Bernoulli's theorem is used to evaluate the boundary pressure generated by vortices moving in an ideal classical fluid. Particular examples include a vortex pair outside a circular cylinder and a vortex pair or ring in a half-space. Although the vortex pair exerts a force on a cylinder, neither the pair nor the ring exerts any net force on the infinite plane wall.

We have developed a set of differential equations which describe the hydrodynamics of a conducting liquid crystal subjected to external electromagnetic fields. The mechanical forces resulting from the interaction of the fields with the liquid are expressed as operations on the Maxwell stress tensor. The use of this description allows a concise statement of the equations of motion. As an example of the validity of the formalism, we rigorously solve the boundary-value problem associated with the Williams domain (vortex) mode in nematic liquids. Using standard constitutive relations, physical boundary conditions, and experimentally measured material $p$-azoxylanisole constants, we quantitatively reproduce the significant experimental observations.

The lattice version of the Maier-Saupe model of a nematic liquid crystal, in which all molecules are restricted to be on a simple-cubic lattice with periodic boundary conditions and to interact only with their nearest neighbors through the interaction energy $E_{\mathrm{ij}}=-\epsilon (\frac{3}{2}{{cos}^2\theta }_{\mathrm{ij}}-\frac{1}{2})$, is investigated using a Monte Carlo technique. The lattice is found to undergo a first-order phase transition at $\frac{\epsilon }{\mathrm{kT}}=0.890\mathrm{}\pm 0.005$ with a spontaneous order of $〈P_2\left(cos\theta \right)〉=0.33\mathrm{}\pm 0.04$ at the transition.

We report some results of a computer simulation of metastable states and critical properties in a finite Ising system consisting of square $n\times n$ lattices with and without periodic boundary conditions.

Characteristics of self-phase-modulation (SPM) spectra observed when intense picosecond pulses are passed through liquids and solids are shown to be consistent with a theoretical model based on an electronic mechanism. Experimental observations and theoretical calculations show that the SPM mechanism must respond on a subpicosecond scale.

A quantum-mechanical treatment is developed for the inelastic scattering of atoms by thermal fluctuations near a surface using Green's functions and diagrammatic methods. A basic set of equations is derived for the Green's function and $T$ matrix by treating the thermal fluctuations, which give inelastic scattering, stochastically. This enables us to express scattering cross sections, adsorption or capture rates of atoms by the surface field, etc., in terms of a fluctuation correlation function which characterizes the surface excitations. The approach presented treats the scattering surface in a continuum approximation making it especially applicable to liquids and to solids when surface-diffraction effects are neglected. The derivation leads to a Dyson equation for the Green's function (the propagator in the presence of the fluctuating surface field) which is formally similar to the equation for the dressed-electron Green's function in the electron-phonon problem. Some essential differences exist, however, and these are discussed. The similarity between these problems is exploited to some extent to generate approximate solutions of the scattering problem to all orders in perturbation theory. The simplest case, corresponding to summing a class of diagrams with no vertex corrections, is examined. The use of separable matrix elements makes the approximation scheme particularly transparent. Expressions for the scattering and capture (adsorption) cross section are given and a resonancelike form of the cross section is shown. Results from lowest-order perturbation theory are presented for comparative purposes and their connection to previous work is described. An analogy with neutron scattering theory as formulated by Van Hove is also examined.

Perturbative calculations are carried out to obtain eigenvalues of the four lowest-lying eigenfunctions of the Hartree Hamiltonian for the Li atom through third order in electron correlation. The expansions are all reasonably convergent and the theoretical analysis concerning the possibility of using zeroth-order functions which do not possess the exact permutational symmetry is confirmed in this particular case.

