A new method for determining vibrational matrix elements in molecules absorbing C${\mathrm{O}}_2$ laser radiation is presented. The technique is based on the measurement of the forward gain doublet which arises in a totally Doppler-broadened three-level system interacting with two fields. The experiment is performed using high harmonic mixing in a Schottky diode and is shown to be independent of pump frequency offset. Experiments are performed on the 496-μm C${\mathrm{H}}_3$F laser.

The behavior of wave packets and localized pulses in linear systems and their duality as the roles of ($\overrightarrow{\mathrm{x}},t$) and ($\overrightarrow{\mathrm{k}},\omega$) spaces are interchanged have been considered previously and are briefly summarized. The main features of dual-ray tracing for localized pulses or solitary waves are the existence of the dual-dispersion equation and the dual-ray equations. Dual-ray tracing displays the behavior of the pulse in the presence of inhomogeneity and dispersion, indicating how it deteriorates. More interesting is the behavior of solitary waves in the presence of nonlinear media discussed here. First, the formalism for wave-packet propagation in dispersive and weakly inhomogeneous nonlinear media is summarized, and a simple example displaying self-focusing is discussed. Then, by invoking the duality considerations once again, a formalism for solitary waves in inhomogeneous weakly dispersive nonlinear media is derived. The dual-dispersion equation and the dual-ray equations for this case are derived. A simple example analogous to the first one is discussed. This provides insight to the behavior of the solitary wave in nonlinear media and its stability in the presence of dispersive effects.

We report a detailed experimental study of the decay rate of the order-parameter fluctuations in the binary liquid 3-methylpentane and nitroethane near the critical mixing point. This system has the advantage that the decay rate can be measured close to the critical temperature without multiple-scattering corrections. The data cover a range $0.1<q\xi <27\mathrm{}$, where $q$ is the wave number of the fluctuations and $\xi$ the correlation length. From the data we conclude that the decay rate $\Gamma$ varies at the critical temperature as $\Gamma \propto q^z$ with $z=3.06\mathrm{}\pm 0.02$. The observed variation of the decay rate as a function of temperature and wave number is consistent with the behavior predicted by the mode-coupling theory of critical dynamics, but an accurate analysis of the data is limited by the lack of a systematic theoretical procedure for dealing with the short-wavelength contributions to the transport coefficients. The paper concludes with a discussion of the Stokes-Einstein relation between the diffusion coefficient and the viscosity coefficient near the critical point.

We show that the stochastic dynamic approach to the decay of an unstable state can be developed in the form of an expansion which allows a systematic resummation of the usual perturbative series in the noise strength. The approach is applied to the laser transient radiation very close to threshold and is shown to give rather good results.

A study of the phase diagram and thermal properties near the nematic—smectic-$A$—smectic-$C$ (NAC) multicritical point reveals the importance of the roles that biaxiality and bare correlation lengths play in the description of this multicritical point. Comparison with models of the NAC point by Chen and Lubensky, and Chu and McMillan, indicate that these models lack qualitative agreement with the data in important areas. There are, however, certain areas of agreement.

Rayleigh-Brillouin spectra of pure gases Xe, ${\mathrm{H}}_2$, ${\mathrm{D}}_2$ and gas mixtures Xe-He, ${\mathrm{H}}_2$-He, ${\mathrm{D}}_2$-He have been measured at room temperature and over a range of pressures, and the results compared with hydrodynamic and kinetic-theory calculations. It is shown that in the concentration range studied, nonideality and thermal-diffusion effects are both small in the hydrogen-helium mixtures, whereas these effects are significant in the Xe-He mixtures. The existing kinetic-model description based on the Boltzmann equation for Maxwell molecules needs to be modified in order to account for the Xe-He data.

Temperature-dependent local-density formalism is applied to the calculation of the screening density profile around a proton embedded in an electron gas. Characteristic quantities such as screening length, density at the proton site, and oscillations at low temperatures are studied. The total energy of the impurity and the entropy are computed and the existence of a bound state discussed. Comparisons are made with other linear and nonlinear theories, particularly the random-phase linear-response theory.

