A long-standing weakness in the theoretical analysis of reciprocity relations is eliminated. The Onsager reciprocity theorem demonstrates the symmetry of phenomenological coefficients for systems described by a discrete set of variables. It has previously been demonstrated that this theorem implies that the divergence of the generalized conductivity tensor is symmetric. After some additional analysis it has been argued that the symmetry of the tensor itself is implied. This argument has been criticized in the literature. In the present paper it is shown that, when boundary conditions are appropriately incorporated into the analysis, one obtains the symmetry of the conductivity tensor from the Onsager relations.

It was shown by Martin and Yalcin that the mean-square fluctuation $〈Q_{\Lambda }^2〉$ in the net electric charge $Q_{\Lambda }$ contained in a subregion $\Lambda$ of an infinitely extended equilibrium Coulomb system (plasma, electrolytes, etc.) grows only as the surface area $S_{\Lambda }$ (not the volume) of $\Lambda$ and that $\frac{Q_{\Lambda }}{\sqrt{S_{\Lambda }}}$ has a Gaussian distribution as $\Lambda \to \infty$. We extend these results to joint charge fluctuations in different spatial regions: Let space be divided into disjoint regions ${\Lambda }_i$, $i=1,2,\dots$, say, cubes of length $L$. We show that as $L\to \infty$, the covariance in $\frac{Q_{{\Lambda }_i}}{L}$ behaves as $L^{-2\mathrm{}}〈Q_{{\Lambda }_i}{Q}_{{\Lambda }_j})=-\frac{1}{6}{L}^{-2\mathrm{}}〈Q_{{\Lambda }_i}^2〉=-\frac{1}{6}K$ if ${\Lambda }_i$ and ${\Lambda }_j$ are adjacent, and is zero if they do not have a common face. Furthermore, the variables $\frac{Q_{\Lambda }}{L}$ approach, as $L\to \infty$, a jointly Gaussian distribution. These results can be proven rigorously whenever the correlations in the system decay faster than the fourth power of the distance, which is known to happen in many cases. This behavior of charge fluctuations is shown to be required for the consistency of the usual statistical-mechanical treatment of neutralmolecular systems.

Diffusion-controlled cluster formation has been simulated on lattices of dimensionality 2-6. For the case of a sticking probability of 1.0 at nearest-neighbor sites, we find that the radius of gyration ($R_g$) of the cluster is related to the number of particles ($N$) by $R_g\sim N^{\beta }$ (for large $N$). The exponent $\beta$ is given by $\frac{\beta \sim 6}{5d}$, where $d$ is the classical (Euclidean) dimensionality of the lattice. These results indicate that the Hausdorff (fractal) dimensionality ($D$) is related to the Euclidean dimensionality ($d$) by $D\approx \frac{5d}{6}$ ($d=2-6\mathrm{}$). Similar results can be obtained from the density-density correlation function in two-dimensional simulations. Nonlattice simulations have also been carried out in two- and three-dimensional space. The radius-of-gyration exponents ($\beta$) obtained from these simulations are essentially equal to those obtained in the lattice model simulations. We have also investigated the effects of sticking probabilities ($S$) less than 1.0 on diffusion-limited cluster formation on two- and three-dimensional lattices. While smaller sticking probabilities do lead to the formation of denser clusters, the radius-of-gyration exponents are insensitive to sticking coefficients over the range $0.1\le S\le 1.0$.

The isochoric temperature derivative of the neutron structure factor is shown to be a useful vehicle for the comparison of simulated and experimental data. This derivative is deduced from detailed measurements of the scattered-neutron intensity on either side of the density maximum at 11.2°C in ${\mathrm{D}}_2$O. It is shown to differ in magnitude from a result deduced from the molecular-dynamics simulation by Impey using the Matsuoka-Clementi-Yoshimine potential and this difference is related to the behavior of the OD and DD correlation functions. These neutron-scattering data are compared to recent x-ray-scattering data to indicate the possible effect of nonadditive forces on the structure.