The equations governing the linearized hydrodynamics of cholesteric liquid crystals are systematically deduced. They are valid for compressible as well as incompressible cholesterics and for arbitrary direction of mode propagation. The variables which contribute to the hydrodynamics are the conserved variables, mass density, energy density, and momentum density, and one additional broken-symmetry variable whose auto correlation function diverges at zero wave vector $\overrightarrow{\mathrm{k}}$. This divergent auto correlation function is determined from the Frank free energy for cholesterics and is found to diverge as ${({k_3}^2+c{k_{\perp }}^4)}^{-1\mathrm{}}$, where $c$ is a constant, $k_3$ is the component of $\overrightarrow{\mathrm{k}}$ parallel to the pitch axis, ${\overrightarrow{\mathrm{p}}}^0$, and $k_{\perp }$ is the component perpendicular to ${\overrightarrow{\mathrm{p}}}^0$. The form of this divergence implies that an infinite cholesteric is unstable with respect to fluctuations. The dephasing distance is, however, astronomical; and any finite sample is stabilized by its boundaries. The mode structure of the hydrodynamical equations is analyzed for an incompressible choleteric and for a compressible cholesteric for $\overrightarrow{\mathrm{k}}$ along the two symmetry directions. The spectrum for $\overrightarrow{\mathrm{k}}$ parallel to ${\overrightarrow{\mathrm{p}}}^0$ includes a diffusive velocity and a diffusive director mode in agreement with the work of Fan, Kramer, and Stephen. The spectrum for $\overrightarrow{\mathrm{k}}$ perpendicular to ${\overrightarrow{\mathrm{p}}}^0$ has a similar structure. For $\overrightarrow{\mathrm{k}}$ at an angle of 45° to ${\overrightarrow{\mathrm{p}}}^0$, there is a propagating shear wave for sufficiently small $k$. The velocity of longitudinal sound is very slightly anisotropic. Hydrodynamical forms of dynamic response functions are derived, and flow of a cholesteric in a cylindrical capillary is discussed.

A simple generalization of the Griffiths and Wheeler postulates for the thermodynamic behavior near a critical point is introduced to describe fluctuations in local dynamical variables. It is proposed that in the classical Hilbert space of the dynamical variables there are only two linearly independent vectors, related to the shape of the coexistence surface and the critical surface, which contain critical fluctuations. It is shown that, as a consequence of the affine structure of the field space, the above assumption leads to the following asymptotic property for the correlation function $f_{\mathrm{ab}}(q, \omega )$ of any two local operators $\tilde{a}\left(\overrightarrow{\mathrm{r}}\right)$ and $\tilde{b}\left(\overrightarrow{\mathrm{r}}\right)$: $f_{\mathrm{ab}}(q, \omega )=a_1(q, \omega )b_1(q, \omega )f_{11}(q, \omega )+a_2(q, \omega )b_2(q, \omega )f_{22}(q, \omega )+a_3(q, \omega )b_3(q, \omega )f_{33}(q, \omega )+\dots$

Here $q$ is the wave number, $\omega$ is a point in the field space, the coefficients $a_i$ and $b_i$ are "generally" well-behaved thermodynamic quantities and the $f_{\mathrm{ii}}$, which are universal functions, have the following properties: ${\lim }_{q\to 0,\omega \to {\omega }_c}{f}_{11}(q, \omega )$ is nondivergent if $i\ge 3$, ${\lim }_{q\to 0,\omega \to {\omega }_c}{f}_{22}(q, \omega )$ is weakly divergent, ${\lim }_{q\to 0,\omega \to {\omega }_c}{f}_{11}(q, \omega )$ is strongly divergent. A few typical examples are worked out to show that if this property is postulated, the Griffiths and Wheeler thermodynamic behavior is reproduced.

The scattering of electromagnetic waves by a large-scale turbulent plasma has recently become of interest again in connection with the formation and study of the nonequilibrium plasma (often turbulent) of controlled fusion machines. Other than the usual Born approximation, it has also become fashionable to use the equivalent of the Dyson and Bethe-Salpeter equations, as well as a transport formulation for the scattering wave. The use of these methods has recently been justified by Frisch. These results are considered in a critical fashion. It has been possible to conclude that the results obtained from a solution of the stochastic transport theory are valid in both the high- and low-frequency limits, while the results of the smoothing approximation for the Dyson and Bethe-Salpeter equations are limited to the low-frequency limit. In addition, it has also been concluded that the secular effects that exist in the ordinary Born series may be fictional.

We observed the spatial period of "chevrons" in an ac-excited sample of room-temperature nematic methoxy benzylidene buty1 aniline. The frequency dependence of the period is explained by the increase in the dielectric relaxation rate due to ionic diffusion currents, with a normal diffusion constant.

