The exchange and correlation contributions to the thermodynamic free energy and the corresponding exchange-correlation potential ($V_{\mathrm{xc}\mathrm{\sigma }}$) are evaluated for a spin-polarized electron gas over a wide range of temperatures and densities. The exchange-correlation potential is parameterized for easy usage in local-spin-density calculations. The result indicates that for t≤0.15 (t=T/$T_F$), the temperature dependence of $V_{\mathrm{xc}\mathrm{\sigma }}$ is negligibly small. The effects of the spin polarization are most significant for t<3. Our results for $V_{\mathrm{xc}}$ for an unpolarized system agree well with those of a previous calculation by Perrot and Dharma-wardana.

The onset of chaos in the rf-biased Josephson junction is studied through numerical simulations. It is shown that the chaotic region predicted by the method of Melnikov spans only a narrow region of rf amplitudes and consists of weakly chaotic solutions which maintain phase lock with the rf bias. The experimentally observed threshold of chaos is shown to coincide with the onset of unlocked chaotic behavior at higher rf amplitudes.

A Thomas-Fermi cell model is used to study the temperature dependence of interatomic forces of normal-density matter and its effect on the equation of state. It is found that the substantial stiffening of the internuclear repulsions between the Fermi temperature and the temperature of complete ionization totally suppresses the configurational heat capacity of the nuclei over this temperature range, as though they had become a gas of hard spheres. When the atom finishes ionizing, the missing heat capacity reappears as a high-temperature anomaly. I suggest that this behavior occurs universally in real matter.

The polarizing microscope, differential scanning calorimeter, and high-resolution ac microcalorimeter were used to study the smectic-A to hexatic–smectic-B (SmA-Sm$B_H$) transition in a binary-mixture system composed of n-hexyl-4’-n-pentyloxybiphenyl-4-carboxylate (65OBC) and 4-propionylphenyl-trans-(4-n-pentyl)cyclohexane carboxylate (PP5CC). The study strongly suggests that a virtual SmA-Sm$B_H$ transition found in PP5CC will exhibit ideal critical behavior which may be different from the critical behavior observed in the extensively studied pure 65OBC system.

The spectrum-resolved radiant energies in the 0.1–1.6 keV range from various plane targets irradiated by a 0.53-μm laser at 0.1–1.0-nsec pulses with intensities of ${10}^{13}$–2×${10}^{15}$ W/${\mathrm{cm}}^2$ are obtained. The conversion efficiency increases with the laser-pulse duration. The physical meaning of the obtained spectrum, such as the correspondence between the emitted photons and the responsible plasma density and temperature region, is clarified from the computational studies by using the one-dimensional hydrodynamic Lagrangian code which is coupled with a nonlocal thermodynamic equilibrium average ion model and multigroup radiation transport. The energy transport of the absorbed laser energy is discussed. Atomic-number dependences of the obtained spectrum and x-ray conversion efficiency show an undulatory structure. This is well reproduced qualitatively and to some extent quantitatively by the code calculation and the contributions of the electronic transitions in different orbital shells are approximately estimated.

For a classical fluid of hard spheres we calculate for large wave numbers the leading correction to the ideal-gas behavior of the incoherent dynamic structure factor. The theoretical prediction agrees with results from neutron scattering experiments on dense hydrogen and sodium.

The stability of Taylor vortex flow with respect to axisymmetric perturbations is calculated numerically for several values of the radius ratio. In the nonlinear regime the resulting band of stable wave vectors is considerably smaller than predicted from amplitude expansions. On the low-q side the stability limit departs rather suddenly from the amplitude-expansion result with increasing reduced Reynolds number ${\varepsilon }_R$ and is influenced by the appearance of two bifurcations, which are connected with the coupling of two flows with resonating wave vectors. The influence of these bifurcations becomes stronger with decreasing radius ratio. The wavelength-changing process, however, is still given by the Eckhaus mechanism. The numerical results are in very good agreement with recent quantitative experimental measurements.

The semiclassical method based on the Einstein-Brillouin-Keller quantization of invariant phase-space tori and the hypothesis of adiabatic invariance of classical action variables is applied in the calculation of highly excited energy levels of two-dimensional coupled oscillator systems. The results obtained are in good agreement with quantum-mechanical calculations even in the regions where the corresponding classical dynamics becomes apparently irregular. General limitations of the method are discussed.

A new definition for the absolute half-cell potential is proposed. An absolute half-cell process is first defined. The absolute half-cell potential is ΔG for that process. (The conversion from energy to voltage is done in the usual way by using Faraday’s constant.) Under this definition the complete thermodynamic states of all species including electrons taking part in an absolute half-cell reaction must be fully specified. This is a departure from earlier treatments and makes it possible to develop a complete and consistent theory of absolute half-cell thermodynamics. Differences between the present approach and earlier treatments are discussed. Determination of Δ$G^0$ is briefly discussed, as well as possible uses for absolute half-cell thermodynamics, particularly in relation to the thermodynamics of ion solvation.