The cumulation of energy by induction of electromagnetic waves $\overrightarrow{B}=r^{-1\mathrm{}}{\partial }_r\mathrm{}\left[rA\right(r,t\left)\right]{\overrightarrow{\mathrm{e}}}_z$ and $\overrightarrow{E}=-{\partial }_{t}A(r,t)\mathrm{}{\overrightarrow{\mathrm{e}}}_{\theta }$ in a cylindrical space $0\le r\le R\mathrm{}\left(t\right)\mathrm{}$, which are excited by imploding an ideally conducting liner at $r=R\mathrm{}\left(t\right)\mathrm{}\le R_0$ with speed $\frac{\mathrm{dR}\mathrm{}\left(t\right)\mathrm{}}{\mathrm{dt}}<0\mathrm{}$ against the initially homogeneous magnetic field $\overrightarrow{B}\mathrm{}(r,t=0\mathrm{})=B_0{\overrightarrow{\mathrm{e}}}_z$ for $0\le r\le R_0$, is treated based on Maxwell's equations with electric displacement current. The associated hyperbolic initial-boundary-value problem with a moving boundary at $r=R\mathrm{}\left(t\right)\mathrm{}$ is solved analytically for arbitrary liner implosions $R\mathrm{}\left(t\right)\mathrm{}$ by means of an extended Fourier method with eigenfunctions which are not only space ($r$) but also time ($t$) dependent, due to the temporal change of the spatial region $0\le r\le R\mathrm{}\left(t\right)\mathrm{}$. The exact hyperbolic electromagnetic solutions $\overrightarrow{B}\mathrm{}(r,t)\mathrm{}$ and $\overrightarrow{E}\mathrm{}(r,t)\mathrm{}$ are shown to be the superposition of elliptic [$\frac{\partial \left(\epsilon \overrightarrow{E}\right)}{\mathrm{dt}}=\overrightarrow{0}$] and wave [$\frac{\partial \left(\epsilon \overrightarrow{E}\right)}{\mathrm{dt}}\ne \overrightarrow{0}$] solutions. The electromagnetic field intensities are finite at all points $0\le r\le R\mathrm{}\left(t\right)\mathrm{}$ during the implosion $0\le t<\mathrm{}\hat{t}$, where $R(t=\hat{t})=0\mathrm{}$ defines the hypothetical time $\hat{t}$ of complete implosion. The similarity theory of Zababakhin et al, according to which the electromagnetic wave fields become infinite upon reflection from the cylinder axis $r=0\mathrm{}$, is criticized.

Precise measurements of acoustic attenuation were carried out near the triple point of argon, krypton, and xenon. The results obtained eliminate the discrepancies in the data for the bulk viscosity ${\eta }_v$ for simple fluids. The value of ${\eta }_v$ does not vanish near solidification and the ratio $\frac{{\eta }_v}{{\eta }_s}$, where ${\eta }_s$ is the shear viscosity, remains low: 0.3-0.5. This result is fundamentally different from the Enskog theoretical value of 1.2 but agrees with those given both by the molecular-dynamic calculations for hard spheres and for Lennard-Jones fluids.

The method of characteristics and multiple-scaling perturbation techniques are used to study the space-charge instability of electron beams. It is found that the stable oscillating state (virtual cathode) created when the space-charge limit is exceeded is similar to a collisionless shock wave. The oscillatory solution originates at the bifurcation point of two unstable steady states. Complementary behavior (virtual anode) results when an ion beam exceeds its space-charge limit. The virtual cathode can also exist in the presence of a neutralizing heavy-ion background. The Pierce instability, where the electron and ion charge densities are equal, is a special case of this broader class. Estimates of the nonlinear growth rate of the instability at the space-charge limit are given.

Just as a finite temperature shift brings the critical viscosity down from its diverging critical-point behavior, a finite frequency produces a similar reduction. We compute in detail the frequency-temperature scaling function to single-loop order and apply it to the problem of critical diffusion. We also present detailed numerical estimates of the "rolloff" to be expected in direct experimental viscosity measurements carried out at finite frequencies.

An analytical theory of the curvature-driven trapped-electron instability including effects of finite $\beta$, toroidal coupling, and realistic aspect ratio is presented. The mode number of the purely growing mode is modified by the effect of finite $\beta$ and inverse aspect ratio, but the "ubiquitous" mode still remains. A destabilizing effect of finite $\beta$ for small Larmor radius is obtained.

In the $N$-level atom (or molecule) model, a set of conditions are developed whereby (i) a band of reaction channels can be approximated by a single reaction channel, and (ii) this single reaction channel can be approximated by a population-loss term. The reactions are restricted to those which remove the system from the laser-excited ladder.

A variational model for an incommensurate epitaxial layer on a relaxing substrate is studied. The corresponding two-dimensional area-preserving maps allow no conclusion about the existence of a phase transition. Explicit expressions for the free energy show the occurrence of second- or first-order transitions, depending upon parameters. The resulting phase diagram is related to a "complete devil's staircase."