To bridge the gap between a physical Langevin equation and a stochastic equation used in the time-series analysis, and to clarify the physical foundations of the latter, the time-series model from the Langevin equation is derived with the aid of two manipulations—elimination of irrelevant variables and projection of state variables upon a space spanned by observed quantities. The order of the two manipulations is shown to be important to find an equation called the Kalman filter in control theory. All the results are summarized in a concise schematic diagram which relates various models and equations established so far in different fields.

Starting from a generalized nonequilibrium entropy, and from an extension of the Einstein formula for the probability of the fluctuations, we obtain the second moments of nonequilibrium fluctuations of the specific energy and the heat flux in rigid heat conductors. This approach leads to nonequilibrium corrections to the usual fluctuation-dissipation expressions for the heat fluctuations. The corresponding numerical corrections are found for phonon heat transport in dielectric solids and for electronic heat transport in metals. The macroscopic results share common features with those obtained for heat transport in harmonic chains by an information-theoretical approach.

The aperiodic or chaotic behavior for one-dimensional maps just before a tangent bifurcation occurs appears as intermittency in which long laminarlike regions irregularly separated by bursts occur. Proceeding from the picture proposed by Pomeau and Manneville, numerical experiments and analytic calculations are carried out on various models exhibiting this behavior. The behavior in the presence of external noise is analyzed, and the case of a general power dependence of the curve near the tangent bifurcation is studied. Scaling relations for the average length of the laminar regions and deviations from scaling are determined. In addition, the probability distribution of path lengths, the stationary distribution of the maps, the correlation function and power spectrum of the map in the intermittent region, and the Lyapunov exponent are obtained.

The validity of a recently proposed theory of the two-dimensional Lorentz model with overlap is examined by direct comparison of theoretical results with molecular-dynamics data in both the diffusion and localization phases. The diffusion coefficient, the shortand intermediate-time behavior of the velocity correlations, and the long-time velocity-correlation decay exhibit reasonable agreement between theory and simulation if considered as functions of the scatterer density measured relative to the percolation density. In particular, the observed but previously unexplained density variation of the effective long-time exponent of the velocity-autocorrelation function is obtained.

The recently developed density gradient and multiterm spherical harmonic expansion technique for the numerical solution of the electron Boltzmann equation is evaluated by comparison of results with those obtained using the conventional two-term spherical harmonic technique and using the Monte Carlo technique. Comparisons are made of electron energy distributions, transport coefficients, and excitation coefficients for electrons in ${\mathrm{N}}_2$ at moderate electric-field to gas-density ratios $\frac{E}{N}$ where the large cross section for vibrational excitation leads to significant errors when conventional solutions of the Boltzmann equation are used. The $\frac{E}{N}$ values were varied from (1 - 200)×${10}^{-21\mathrm{}}$ V ${\mathrm{m}}^2$, corresponding to mean electron energies from 0.3 to 5 eV. The first two terms of the density-gradient expansion are used. As the number of terms $n$ in the spherical harmonic expansion is increased from the conventional two terms to $n\ge 4$, the spherically symmetric component of the electron energy distribution and the transport and excitation coefficients become independent of $n$ and close to results obtained from the Monte Carlo calculation. The errors resulting from the use of two spherical harmonics at $\frac{E}{N}=7\mathrm{}\times {10}^{-20\mathrm{}}$ V ${\mathrm{m}}^2$, for example, are approximately 1, 5, and 30% for the drift velocity, the transverse diffusion coefficient, and the electronic excitation coefficients, respectively. For the lower $\frac{E}{N}$ values the errors in the transport coefficients are approximately proportional to an energy-loss-per-collision parameter. The variation of the coefficients of the lower-degree terms in the spherical-harmonic expansion with $n$ is examined through a comparison with an analytical solution of the Boltzmann equation for a model atom valid in the case of low $\frac{E}{N}$ and high electron energies. Monte Carlo techniques are used to show that the effects of electrodes are negligible for the conditions of recent measurements of electron excitation coefficients in ${\mathrm{N}}_2$.