The intensity of the small-angle x-ray or neutron scattering has been calculated for two nonrandom (regular) fractals: the Menger sponge and a related fractal, called the fractal jack (a form similar to the metal six-pointed object used in the American children’s game). The scatterers are assumed to be systems of independently scattering, randomly oriented identical nonrandom fractals constructed from a material with uniform density. The scattered intensity I(q) can be expressed as a function of qa, where q=4π${\lambda }^{\mathrm{-}1}$sin(theta/2); λ is the scattered wavelength; theta is the scattering angle, and a is the edge of the cube which is the starting approximant to the fractal. The calculations show that I(q) is a monotonically decreasing function on which maxima and minima are superimposed. For large qa the monotonic decay is proportional to $q^{\mathrm{-}D}$, where D is the fractal dimension. The first maximum for q>0 is a single peak located at q=$q_1$. Groups of maxima are found at q${=3\mathrm{}}^k$$q_1$, where k is a positive integer greater than 1. The number of maxima within a group becomes greater as k increases. Numerical calculations of I(q) provide no evidence that the maxima and minima are damped and die out as q becomes larger. Thus I(q) for the two nonrandom fractals does not appear to approach the simple power-law scattering proportional to $q^{\mathrm{-}D}$ which is characteristic of the small-angle scattering from random fractals. The techniques developed to calculate I(q) for the Menger sponge and the fractal jack can also be employed to find the small-angle scattering from other nonrandom (regular) fractals.

The formation of a one-dimensional periodic pattern from an originally homogeneous infinite system is analyzed. We develop a mean-field-like theory for the structure function. The method gives predictions for the temporal evolution towards the final stationary state. It predicts a shift of the finally selected wave vector away from the maximum of the linear spectrum. Numerical simulation confirms this behavior for intermediate times but shows a ‘‘lock-in’’ of the pattern with subsequent conservation of ‘‘nodes.’’ Thus the final wave vector in general is neither the one predicted by our modified mean-field calculation nor one of those predicted by other selection criteria based on stationary solutions only. At long times a phase diffusion regime is observed where the node distances equilibrate. This results in a $t^{\mathrm{-}1/4}$ law for the width of the structure function which can be understood in terms of a linear diffusion equation for the phase by assuming a random distribution of the gradient of the phase at the lock-in time.

A discussion is given of what it means for a coin toss to be random. To aid in that discussion, we produce and solve numerically a physically realistic model of such a toss. The ideas we develop should apply in a general way to other commonly used mechanical randomizers. The coin’s randomness is determined by the nature of the basins of attraction of heads and tails. Although mechanical systems are known which are intrinsically random, we conclude that the coin flip is not among them. Rather, the effective randomness in practice is based on the magnitude of the scale of the variation of the basins of attraction relative to the precision of the flipping mechanism.

In this paper a new kind of superposition which mixes a dead-time-distorted Poisson process with periodic pulses is extensively described. The two original sequences are assumed distorted separately by insertion of proper dead times and are then subsequently superimposed: this method allows one an exact theoretical treatment valid in general for arbitrary values of the parameters. This technique and the relative formulas have been subjected to experimental check. The excellent agreement between theory and experiment supports the reliability of the method when it is applied to dead-time measurements.

A functional-integral representation for the partition function of interacting, uniaxial molecules is derived using the Hubbard-Stratonovich transformation. The mean-field evaluation of the partition function gives four possible liquid-crystalline phases (isotropic, nematic, smectic-A, smectic-C) in systems composed of uniaxial molecules. The nature of the multicritical nematic, smectic-A, smectic-C (NAC) point is investigated. Expressions for the parameters that appear in the Landau–de Gennes free energy are derived and the effect of truncating polynomial expansions of the free energy is investigated. It is found that truncation effects can be large.

The Kustaanheino-Stiefel transformation is used to transform the Coulomb problem to a four-dimensional isotropic harmonic oscillator with a constraint. Ordinary coherent states are introduced over this oscillator and are shown to evolve in a fictitious time. When projected back into the physical space, the states follow the classical Kepler orbits in physical time. The resulting quasiclassical picture is obtained without the Bohr correspondence principle of taking only contributions from high principal quantum numbers.

We derive high-frequency sum-rule expansion for the transverse elements of the plasma dielectric tensor. The correlation contribution to the ${\omega }^{\mathrm{-}4}$ sum-rule coefficient has a sign opposite to that of the longitudinal element. In addition, photon contributions add to the coefficient.

Ultrasonically induced birefringence has been used to study coupled translational and rotational motions of large (100-nm) nonspherical colloidal gold particles in fluids. The effect is nonlinear in that the induced birefringence is quadratic in the ultrasonic amplitude. A theory is developed to explain the dependence of the observed signal on concentration, viscosity, temperature, particle size, and on the ultrasonic intensity and frequency. This enables us to determine the frequency dependence of the viscous drag on the translational motion of nonspherical Brownian particles.

A molecular expression for the polarization-dependent part of the photoacoustic signal in gases is derived [see D. Ronis, Phys. Rev. A 29, 2125 (1984)]. The effect is found to be proportional to the viscosity η, the absorption coefficient α(ω), and the branching ratio for anisotropic versus isotropic energy transfer to the translational degrees of the solvent. The branching ratio is given in terms of the inelastic scattering cross sections for the excited species.

Near the onset of a dynamical instability, any time-periodic system can act to amplify small periodic perturbations. The details of this small-signal sensitivity depend solely on the type of bifurcation involved: Explicit expressions are derived for the power spectra in the vicinity of the simplest classes of codimension-1 bifurcations. Results obtained from analog simulations of a period-doubling system are in good agreement with the theory. We propose that the superconducting Josephson-junction parametric amplifier is an example of this amplification process.

We derive the dynamic equations for the macroscopic variables close to the nematic– to–hexagonal-columnar transition in discotic liquid crystals. We discuss especially the physical consequences of a static cross-coupling term between fluctuations of the discotic order parameter and gradients of the nematic director, a term omitted by previous workers. Furthermore, we predict the breakdown of flow alignment in disklike nematics close to the transition to a columnar phase and we discuss the microscopic reasons for this effect and, in general, the same type of behavior for other liquid crystalline phases with positional order such as smectic-A, -B, -C, -G, etc.