A method for calculating the first quantum corrections to the moments of depolarized interaction-induced light-scattering spectra has been applied for a many-body system. Classical averages have been evaluated via the molecular-dynamics simulation technique. The numerical evaluation of the first quantum correction to a "static" and a "dynamical" property is given for simple fluids. We also find that systems which are usually considered classical from the point of view of static properties may exhibit a non-negligible quantum contribution to their "dynamical" behavior.

A study of degrees of freedom activated by the strand separation in deoxyribonucleic acid (DNA) is initiated. Thermal effects of activated degrees of freedom are analyzed beyond phenomenological treatments. It is shown that these effects may be observed by simultaneously measuring melting profiles and specific-heat curves of DNA.

Restricted multiple three-wave interactions, in which a set of wave triads interact through one shared wave, are discussed. The integrability of this system is explored through the use of Painlevé analysis. Numerical results in the special case where there are only two triads are also reported. The results are consistent with the Painlevé analysis.

Relativistic particle motion in an electromagnetic wave pulse propagating in vacuum along a static magnetic field is studied. A condition for synchronous particle acceleration which relates to the pulse width is given. As the particle energy increases, the particle motion becomes highly directional, and the associated radiation power is found to be proportional to the first power, rather than to the fourth power, of the particle energy.

The phenomenon of the motion of suspended particles induced by temperature gradients in fluids, known as thermophoresis, is considered. We show that thermophoresis is related to the Soret effect. The thermophoretic force acting on a particle immersed in a fluid which has a temperature gradient, $\overrightarrow{\nabla }T$, is given phenomenologically by $-{\eta }_T\overrightarrow{\nabla }T$. ${\eta }_T$ is shown to be related to the thermal-diffusion ratio by ${\eta }_T=k_B(k_T-1)$. In the limit of a dilute suspension we find a molecular expression for $k_T$ in terms of an equilibrium time-correlation function of the momentum of a suspended particle and the dissipative heat current. As a by-product, we also obtain the force acting on a such a particle due to a pressure gradient. We further show, using time-scale arguments, that a local-equilibrium calculation of the thermophoretic force cannot be adequate. Finally, we show, using a mode-coupling approach, that the hydrodynamic contribution to the thermophoretic force coefficient is negligible, unlike in the case of Stokes friction. We conclude that although thermophoresis is a macroscopic effect (not a fluctuating one) observed in fluids, it is not given by standard hydrodynamics. In a subsequent paper, with the use of kinetic theory, we identify the microscopic processes responsible for thermophoresis, calculate the thermophoretic force coefficient for moderately dense gases, and compare our results to experiment.

Kinetic theory, in the repeated-ring approximation, is employed to calculate the general expressions for thermophoretic forces and velocities which were obtained in the preceding paper (I). The velocity is not renormalized by the repeated-ring terms, since they all cancel. The thermophoretic force, on the other hand, is strongly renormalized by these terms, since the friction constant is. The latter changes from Boltzmann-type behavior at low densities of the host gas to Stokes-type behavior. In the limit in which the guest particle is represented by a hard-sphere potential we regain known results in the Boltzmann regime. These results are at variance with experiment. A realistic attractive tail, added to the hard-sphere potential yields a vanishingly small correction because of the typical short ranges of such tails. When accommodation processes are included, one obtains excellent agreement with experiment, provided the longitudinal and transverse momentum have different accommodation coefficients.

The Milne problem is considered with the Boltzmann equation without approximation to the collision operator. The general solution is given as the sum of spatial transient and asymptotic functions. Solutions of the Boltzmann equation with a hard-sphere cross section are obtained by expansions in Burnett functions. Convergence of the distribution function and associated quantities, such as spatial eigenvalues, extrapolation length, diffusion coefficient, and density profile is studied. It is found that convergence can be achieved with the expansion in Burnett functions. In particular, the importance of retaining a large number of polynomials in angle is demonstrated. The dependence of the solution and associated quantities on the mass ratio $\gamma =\frac{m_1}{m}$ is examined, where $m_1$ and $m$ are the mass of medium and test particles, respectively. Wherever possible, comparison with the results of previous researchers is given.

We show that mean $K$-shell binding energies ${\overline{E}}_K$ for highly stripped ions moving in solids at a given velocity can be determined with reasonable accuracy from measured centroid energies for radiative electron capture. The method is used to determine ${\overline{E}}_K$ for 20-80-MeV Cl ions in collisions with carbon targets.

Dielectronic-recombination-rate coefficients for the ${\mathrm{Ar}}^{14+}$ target ion have been recalculated, and an improved estimate of the contribution of high Rydberg states has been included. This corrects and supersedes our earlier work for this ion. The temperature range considered was $0.2\lesssim \mathrm{kT}\lesssim 2$ keV.