The temperature dependence of the Scott thermomagnetic torque has been measured in ${\mathrm{N}}_2$, C${\mathrm{H}}_4$, and HD. Measurements were made from a temperature of 75 up to 300 °K, from a presure of 0.003 up to 1 Torr, and from a magnetic field of a few oersted up to 440 Oe. In both ${\mathrm{N}}_2$ and C${\mathrm{H}}_4$, the maximum torque measured at each temperature was found to increase when the temperature was increased from 75 to 300 °K. In HD this maximum torque increased when the temperature was increased from 75 up to about 170 °K but then decreased as the temperature was increased further up to 300 °K. When the pressure is large enough, the Scott torque multiplied by the pressure plotted as a function of $\frac{H}{P}$ reaches a limiting curve which has a maximum value at a field-to-pressure ratio ${\left(\frac{H}{P}\right)}_{max}$. The temperature dependence of ${\left(\frac{H}{P}\right)}_{max}$ for ${\mathrm{N}}_2$ and C${\mathrm{H}}_4$ has been measured, and from these data the value for the optimum ratio of precession frequency to collision frequency ${\left(\frac{{\nu }_L}{{\nu }_c}\right)}_{\mathrm{opt}}$ determined. The value of ${\left(\frac{{\nu }_L}{{\nu }_c}\right)}_{\mathrm{opt}}$ for ${\mathrm{N}}_2$ was found to be 0.113 and for C${\mathrm{H}}_4$ 0.128. This means a precession of the rotational magnetic moment about the field axis of only $\frac{1}{8}$ of a revolution between two collisions. There is no adequate theory with which we have been able to fit these temperature-dependent data of the Scott thermomagnetic torque.

The polarization correlation of photons emitted in an atomic cascade is treated in the framework of a general semiclassical radiation theory. The resulting predictions are contrasted with those of orthodox quantum-radiation theory. Experimental evidence is discussed which is in agreement with the latter theory, but excludes semiclassical theories in general.

Electrons carried by vortex rings toward a free surface in liquid ${\mathrm{He}}^4$ are found to evaporate from the surface with an energy independent of the ring energy. The energy of the electron is found to depend upon the amount of charge stored near the surface. We find also that the percentage of the ring current which crosses the surface depends on temperature, ring energy, and conditions at the surface. Finally, we hypothesize a trapped state near the surface and analyze our results in terms of the lifetime of this state.

Bogoliubov-Zubarev's exact transformation, specific to a weakly interacting Bose gas having a condensate, yields a Hamiltonian describing a gas of interacting excitations. The non-Hermiticity of the Hamiltonian arises from the nonorthogonality of the physical states; it has some significant consequences. The excitation spectrum is gapless in every approximation; the lowest-order correction is evaluated numerically and shown to be small. It is concluded that the approach presents a prospective method for a quantitative description of the weakly interacting Bose gas.

Recent numerical results are compared with an exact calculation for several second-order radiative processes.

A nonperturbative time-dependent theory which gives Stark-quenching lifetimes in agreement with experiment for both one- and two-electron $2S$ states is presented. This theory differs from the conventional Bethe-Lamb theory of Stark quenching, but reduces to this older theory, for one electron atoms only, when a well-known sum rule is applied.

We argue that the recent calculations of Ruvalds and Zawadowski only make sense in the context of a semiphenomenological quantum-hydrodynamic Hamiltonian. In particular, the hybridizing strength is not expected to be simply related to the microscopic condensate fraction $n_0$.

We suggest some classifications for the spectra observed by Sellin et al. [Phys. Rev. Letters 27, 1108 (1971)] of autoionization electrons from highly ionized oxygen and fluorine atoms, and comment on some of their suggestions. They appear to have observed the lowest nonautoionizing doubly excited doublet term in the Li r sequence, $1s2p^2{}_{}{}^2{}_{}{}^{}P$. High-angular-momentum states may be responsible for their observed resonances of higher energy.

The elastic constants for hcp solid ${\mathrm{He}}^4$ recently published by Crepeau, Heybey, Lee, and Strauss are used for calculating the wave surfaces associated with elastic waves, according to the recent method of Wanner. The deviation of the energy path or ray from the wave normal is calculated and is correlated with experimental sound-velocity data previously obtained by the authors.