A perturbation study of a number of states of four- through ten-electron atoms has been made. Second-order energy coefficients for these states are calculated and estimates of the relativistic corrections are also obtained. Higher-order energy coefficients are obtained by a semiempirical fitting of experimental data. Comparisons with experiment are made. The extent of the agreement with experiment is good.

Using the hydrodynamic model for a homogeneous plasma, we have investigated the modulational instability of an electromagnetic ion-cyclotron wave by a low-frequency electrostatic ion acoustic mode in a collisionless plasma. The low-frequency nonlinearity of the instability arises through the parallel ponderomotive force on the ions, and the high-frequency nonlinearity arises through the nonlinear current densities of the ions. For typical plasma parameters $n_0^0={10}^{13}$ ${\mathrm{cm}}^{-3\mathrm{}}$, $\frac{{\omega }_{\mathrm{ci}}}{{\omega }_0}=1.2\mathrm{}$, $B_s=10\mathrm{}$ kG, $T_i=1\mathrm{}$ keV, $T_i=0.05\mathrm{}$ keV, and $\theta =30\mathrm{}°$, the growth rate of the instability turns out to be ∼${10}^4$ rad ${\sec }^{-1\mathrm{}}$ for $\left|v_{0ix}\right|C_s|={10}^{-2\mathrm{}}$, where $v_{0ix}$ is the pump-induced drift velocity of the ions and $C_s$ is the ion acoustic velocity in the plasma.

We investigate the conditions for Bose-Einstein condensation of an ideal relativistic Bose gas in various spatial dimensions. From the direct numerical evaluations of the equations for the density and the specific-heat anomaly, we are able to show the qualitative difference between the massive and massless relativistic systems. As a consequence we are able to discuss the dependence of the critical exponents upon the spatial dimensionality for this system.

We report our measurements of the rate constants for formation of Na $4d$ and Na $5s$ in Na $3p$ — Na $3p$ collisions. The magnitudes of these rate constants indicate that Na $4d$ and Na $5s$ are the preponderant excited atomic products formed; however, the rate constant for $3p-3p$ associative ionization, with product $\mathrm{Na}_2^{}{}_{}{}^{+}$, is about one-hundred times greater.

It is suggested that the critical-point behavior of the Yvon-Born-Green integral equation for fluids for dimensions $d\le 4$ is described by a net correlation function which vanishes faster than any power of $r$ as $r\to \infty$, even though the isothermal compressibility $K_T$ diverges at the critical point.

The process of formation and decay of laser-generated shock waves is described by a hydrodynamic model. Measurements of shock velocities are performed on copper foils for incident intensities between 3×${10}^{11}$ and 3×${10}^{12}$ W/${\mathrm{cm}}^2$, with the use of piezoelectric detectors. Maximum induced pressures are found between 0.5 and 1.2 Mbar in the intensity range considered. Analysis of the results with the shock-evolution model outlines the importance of the decay process of laser-generated shocks.

Core-exchange polarization (CEP) effects in free atoms have been calculated for 15 different atomic configurations of Li, Be, B, C, N, O, F, Na, Cl, K, Rb, and Cs using the self-consistent-field-$X\alpha$ wave functions. Comparison with other results from the unrestricted Hartree-Fock (UHF) calculations and with experiments revealed that the $X\alpha$ approximation does not reproduce well the CEP effects for each $s$ orbital, but it presents rather a good value for the total CEP effect.

Sine-Gordon kinks under the influence of a constant force do not travel along the classical trajectory. It is shown here that solitons and kinks which obey one of the nonlinear Schrödinger equations and which are also subject to a constant force, on the contrary, do travel along the classical trajectory.