The propagation of two short different-wavelength optical pulses in three-level absorbers is studied. Combined numerical and analytic techniques are used to solve the three-level Maxwell-Bloch equations that provide the semiclassical description of the problem. The electric field in the model studied consists of two copropagating plane waves, each of which is in near resonance with a transition in the absorber. A new conservation law, holding in the absence of relaxation mechanisms, and independent of particular values of fields and detunings, is given. It is an analog of the law expressing conservation of the Bloch vector length known for two-level atoms. The possibility of simultaneous lossless propagation of the two optical pulses is established. New analytic solutions having the form of simultaneous different-wavelength optical solitons have been found. These pairs of solitons are called simultons. In order for simulton propagation to occur, both the pulses and the medium have to be prepared in a manner determined by the medium's physical parameters. The conditions for such preparation are given. Simultons are predicted to be distinct from the single-wavelength multiple-pulse solutions resulting from large-area-pulse breakup known in two-level absorbers, as well as from two-photon self-induced transparency. Results of numerical experiments on different-wavelength simultaneous propagation are also presented and indicate that simultaneous propagation may also be obtained under less stringent conditions than those predicted by the analytic solutions. Evidence of pulse evolution and breakup is seen.

The linear stability analysis of a superfluid mixture subject to a vertical temperature gradient is presented. The main result obtained in this paper is the existence of an oscillatory instability in a superfluid mixture heated only from below. The criteria for onset of oscillatory instability and the corresponding neutral frequencies in a superfluid region of the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-${}_{}{}^4{}_{}{}^{}\mathrm{He}$ phase diagram are treated. Depending on the magnitude of dissipation of superfluid motion, two different types of overstabilities exist. These have different physical origins. In the case of large dissipation of superfluid motion the oscillatory criterion and the neutral frequency are similar to those in a regular binary mixture with large abnormal thermal diffusion. In the case of small dissipation of superfluid motion a fundamentally new type of oscillatory convective instability is predicted. This instability is actually the undamped standing second-sound waves. We believe it should be possible to observe the predicted effect in the vicinity of the tricritical point.

Known analytical results are used to analyze molecular-dynamics experiments of shock waves in the one-dimensional Toda lattice. (This lattice provides a physically realistic model which contains the hard-sphere and harmonic lattices as limits.) Both explicit solutions and rather general theoretical properties have been employed. The leading edge of the shock front is well represented quantitatively by a single isolated solition. Once compression is properly taken into account, the interior of the shock wave is accurately described by a slowly varying Toda wave train. A sharp transition in the dynamical response exists as the shock strength passes a critical value; this critical value is identified mathematically by the spectral transform for the Toda lattice. Finally, a local spectral transform is used to measure, directly from the numerical data, the wave-train characteristics of the shock profile.

We report a high-resolution heat-capacity and x-ray study of the nematic—smectic-$A$ transition in the single-layer smectic material butyloxybenzylidene octylaniline (40.8). We find that the transition is second order to within 3 mK, with critical behavior closely similar to that observed previously in bilayer smectic materials such as octyloxycyanobiphenyl (8OCB). For the critical exponents we measure $\gamma =1.31\mathrm{}\pm 0.02$, ${\nu }_{\parallel }=0.70\mathrm{}\pm 0.01$, ${\nu }_{\perp }=0.57\mathrm{}\pm 0.01$, and $\alpha ={\alpha }^{\prime }=0.15\mathrm{}\pm 0.05$. These exponents are consistent with the anisotropic hyperscaling relation ${\nu }_{\parallel }+2\mathrm{}{\nu }_{\perp }=2-\alpha$. In addition, we find that the ratio of the amplitudes of the critical heat capacities in 40.8 and 8OCB is inversely proportional to the ratio of the correlated volumes as measured with x rays. The smectic longitudinal correlation length measured directly with x rays agrees quantitatively with that deduced by von Känel and Litster from the director fluctuations. Substantial disagreements with the superconducting analog model remain unexplained.

