coulomb and magnetic correlations are taken into account.

A storage-ring free-electron laser at Orsay has been operating since 1989 in the visible wavelength range. In contrast with previous experiments, it operates with positrons and at higher energies (600–800 MeV), with the storage ring Super-ACO (ACO denotes Anneau de Collisions d’Orsay). The optical gain, the laser power, the transverse profile, and the macrotemporal structure of the laser are analyzed. In particular, we show that the gain matrix possesses many off-diagonal elements, which results in lasing on a combination of noncylindrical Gaussian modes. The eigenmode of the laser oscillation is a combination of one or two main Gaussian modes and several higher-order modes, which results in most of the power being extracted in these modes.

We have used Monte Carlo calculations to verify the classical electrodynamics result describing the multiparticle coherent enhancement at long wavelengths for synchrotron-radiation emission. In addition we show the derivation of the result that, for a bunch of electrons in a storage ring, the synchrotron-radiation emission has a multiparticle coherent enhancement that is given by the square of the Fourier transform of the longitudinal spatial distribution function of the electrons. The result has been verified for Gaussian and sinusoidal distributions. For a Gaussian distribution of particles in a bunch, this is seen to have an effect only at wavelengths close to the bunch length. For a sinusoidal distribution as in the transverse optical klystron, the enhancement can easily be seen to occur at one specific wavelength.

Scattering of light by relatively large and numerous particles suspended in a liquid with a nearly matched index of refraction results in deflection through very small angles. The cumulative effect of many scatterings can, however, be substantial. Taking advantage of this small-angle-scattering property, we derive a simple asymptotic expression for the Nth-order multiple-scattering term based on steepest-descents evaluation of the Nth-order multiple integrals. When the dominant contribution to the scattering is high order (large N), the path followed by photons can be described by analogy with a deformed elastic rod, for which a constrained variational principle or principle of least action is specified. Euler-Lagrange equations are obtained for this constrained-end-point problem.

Principal-axis hyperspherical coordinates (made up of one hyperradius and 3N-7 angles as internal coordinates) and three Eulerian angles as external (rotational) coordinates are defined from the Eckart coordinate system [Phys. Rev. 46, 383 (1934)]. They can describe any N-particle system. The exact classical Hamiltonian of the system in terms of these coordinates is derived, and it is remarkably simple. The quantization of this Hamiltonian is deferred for future study.

A wave passing through a one-dimensional fractal layer described by the Weierstrass function is studied within a framework of a perturbation method. It is shown that a transmission coefficient in a region of sufficiently small wavelengths consists of two components. The first corresponds to boundary scattering and describes resonance effects. The second describes the internal scattering by a small-scale fractal structure. It falls off with wavelength, decreasing according to the same law as that describing the decay of amplitudes of medium harmonics. In the case under consideration, the ‘‘fractal’’ part of the transmission coefficient is proportional to ${\mathit{k}}^{\mathit{D}\mathrm{-}2}$ (k is a wave vector and D is a local measure of a fractal). The validity limits as well as a generalization of the perturbation theory are stated.

The coherent light inelastically scattered from an ideal fluorescent sphere illuminated by an electromagnetic wave is analyzed using an extension of Mie theory. Scattering coefficients are solved specifically for plane-wave illumination. The resulting inelastically scattered radiation is similar to that of elastically scattered radiation from a sphere. These results are illustrated by numerical calculations for several specific, but arbitrary, cases.

In this paper we present a model describing the dynamics of biological membranes. The description presented here is based both on Frölich’s earlier conjectures and on the actual biophysical data concerning the structure, composition, and functions of biological membranes. A model Hamiltonian is proposed that involves the oscillations of both the lipid head groups and hydrocarbon chains of the membrane. The presence of dielectrically active material, mainly water, is also accounted for. It is subsequently demonstrated that, depending on the form of the coupling constant between head- and tail-group oscillations, two limiting regimes may occur. The Fröhlich regime is manifested by Bose condensation in the space of dipole oscillation frequencies. This results in self-focusing in the frequency domain. On the other hand, the Davydov regime is associated with spatial localization of the polarized state and leads to soliton formation. Thermal dissipation of the membrane’s energy and damping effects are also examined.

The information gain in a neural network cannot be larger than the bit capacity of the synapses. It is shown that the equation derived by Engel et al. [Phys. Rev. A 42, 4998 (1990)] for the strongly diluted network with persistent stimuli contradicts this condition. Furthermore, for any time step the correct equation is derived by taking the correlation between random variables into account.