The Fourier transform of the electric microfield distribution function is expressed, without approximations, in terms of a two-body function. The two-body function may be interpreted as a "generalized" radial distribution function and therefore is amenable to integral-equation techniques. In particular, the formalism is shown to simplify considerably in the hypernetted-chain approximation.

The slow motions of cellular structures of parallel rolls are described by the amplitude equation in the weakly nonlinear domain. As this equation has a variational structure, the Peach-Köhler force exerted on a dislocation can be computed in the same way as for usual crystals. When the cellular structure is really described by variational equations, this force keeps its variational origin (it is the gradient of some energy) and vanishes for some optimal wave number. In thermoconvection in porous layers, this variational structure of the dynamics is lost at perturbative order beyond the one giving the usual amplitude equation. Therefore, the notion of an optimal wave number loses its meaning, and the quantity equivalent to the Peach-Köhler force does not vanish anymore at the wave number of marginal stability for perpendicular diffusion, contrary to what happens in variational systems where this condition defines the optimal structure. Another consequence of this nonvariational dynamics is the occurrence of gliding motion of dislocations in uniformly curved rolls, a situation where no Peach-Köhler force exists in variational systems.

We calculate the effective longitudinal diffusion coefficient $K$ of a Brownian particle suspended in a fluid of different specific weight (difference $\Delta \rho$), in laminar flow between two plane parallel plates (at a distance $L$). In the case of spherical particles (radius $a$), one finds a fast decrease of $K$ due to sedimentation for values of $a$ larger than the value $a_M$ for which $K$ reaches a maximum. Typically $a_M$ is of the order of ${10}^{-5\mathrm{}}$ cm. Its precise value depends on $\Delta \rho$, $L$, and the characteristics of the flow (Poiseuille or linear shear). The possible experimental verification is discussed.

Solutions to the diamagnetic Hamiltonian for Rydberg states of hydrogen are studied in the low-magnetic-field regime where term mixing can be ignored. Several recently proposed approximate bases are compared by calculating the overlap integrals with an accurate numerically generated basis.

It is shown that the proper dependence of eigenvalues with respect to the parameters and quantum numbers can be found by calculating the extremum of the energy functional.

The yield of ${}_{}{}^3{}_{}{}^{}\mathrm{He}_{}^{1+}{}_{}{}^{}$ ions produced by a ${}_{}{}^3{}_{}{}^{}\mathrm{He}_{}^{2+}{}_{}{}^{}$ beam in C, Al, Ni, Ag, and Au foils was measured at 68, 99, and 130 MeV in order to determine the electron-capture cross sections ${\sigma }_c$. Measurements were performed using targets thicker than 60 μg/${\mathrm{cm}}^2$, where charge equilibrium was found. The results are compared with electron-stripping and -capture theories, which are found to explain fairly well the yield of ${}_{}{}^3{}_{}{}^{}\mathrm{He}_{}^{1+}{}_{}{}^{}$.

Cross sections are calculated for the charge transfer of ${\mathrm{O}}^{3+}$ ions in collisions with hydrogen atoms. The cross sections are in satisfactory agreement with ion-trap measurements at energies near 2.5 eV and with ion-beam measurements between 40 eV and 5 keV. The calculated cross sections uniformly exceed the ion-beam values by about 25%. The discrepancy, if real, may be attributed to the presence of less reactive metastable ions in the beam. The theory demonstrates that the charge-transfer process results in the emission of visible and ultraviolet photons of specific wavelengths whose detection would serve as a diagnostic probe of the detailed mechanism by which charge transfer proceeds.

Using the Magnus approximation we show that the Rosen-Zener conjecture holds for a two-level system in near-resonant interaction with a Gaussian-modulated pulse of sufficiently short duration.

We present a detailed calculation of, and experimental results on, the dependence of degenerate four-wave mixing and nonlinear diffraction in a nematic film on the spatial frequency of the intensity grating generated by two overlapping lasers. The explicit analytical expressions allow a critical reexamination of previous results and lead to better agreement between theory and experiments. Some of the previous theoretical and experimental results are reconfirmed. We also present further detailed results on the temperature dependence of nonlinear diffraction.

A laser-initiated, gas-embedded $Z$ pinch is operated with a preheat current which adjusts the plasma parameters by Joule heating and expansion so that when the main current is injected, the plasma core is heated under conditions of pressure balance. This results in a pinch which has a constant radius during the time of current rise. The pinch is stable during this time and thereafter undergoes a rapid transformation into a radially expanding helical structure. The growth time and wavelength of the instability is in good agreement with the theoretical predictions of the $m=1\mathrm{}$ magnetohydrodynamic instability.