The destabilization of a normal mode of the uniform stationary state of a spatially extended system may initiate a whole cascade of bifurcations of families of states of increasing complexity. We discuss methods for the linear-stability analysis of the new solutions based on symmetry and continuity requirements which may be applied when no explicit analytic representation is available. We always find a family of simply periodic traveling-wave states bifurcating from the uniform stationary state (primary bifurcation). Stabilization of these simply periodic states is connected with a secondary bifurcation of a family of doubly periodic states, which upon stabilization may in turn be connected with a tertiary bifurcation of triply periodic states, etc. Each of the families may contain solitary states as limiting cases. The general theory is applied to a few representative examples.

Experimental studies of inertially confined plasmas irradiated with C${\mathrm{O}}_2$ laser intensities greater than ${10}^{15}$ W/${\mathrm{cm}}^2$ at 10.6-μm wavelength reveal the generation of harmonic spectral components up to the 46th order (∼230 nm). These harmonics are of very short duration (<200 ps), have a polarization parallel to that of the incident 10.6-μm electric field, and exhibit a conversion efficiency approximately independent of the harmonic order up to a maximum order. The plasma-physics phenomena responsible for the high-harmonic emission are examined. The data and theory are consistent with the presence of self-focusing.

The statistical properties of periodic impulse maps may be obtained from the characteristic functions. Series representations for the characteristic functions, the force correlations, and the momentum diffusion coefficient are presented. These results are applied to the sawtooth map for integer values of the perturbation parameter $\epsilon$, in which case the series may be summed explicitly. It is found that the diffusion coefficient has the quasilinear value for $|\epsilon +2|\ge 2$, it vanishes for $\epsilon =-2\mathrm{}$ and -1, and it is infinite for $\epsilon =-3\mathrm{}$.

This paper studies the iterative properties of the two-parameter family of maps $x_{n+1\mathrm{}}=1+a{x}_n^2+b{x}_n^4$. These maps can have either one or three extrema. Multiple extrema lead to a complex region of iterative stability and to new types of iterative behavior. In particular, the Feigenbaum critical line (locus of $2^n$-cycle accumulations) present for $b\approx 0$ terminates at two tricritical points $T$ and $T^{\prime }$ with coordinates $\mathrm{}(a,b)=(0,-1.594\mathrm{}90) \mathrm{and} (-2.814\mathrm{}03,1.40701)$, respectively. There is also a "dual" critical line terminating in two additional tricritical points $\tilde{T}=(-3.189\mathrm{}80,2.54371)$ and ${\tilde{T}}^{\prime }=(0.955\mathrm{}61,-1.14981)$. Behavior near the tricritical points is controlled by a new fixed point $f_T^{*}$ of the functional recursion relation $f_{n+1\mathrm{}}\mathrm{}\left(x\right)=\left[\frac{1}{f_n\mathrm{}\left(1\right)\mathrm{}}\right]f^{\mathrm{}\left(2\right)\mathrm{}}\left(x{f}_n\mathrm{}\right(1\left)\right)$. This fixed point has two relevant directions and, therefore, behavior near a tricritical point depends on two new universal numbers ${\delta }_T^{\mathrm{}\left(1\right)\mathrm{}}=7.284\mathrm{}69$ and ${\delta }_T^{\mathrm{}\left(2\right)\mathrm{}}=2.857\mathrm{}13$. Crossover and scaling behavior near the tricritical points are explored.

The theory of relaxation processes is reviewed starting from first principles. The resulting equations of motion describing the temporal behavior of two subsystems—dynamic and dissipative—are discussed. In existing theories the dissipative system or a thermal bath is assumed to be in thermal equilibrium all the time. The basic aim of this paper is a derivation of the instability conditions of the thermal bath. For this purpose two specific models are examined. One is an ensemble of inhomogeneously broadened two-level systems coupled with harmonic excitations (phonons) and the other is the ensemble of homogeneously broadened two-level systems interacting with a phonon bath. Possible implications, including biological ones, of the derived instability conditions are mentioned.

The x-ray diffraction pattern from aligned samples of the smectic-$I$ ($\mathrm{Sm}I$) phases of a number of compounds has been considered, with particular emphasis on TBDA (${\mathrm{C}}_{10}$${\mathrm{H}}_{21}$ PhNCHPhCHNPh${\mathrm{C}}_{10}$${\mathrm{H}}_{21}$, where Ph stands for the phenyl group) which exhibits both $\mathrm{Sm}I$ and smectic-$F$ ($\mathrm{Sm}F$) phases. It is established that both $\mathrm{Sm}I$ and $\mathrm{Sm}F$ phases are quasi-two-dimensional structures, with essentially no correlation of molecular positions between layers. They each have C-centered monoclinic lattices with long-range three-dimensional order of the lattice directions (bond orientational order) but do not have long-range positional order. The $\mathrm{Sm}F$ and $\mathrm{Sm}I$ phases differ in the direction of molecular tilt relative to the hexagonal packing of the molecular long axes: In terms of the unit cell axes, with $b$ the unique axis, $a>b$ for $\mathrm{Sm}F$ and $b>a$ for $\mathrm{Sm}I$. Analysis of intensity profiles from high-resolution powder measurements has led to a quantitative description of the correlation function for the molecular positions in the smectic layers. The $\mathrm{Sm}F$ phase has exponential decay of correlation with correlation lengths of order 100 Å, while the (higher temperature) $\mathrm{Sm}I$ phases show algebraic decay as expected for a truly two-dimensional crystal. Current theories do not account for this result.

Several spectral lines produced by charge transfer of neutral-beam hydrogen atoms with completely ionized oxygen have been detected in the impurity studies experiment $B$ ($\mathrm{I}\mathrm{S}\mathrm{X}-B$) tokamak, and have been used to compute the absolute concentrations of ${\mathrm{O}}^{8+}$. charge-exchange recombination is found to have a minor effect on the total radiative losses, but enhanced transport during neutral-beam injection appears to raise the oxygen radiation from the interior of the discharges by factors of 3 to 5. This result may reflect an increase of anomalous transport rates that could account for the density "clamping" often observed with injection.

The effect of surface-relief gratings on alignment of the nematic phase of butoxybenzilidene octylaniline has been studied for gratings of 1-μm and 300-nm period with grating depth from 22 to 410 nm. A planar-to-homeotropic alignment change was observed on flat surfaces and interpreted quantitatively by a model invoking the entropy change due to smectic short-range order imposed by the surface in the homeotropic state. The alignment change was suppressed by gratings of sufficient depth or short enough period.

Biaxial nematics are usually regarded as characterized by a symmetric, traceless tensor having three different eigenvalues. It is argued that this definition is too restrictive and that a natural extension would embrace any system that breaks all three rotational symmetries while preserving translational invariance. That is, biaxial nematics need not have orthorhombic symmetry, but may be triclinic, hexagonal, cubic, or even isotropic. A non-linear hydrodynamic theory is presented which emphasizes the fundamental similarities between the different biaxial nematics and clarifies the changes in the static and dynamic behavior as the discrete symmetries vary. The Goldstone modes of any biaxial nematics are identified as two pairs of orbital waves with a complex, and one orbital diffusion with a purely imaginary, dispersion relation. If the longitudinal and transverse variables decouple, it is the longitudinal rotation angle that diffuses.

A theory of turbulent binary fluid mixtures is applied to situations where the diffusive Prandtl number, $P=\frac{\nu }{D}$, far exceeds the Reynolds number $R$. This regime is accessible just above the consolute point in binary mixtures, where Prandtl numbers in excess of ${10}^6$ have been observed. We find that sizable large-scale inhomogeneities are mixed to uniformity quite slowly, in a time of order $\tau =\frac{t_{0}P}{R}$, where $t_0$ is a characteristic stirring time. The spectrum of concentration fluctuations rapidly acquires a peak at wave vector $k^{*}\sim k_{0}R$, where $k_0^{-1\mathrm{}}$ is the scale of the initial inhomogeneity. Mixing times of ten minutes or more are possible.