A new type of "crisis" is found in a quadratic logistic map with periodic modulation. This shows a hysteresis followed from coexistence of two attractors. It is also shown that crises are characterized by discontinuous changes in the power spectrum and Lyapunov number.

Corrections to scaling, as well as the critical exponent $\nu$, are calculated for self-avoiding walks, with the use of a new highly accurate method based on fractal dimensionality. Numerical results are obtained for 2, 3, 4, and 5 dimensions and are shown to be in excellent agreement with the prediction of the $n=0\mathrm{}$ vector model.

The heat capacity of racemic $4-(2^{\prime }-\mathrm{methylbutyl})\mathrm{phenyl}-4^{\prime }-n-\mathrm{nonyloxybiphenyl}-4-\mathrm{carboxylate}$ (2M4P9OBC) has been measured in the vicinity of the $\mathrm{Sm}C-\mathrm{Sm}I$, $\mathrm{Sm}I-\mathrm{Sm}G$, and $\mathrm{Sm}G-\mathrm{Sm}H$ phase transitions. The nature of the $\mathrm{Sm}C-\mathrm{Sm}I$ transition will be discussed in the context of known microscopic pictures of each phase. In contrast to the continuous $\mathrm{Sm}A-\mathrm{hexatic}-B$ phase transition found in $n-\mathrm{hexyl}-4^{\prime }-n-\mathrm{pentyloxybiphenyl}-4-\mathrm{carboxylate}$, an asymmetric heat-capacity anomaly is identified in the $\mathrm{Sm}C-\mathrm{Sm}I$ transition of 2M4P9OBC.

We have measured the Stark shift of the $6S-7S$ transition in a beam of atomic cesium with the use of laser spectroscopy. We find this shift to be 0.7103(24) Hz ${\mathrm{}(\mathrm{V}/\mathrm{c}\mathrm{m})\mathrm{}}^{-2\mathrm{}}$. From this value we determine the static polarizability of the $7S$ state, ${\alpha }_{7S}=\left[6111\mathrm{}\mathrm{}\right(21\left)\right]a_0^3$, and the $7P-7S$ oscillator strength, $f_{7P,7S}=1.540\mathrm{}\left(7\right)\mathrm{}$. Finally, we derive a new empirical value for the $6S-7S$ Starkinduced electric dipole transition probability.

Measurement of the coexistence curve of the binary-fluid mixture methanol-cyclohexane with increasing amounts of water impurity showed essentially a linear dependence of the critical temperature, critical exponent $\beta$, and critical concentration with impurity. Adding 0.10 vol% water impurity caused the critical temperature to increase by 3.8 K, the effective critical exponent $\beta$ to increase by 0.0021, and the critical concentration, as measured by volume fraction of methanol, to increase by 0.004. Surface wetting was also observed in the impure samples and observations are reported on one impure mixture.

The energy and width of the ${}_{}{}^1{}_{}{}^{}\sigma _u^2{}_{}{}^{}{}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$ state of ${\mathrm{H}}_2$ are calculated using Feshbach projection operators and the Stieltjes moment method. The results are compared with an analysis of the double minima in the potential-energy curves of the ${}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$ Rydberg states. The doubly excited ${}_{}{}^1{}_{}{}^{}\sigma _u^2{}_{}{}^{}$ configuration is unstable with respect to autoionization for $R<\mathrm{}2.65\mathrm{}{a}_0$, and the autoionization rate is sensitive to both the value of the internuclear separation and the energy of the emitted electron.

We have analyzed Dyson's $U$-matrix theory of solving the Schrödinger equation in the interaction picture and are able to express the $U$ matrix as a dominant term plus an infinite series involving multiple integrals of time. For a certain rather restrictive class of Hamiltonians, our theory is exact for a general time-dependent problem. For other Hamiltonians, we can only obtain approximate expressions for our $U$ matrix and hence the wave function. Treating a time-independent problem as a special case of the time-dependent situation with a sudden-switching process, we have shown that our $U$ matrix is exact. To demonstrate the working procedures of our theory, we apply it to study the well-known time-independent charged harmonic-oscillator problem and the more general harmonic oscillator with a time-dependent driving force. Compared with other methods, our new theory appears to lead to a result which contains more information than others due to the inclusion of noncommutability properties of operators in the operator Schrödinger equation. It has been shown that the classical Feynman path-integral formalism can be deduced from quantum mechanics with the use of the Green's-function operator. It is interesting to note that apart from a step function, the Green's-function operator is the same as that of our $U^{\mathrm{}\left(s\right)\mathrm{}}$ matrix, which is the $U$ matrix obtained within the regime of the Schrödinger picture for a time-independent Hamiltonian, as a special case of our general time-dependent treatment.