The melting in a two-dimensional Lennard-Jones system is investigated by the molecular-dynamics technique. "Final-size" effects on the melting are analyzed by performing calculations for systems with up to 3600 particles. The phase transition is weakly first order, but analysis of the crystal shows that there is a weak increase in the density of crystal defects as the size of the system is increased. The defects appear in large loops just before melting. The size effect on the defects in the lattice will weaken the first-order transition further when the size of the system is increased.

We have studied by means of molecular dynamics the propagation of a planar shock wave in a dense, three-dimensional column of a simple modified Lennard-Jones liquid. The column is $49.37{\sigma }^2$ in cross section, and $238.5\sigma$ in length, where $\sigma$ is the length parameter in the potential. The column contains approximately 10 000 atoms. It is initially in equilibrium at a density of $0.85{\sigma }^{-3\mathrm{}}$ and temperature of $\frac{1.16\epsilon }{k}$, where $\epsilon$ is the energy parameter in the potential. Shock compression is effected by causing the column to move in the longitudinal direction with a velocity of — $U_p$ and to collide with its mirror image across a mirror located at the origin. From the motion of the atoms in response to this kind of excitation, we calculate the shock velocity and the shock-front structure in the liquid, as well as the profiles of mass density, stress distribution, and energy density behind the shock front. Our shock-front structure agrees well with that obtained from the Navier-Stokes equations, but we also find important differences between our shock profiles and those postulated or computed from the continuum theory. In particular, we find that in 4×${10}^{-11\mathrm{}}$ s, the longest time of our calculations, the stress components did not relax to a hydrostatic condition, and the corresponding kinetic temperature profile showed a relaxation process similar to what we found earlier in a crystalline solid. We examine the atomistic mechanisms of the various relaxation processes, and discuss their implications on the shock compression of dense systems of solids and liquids as opposed to rarefield systems of gases.

Areas of interest for charged-particle beams are mentioned, and the classical beam concepts due to Alfvén, Lawson, and Bennett are described. From the equation of plasma mass transport the virial theorem of plasma physics is derived and evaluated for rotationally symmetric configurations so as to apply to long particle beams of nonrelativistic plasma character. A general global equation for such a beam expansion or compression is obtained and discussed. New aspects are given on the classical concepts, and the Alfvén-Lawson limiting current is slightly modified. With respect to certain important electron-beam properties observed in fusion research, special consideration is given to beam internal magnetic field generation and beam transverse mass rotation, and an important conversion mechanism is described.

The dielectric properties of a system of rigid dipolar particles in the presence of an external electric field are investigated. A general expression in terms of microscopic correlations is obtained for the dielectric susceptibility of the fluid expressed as the ratio of polarization to Maxwell field, in the low-field limit, via the use of the orientational one-particle density function. The expression is found to be identical to one recently derived from the two-particle density function in a field-free system of the same particles. Use of the method is extended to a consideration of several approximations which incorporate nonlinear effects. In particular, results for dielectric saturation and electrostriction effect are derived and compared with other theories.

A method for obtaining exact periodic solutions of relativistically strong-coupled transverse-longitudinal waves in an electron-ion plasma is presented. Suitable choice of initial conditions yields wave solutions whose longitudinal component has twice the frequency of the transverse. In addition, the significance of the plasma stream velocity in the nonlinear theory is discussed.

The nonlinear hydrodynamic equations for biaxial discotics with two broken translational symmetries (which have been identified experimentally very recently) are presented and the structure of the hydrodynamic excitations is considered. For biaxial discotics with broken rotational symmetries, owing to the existence of two preferred axes, the gradient free energy, representing a generalization of the Frank free energy for nematic liquid crystals, is given and the nonlinear hydrodynamic equations are derived. As a striking result a set of three commutator-type relations reflecting the anholomomity of the hydrodynamic variables characterizing the broken symmetries is found for the first time in the physics of liquid crystals. The influence of a static external magnetic field on both types of biaxial discotics is discussed.